Zeo sleep self-experiments

EEG recordings of sleep and my experiments with things affecting sleep quality or durations: melatonin, potassium, vitamin D etc
experiments, biology, psychology, nootropics, statistics, predictions, Zeo, Haskell, R, power-analysis, Bayes
2010-12-282018-02-28 in progress certainty: likely importance: 8


I dis­cuss my be­liefs about Quan­ti­fied Self, and demon­strate with a se­ries of self­-ex­per­i­ments us­ing a Zeo. A Zeo records sleep via EEG; I have made many mea­sure­ments and per­formed many ex­per­i­ments. This is what I have learned so far:

  1. the Zeo head­band is wear­able long-term
  2. mela­tonin im­proves my sleep
  3. one-legged stand­ing does lit­tle
  4. Vi­t­a­min D at night dam­ages my sleep & Vi­t­a­min D in morn­ing does not affect my sleep
  5. potas­sium (over the day but not so much the morn­ing) dam­ages my sleep and does not im­prove my mood/productivity
  6. small quan­ti­ties of al­co­hol ap­pear to make lit­tle differ­ence to my sleep qual­ity
  7. I may be bet­ter off chang­ing my sleep tim­ing by wak­ing up some­what ear­lier & go­ing to bed some­what ear­lier
  8. lithium oro­tate does not affect my sleep
  9. Red­shift causes me to go to bed ear­lier
  10. ZMA: in­con­clu­sive re­sults slightly sug­ges­tive of ben­e­fits

(QS) is a move­ment with many faces and as many vari­a­tions as par­tic­i­pants, but the core of every­thing is this: ex­per­i­ment with things that can im­prove your life.

What is QS?

Quan­ti­fied Self is not ex­pen­sive de­vices, or meet-ups, or videos, or even ebooks telling you what to do. Those are tools to an end. If read­ing this page does any­thing, my hope is to pass on to some read­ers the Quan­ti­fied Self at­ti­tude: a play­ful thought­ful at­ti­tude, of won­der­ing whether this thing affects that other thing and what im­pli­ca­tions could be eas­ily test­ed. “Sci­ence” with­out the cap­i­tal “S” or the be­lief that only sci­en­tists are al­lowed to think.

That’s all Quan­ti­fied Self is, no mat­ter how sim­ple or com­pli­cated your de­vices, no mat­ter how au­to­mated your data col­lec­tion, no mat­ter whether you found a pe­dome­ter ly­ing around or hand-engi­neered your own EEG head­set.

Quan­ti­fied Self is sim­ply about hav­ing ideas, gath­er­ing some data, see­ing what it says, and im­prov­ing one’s life based on the da­ta. If gath­er­ing data is too hard and would make your life worse off—then don’t do it! If the data can’t make your life bet­ter—then don’t do it! Not every idea can or should be test­ed.

The QS cy­cle is straight­for­ward and flex­i­ble:

  1. Have an idea
  2. Gather data
  3. Test the data
  4. Make a change; GOTO 1

Any of these steps can over­lap: you may be col­lect­ing sleep data long be­fore you have the idea (in the ex­pec­ta­tion that you will have an idea), or you may be mak­ing the change as part of the data in an ex­per­i­men­tal de­sign, or you may in­ad­ver­tently en­gage in a “nat­ural ex­per­i­ment” be­fore won­der­ing what the effects were (per­haps the baby wakes you up on ran­dom nights and lets you in­fer the costs of poor sleep).

The point is not pub­lish­able sci­en­tific rig­or. If you are the sort of per­son who wants to run such rig­or­ous self­-ex­per­i­ments, fan­tas­tic! The point is mak­ing your life bet­ter, for which sci­en­tific cer­tainty is not nec­es­sary: imag­ine you are choos­ing be­tween equally priced sleep pills and equal safe­ty; the first sleep pill will make you go to sleep faster by 1 minute and has been val­i­dated in count­less sci­en­tific tri­als, and while the sec­ond sleep pill has in the past week has ended the sweaty night­mares that have plagued you every few days since child­hood but alas has only a few small tri­als in its fa­vor—which would you choose? I would choose the sec­ond pill!

To put it in more economic/statistical terms, what we want from a self­-ex­per­i­ment is for it to give us a con­fi­dence just good enough to tell whether the ex­pected value of our idea is more than the idea will cost. But we don’t need more con­fi­dence un­less we want to per­suade other peo­ple! (So from this per­spec­tive, it is pos­si­ble to do a QS self­-ex­per­i­ment which is “too good”. Much like one can over­pay for safety and buy too much in­sur­ance—­like ex­tra war­ranties on elec­tron­ics such as video game con­soles, a no­to­ri­ous rip-off.)

What QS Is Not: (Just) Data Gathering

One fail­ure mode which is par­tic­u­larly dan­ger­ous for QSers is to overdo the data col­lec­tion and col­lect masses of data they never use. Fa­mous com­puter en­tre­pre­neur & math­e­mati­cian ex­em­pli­fied this for me in March 2012 with his lengthy blog post “The Per­sonal An­a­lyt­ics of My Life” in which he did some im­pres­sive graph­ing and ex­plo­ration of data from 1989 to 2012: a third of a mil­lion (!) emails, full key­board log­ging, cal­en­dar, phone call logs (with missed calls in­clude), a pe­dome­ter, re­vi­sion his­tory of his tome A New Kind of Sci­ence, file types ac­cessed per date, pars­ing scanned doc­u­ments for dates, a tread­mill, and per­haps more he did­n’t men­tion.

Wol­fram’s dataset is well-de­picted in in­for­ma­tive graphs, breath­tak­ing in its thor­ough­ness, and even more im­pres­sive for its du­ra­tion. So why do I read his post with sor­row? I am sad for him be­cause I have read the post sev­eral times, and as far as I can see, he has not ben­e­fited in any way from his data col­lec­tion, with one mi­nor ex­cep­tion:

Very early on, back in the 1990s, when I first an­a­lyzed my e-mail archive, I learned that a lot of e-mail threads at my com­pany would, by a cer­tain time of day, just re­solve them­selves. That was a use­ful thing to know, be­cause if I jumped in too early I was just wast­ing my time.

Noth­ing else in his life was bet­ter 1989-2012 be­cause he did all this, and he shows no in­di­ca­tion that he will ben­e­fit in the fu­ture (be­sides hav­ing a very nifty blog post). And just read­ing through his post with a lit­tle imag­i­na­tion sug­gests plenty of ex­per­i­ments he could do:

  1. He men­tions that 7% of his key­strokes are the Back­space key.

    This seems re­mark­ably high­—­vastly higher than my own use of back­space—and must be slow­ing down his typ­ing by a non­triv­ial amount. Why does­n’t he try a typ­ing tu­tor to see if he can im­prove his typ­ing skill, or learn the key­board short­cuts in his text ed­i­tor? If he is wasted >7% of all his typ­ing (be­cause he had to type what he is Backspac­ing over, of course), then he is wast­ing typ­ing time, slow­ing things done, adding frus­tra­tion to his com­puter in­ter­ac­tions and worst, putting him­self at greater risk of crip­pling RSI.

  2. How often does he ac­cess old files? Since he records ac­cess to all files, he can ask whether all the log­ging is pay­ing for it­self.

  3. Is there any con­nec­tion be­tween the steps his pe­dome­ter records and things like his mood or email­ing? Ex­er­cise has been linked to many ben­e­fits, both phys­i­cal and men­tal, but on the other hand, walk­ing is­n’t a very quick form of ex­er­cise. Which effect pre­dom­i­nates? This could have the prac­ti­cal con­se­quence of sched­ul­ing a daily walk just as he tries to make sure he can have din­ner with his fam­i­ly.

  4. Does a flurry of emails or phone calls dis­rupt his other forms of pro­duc­tiv­ity that day? For ex­am­ple, while writ­ing his book would he have been bet­ter off bar­ri­cad­ing him­self in soli­tude or work­ing on it in be­tween other tasks?

  5. His email counts are as­ton­ish­ingly high in gen­er­al:

    Is an­swer­ing so many emails re­ally nec­es­sary? Per­haps he has put too much em­pha­sis on email com­mu­ni­ca­tion, or per­haps this in­di­cates he should del­e­gate more—or if run­ning is so time-con­sum­ing, per­haps he should re-e­val­u­ate his life and ask whether that is what he truly wants to do now. I have no idea what the an­swer to any of these ques­tions are or whether an ex­per­i­ment of any kind could be run on them, but these are key life de­ci­sions which could be prompted by the data—but weren’t.

An­other QS piece(“It’s Hard to Stay Friends With a Dig­i­tal Ex­er­cise Mon­i­tor”) struck me when the au­thor, Jenna Wortham, re­flected on her ex­pe­ri­ence with her mo­tion sen­sor:

The for­get­ful­ness and guilt I ex­pe­ri­enced as my Fu­el­Band hon­ey­moon wore off is not un­com­mon, ac­cord­ing to peo­ple who study be­hav­ioral sci­ence. The col­lected data is often in­ter­est­ing, but it is hard to an­a­lyze and use in a way that spurs change. “It does­n’t trig­ger you to do any­thing ha­bit­u­al­ly,” said Michael Kim, who runs Kairos Labs, a Seat­tle-based com­pany spe­cial­iz­ing in de­sign­ing so­cial soft­ware to in­flu­ence be­hav­ior…Mr. Kim, whose ré­sumé in­cludes a stint as di­rec­tor of Xbox Live, the on­line gam­ing sys­tem cre­ated by Mi­crosoft, said the game-like mech­a­nisms of the Nike de­vice and oth­ers like it were “not enough” for the av­er­age user. “Points and badges do not lead to be­hav­ior change,” he said.

Fi­nal­ly, Neal Stephen­son, in dis­cussing his tread­mill desk use fo­cuses on es­ti­mat­ing mileage & caloric ex­pen­di­ture and show­ing the effects of bad pos­ture he de­vel­ope­d—but he en­tirely ig­nores is­sues of whether it affected his typ­ing, his writ­ing, or any­thing that might ac­tu­ally mat­ter.

One thinks of a say­ing of : “Ex­pe­ri­ence by it­self teaches noth­ing.” In­deed. A QS ex­per­i­ment is a 4-legged beast: if any leg is far too short or far too long, it can’t carry our bur­dens.

And with Wol­fram and Wortham, we see that 2 legs of the poor beast have been am­pu­tat­ed. They col­lected data, but they had no ideas and they made no changes in their life; and be­cause QS was not part of their life, it soon left their life. Wortham seems to have dropped the ap­proach en­tire­ly, and Wol­fram may only per­se­vere for as long as the data con­tin­ues to be use­ful in demon­strat­ing the abil­i­ties of his com­pa­ny’s prod­ucts.

Zeo QS

On Christ­mas 2010, I re­ceived one of ’s (founded 2003, shut­ting down 2013) Zeo bed­side unit after long cov­et­ing it and dream­ing of us­ing it for all sorts of sleep­-re­lated ques­tions. (As of Feb­ru­ary 2013, the bed­side unit seems to’ve been dis­con­tin­ued; the most com­pa­ra­ble Zeo Inc. prod­uct seems to be the Zeo Sleep Man­ager Pro, ~$90.) With it, I be­gin to ap­ply my thoughts about Quan­ti­fied Self.

A Zeo is a scaled-down (one-elec­trode) sen­sor-head­band, which hap­pens to have an alarm clock at­tached. The EEG data is processed to es­ti­mate whether one is asleep and what of sleep one is in. Zeo breaks sleep down into wak­ing, , , and . (The phases aren’t nec­es­sar­ily that phys­i­o­log­i­cally dis­tinc­t.) It’s been com­pared with reg­u­lar by Zeo Inc and oth­ers1 and seems to be rea­son­ably ac­cu­rate. (S­ince reg­u­lar sleep tests cost hun­dreds to thou­sands of dol­lars per ses­sion and are of ques­tion­able ex­ter­nal va­lid­ity since they are a differ­ent un­com­fort­able set­ting than your own bed­room, I am fine with a Zeo be­ing just “rea­son­ably” ac­cu­rate in pre­dict­ing PSG rat­ings.)

The data is much bet­ter than what you would get from more pop­u­lar meth­ods like cell­phones with ac­celerom­e­ters, since an ac­celerom­e­ter only knows if you are mov­ing or not, which is­n’t a very re­li­able in­di­ca­tor of sleep2. (You could just be ly­ing there star­ing at the ceil­ing, wide awake. Or per­haps the cat is knead­ing you while you are in light sleep.) As well, half the in­ter­est is how ex­actly sleep phases are arranged and how long the cy­cles are; you could use that in­for­ma­tion to de­vise a cus­tom polypha­sic sched­ule or just fig­ure out a bet­ter nap length than the rule-of-thumb of 20 min­utes. And the price is­n’t too bad—$150 for the nor­mal Zeo as of Feb­ru­ary 2012. (The ba­sic mo­bile Zeo is much cheap­er, but I’ve seen peo­ple com­plain about it and ap­par­ently it does­n’t col­lect the same data as more ex­pen­sive mo­bile ver­sion or the orig­i­nal bed­side unit.)

Tests

“A thinker sees his own ac­tions as ex­per­i­ments & ques­tion­s—as at­tempts to find out some­thing. Suc­cess and fail­ure are for him an­swers above all.”

, §41

I per­son­ally want the data for a few dis­tinct pur­pos­es, but in the best Quan­ti­fied Self vein, mostly ex­per­i­ment­ing:

  1. more thor­oughly quan­ti­fy­ing the ben­e­fits of

    • and dose lev­els: 1.5mg may be too much. I should ex­per­i­ment with a va­ri­ety: 0.1, 0.5, 1.0, 1.5, and 3mg?
  2. quan­ti­fy­ing the costs of

  3. test­ing ben­e­fits of 3

  4. de­sign­ing & start­ing

  5. as­sist­ing

  6. re­duc­ing sleep time in gen­eral (bet­ter & less sleep)

  7. in­ves­ti­gat­ing effects of n-back­ing:

    • do n-back­ing just be­fore sleep, and see whether per­cent­ages shift (more deep sleep as the brain grows/changes?) or whether one sleeps bet­ter (fewer awak­en­ings, less light sleep).
    • do n-back­ing after wak­ing up, to look for cor­re­la­tion be­tween good/bad sleeps and per­for­mance (one would ex­pect good sleep → good scores).
    • test the costs of polypha­sic sleep on mem­ory4
  8. (pos­i­tive) effect of one-legged stand­ing on sleep depth/efficiency

  9. pos­si­ble sleep re­duc­tions due to med­i­ta­tion

  10. se­r­ial ca­ble us­es:

    • quan­ti­fy­ing med­i­ta­tion (eg. length of gamma fre­quen­cies)
    • rank mu­sic by dis­tractibil­i­ty?
    • mea­sure fo­cus over the day and dur­ing spe­cific ac­tiv­i­ties (eg. cor­re­late fre­quen­cies against n-back­ing per­for­mance)
  11. Mea­sure neg­a­tive effect of nico­tine on sleep & de­ter­mine ap­pro­pri­ate buffer

  12. test claims of sleep ben­e­fits from mag­ne­sium

  13. caffeine pill wake-up trick

I have tried to do my lit­tle self­-ex­per­i­ments as well as I know how to, and hope­fully my re­sults are less bo­gus than the usual anec­dotes one runs into on­line. What I would re­ally like is for other peo­ple (e­spe­cially Zeo own­ers) to repli­cate my re­sults. To that end I have taken pains to de­scribe my se­tups in com­plete de­tail so oth­ers can use it, and pro­vided the data and com­plete or pro­grams used in analy­sis. If any­one repli­cates my re­sults in any fash­ion, please con­tact me and I would be happy to link your self­-ex­per­i­ment here!

First impressions

First night

Christ­mas morn­ing, I un­packed it and ad­mired the pack­ag­ing, and then looked through the man­u­al. The base-station/alarm-clock seems pretty sturdy and has a large clear screen. The head­band seemed com­fort­able enough that it would­n’t bother me. The var­i­ous writ­ings with it seemed rather fluffy and prep­py, but I did my tech­ni­cal home­work be­fore hand, so could ig­nore their crap.

Late that night (quite late, since the girls stayed up play­ing and Xbox danc­ing games and what not), I turn in weari­ly. I had no­ticed that the alarm seemed to be set for ~3:30 AM, but I was very tired from the long day and tak­ing my mela­ton­in, and did­n’t in­ves­ti­gate fur­ther—I mean, what elec­tronic would ship with the alarm both en­abled and en­abled for a bizarre time? It was­n’t worth both­er­ing the other sleeper by turn­ing on the light and mess­ing with it. I put on the head­band, ver­i­fied that the Zeo seemed to be do­ing stuff, and turned in. Come 3 AM, and the damn mu­sic goes off! I hit snooze, too dis­com­bob­u­lated to fig­ure out how to turn off the alarm.

So that ex­plains the strange Zeo data for the first day:

First night

The ma­jor sur­prise in this data was how quickly I fell asleep: 18 min­utes. I had al­ways thought that I took much longer to fall asleep, more like 45 min­utes, and had bud­geted ac­cord­ing­ly; but ap­par­ently be­ing de­luded about when you are awake and asleep is com­mon—which leads into : if your mem­o­ries dis­agree with the Zeo, who should you be­lieve? The rest of the data seemed too messed up by the alarm to learn any­thing from.

Uses

Meditation

One pos­si­ble ap­pli­ca­tion for Zeo was med­i­ta­tion. Most med­i­ta­tion stud­ies are very small & method­olog­i­cally weak, so it might be worth­while to ver­ify for one­self any in­ter­est­ing claims. If Zeo’s mea­sur­ing via EEG, then pre­sum­ably it’s learn­ing some­thing about how re­laxed and ac­tiv­i­ty-less one’s mind is. I’m not seek­ing en­light­en­ment, just calm­ness, which would seem to be in the purview of an EEG sig­nal. (As Charles Bab­bage said. er­rors made us­ing in­suffi­cient data are still less than er­rors made us­ing no data at al­l.) But alas, I med­i­tated for a solid 25 min­utes and the Zeo stub­bornly read at the same wake level the en­tire time; I then read my book, Mod­ern Japan­ese di­aries, for a sim­i­lar pe­riod with no change at all. It is pos­si­ble that the 5-minute av­er­ag­ing (Zeo mea­sures every 2 sec­onds) is hid­ing use­ful changes, but prob­a­bly it’s sim­ply not pick­ing up any real differ­ences. Oh well.

Smart alarm

The sec­ond night I had set the alarm to a more rea­son­able time, and also en­abled its smart alarm mode (“Smart­Wake”), where the alarm will go off up to 30 min­utes early if you are ever de­tected to be awake or in light sleep (as op­posed to REM or deep sleep). One thing I for­got to do was take my mela­ton­in; I keep my sup­ple­ments in the car and there was a howl­ing bliz­zard out­side. It did­n’t bother me since I am not ad­dicted to mela­tonin.

In the morn­ing, the smart alarm mode seemed to work pretty well. I woke up early in a good mode, thought clearly and calmly about the sit­u­a­tion—and went back to sleep. (It’s a hol­i­day, after al­l.)

Replacing headband

Around 2011-05-15, I gave up on the orig­i­nal head­band—it was get­ting too dirty to get good read­ings—and de­cided to rip it apart to see what it was made of, and to or­der a new set of three for $35 (which seems rea­son­able given the ex­pen­sive ma­te­r­ial that the con­tacts are made of—sil­ver fab­ric); they then cost $50. A lit­tle googling found me a coupon, FREESHIP, but ap­par­ently it only ap­plied to the Zeo it­self and so the pads were ac­tu­ally $40, or ~$13 a piece. I won’t say that buy­ing re­place­ment head­bands semi­-an­nu­ally is some­thing that thrills me, but $20 a year for sleep data is a small sum. Cer­tainly it’s more cost-effec­tive than most of the I have used. (Full dis­clo­sure: 9 months after start­ing this page, Zeo offered me a free set of head­bands. I used them and when the news broke about Zeo go­ing out of busi­ness, I bought an­other set.)

The old head­band, with elec­tri­cal tape residue

The dis­pos­able head­band with the cloth cov­er­ing re­moved/

Said head­band with plas­tic re­moved; no­tice dis­col­oration of metal de­spite clean­ing

The re­verse side/

The new head­band’s wrap­per

The new head­band/

In the fu­ture, I might try to make my own; eok.g­nah claims that buy­ing the sil­ver fab­ric is ap­par­ently cheaper than or­der­ing from Zeo, mar­ciot re­ports suc­cess in mak­ing head­bands, and it seems one can even hook up other sen­sors to the head­band. An­other al­ter­na­tive is, since the Zeo head­band is a one-elec­trode EEG head­set, to take an ap­proach sim­i­lar to the EEG peo­ple and oc­ca­sion­ally add small dabs of con­duc­tive paste, since fairly large quan­ti­ties are cheap (eg. 12oz for $30). There was a dis­pos­able ad­he­sive gel ECG elec­trodes with off­set press-s­tud con­nec­tions be­ing ex­per­i­mented with by Zeo Inc, but they never en­tered wide use be­fore it shut down.

One prob­lem with the sen­sor mounted on the head­band is that the lithium bat­tery in­side it can stop hold­ing a charge. The cas­ing is ex­tremely diffi­cult to open with­out dam­ag­ing the cir­cuitry or con­nec­tions, and the bat­tery in­side is sol­dered to the cir­cuit board:

An opened Zeo head­band sen­sor

Once safely opened, the bat­tery can be re­placed by an­other one of sim­i­lar size. For de­tails, see the Quan­ti­fied Self fo­rum thread.

Melatonin

Be­fore writ­ing my ar­ti­cle, I had used mela­tonin reg­u­larly for 6+ years, ever since I dis­cov­ered (some­when in high school or col­lege) that it was use­ful for en­forc­ing bed­times and seemed to im­prove sleep qual­i­ty; when I posted my writeup to Less­Wrong peo­ple were nat­u­rally a lit­tle skep­ti­cal of my spe­cific claim that it im­proved the qual­ity of my sleep such that I could re­duce sched­uled time by an hour or so. Now that I had a Zeo, would­n’t it be a good idea to see whether it did any­thing, lo these many years lat­er?

The fol­low­ing sec­tion rep­re­sents 5 or 6 months of data (raw CSV data; guide to Zeo CSV). My ba­sic dosage was 1.5mg of mela­tonin taken 0-30 min­utes be­fore go­ing to sleep.

Graphic

Deep sleep and ‘time in wake’ were both ap­par­ently un­affect­ed; ‘time in wake’ ap­par­ently had too small a sam­ple to draw much con­clu­sion:

Mela­ton­in, time in deep over five months,

Sur­pris­ing­ly, to­tal REM sleep fell:

Mela­ton­in, time in REM

While the raw ZQ falls, the re­gres­sion takes into ac­count the cor­re­lated vari­ables and in­di­cates that this is some­thing of an

Mela­ton­in, ZQ

REM’s av­er­age fell by 29 min­utes, deep sleep fell by 1 min­ute, but to­tal sleep fell by 54 min­utes; this im­plies that light sleep fell by 24 min­utes. (The av­er­ages were 254.2 & 233.3) I am not sure what to make of this. While my orig­i­nal heuris­tic of a one hour re­duc­tion turns out to be sur­pris­ingly ac­cu­rate, I had ex­pected light and deep sleep to take most of the time hit. Do I get enough REM sleep? I don’t know how I would an­swer that.

I did feel fine on the days after mela­tonin use, but I did­n’t track it very sys­tem­at­i­cal­ly. The best I have is the ‘morn­ing feel’ pa­ra­me­ter, which the Zeo asks you on wak­ing up; in prac­tice I en­tered the val­ues as: a ‘2’ means I woke feel­ing poor or un­rest­ed, ‘3’ was fine or medioc­re, and ‘4’ was feel­ing good. When we graph the av­er­age of morn­ing feel against mela­tonin use or non-use, we find that mela­tonin was no­tice­ably bet­ter (2.95 vs 3.17):

Mela­ton­in, Morn­ing Feel

Graph­ing some more of the raw data:

Mela­ton­in, To­tal Time Asleep (To­tal Z)
Mela­ton­in, Times Woken per Night

Un­for­tu­nate­ly, dur­ing this pe­ri­od, I did­n’t reg­u­larly do my n-back­ing ei­ther, so there’d be lit­tle point try­ing to graph that. What I spent a lot of my free time do­ing was edit­ing Gw­ern.net, so it might be worth look­ing at whether nights on mela­tonin cor­re­spond to in­creased ed­its the next day. In this graph of ed­its, the red dots are days with­out mela­tonin and the green are days with mela­ton­in; I don’t see any clear trend, al­though it’s worth not­ing al­most all of the very busy days were mela­tonin days:

Days ver­sus # of ed­its ver­sus mela­tonin on/off

Melatonin analysis

The data is very noisy (e­spe­cially to­wards the end, per­haps as the head­band got dirty) and the re­sponse vari­ables are in­ter­cor­re­lated which makes in­ter­pre­ta­tion diffi­cult, but hope­fully the over­all con­clu­sions from the are not en­tirely un­trust­wor­thy. Let’s look at some av­er­age. Zeo’s web­site lets you en­ter in a 3-val­ued vari­able and then graph the av­er­age day for each vari­able against a par­tic­u­lar recorded prop­erty like ZQ or to­tal length of REM sleep. I de­fined one dummy vari­able, and de­cided that a ‘0’ would cor­re­spond to not us­ing mela­ton­in, ‘1’ would cor­re­spond to us­ing it, and ‘2’ would cor­re­spond to us­ing a dou­ble-dose or more (on the rare oc­ca­sions I felt I needed sleep in­sur­ance). The fol­low­ing ad­di­tional -style5 analy­ses of p-val­ues is done by im­port­ing the CSV into R; given all the is­sues with self­-ex­per­i­men­ta­tion (these mela­tonin days weren’t even blind­ed), the p-val­ues should be treated as gross guess­es, where <0.01 in­di­cates I should take it se­ri­ous­ly, <0.05 is pretty good, <0.10 means I should­n’t sweat it, and any­thing big­ger than 0.20 is, at most, in­ter­est­ing while >0.5 means ig­nore it; we’ll also look at cor­rect­ing for mul­ti­ple com­par­isons6, for the heck of it. A mnemon­ic: p-val­ues are about whether the effect ex­ists, and d-val­ues are whether we care. For a vi­su­al­iza­tion of effect sizes, see “Win­dow­pane as a Jar of Mar­bles”.

The analy­sis ses­sion in the R in­ter­preter:

# Read in data w/ variable names in header; uninteresting columns deleted in OpenOffice.org
zeo <- read.csv("https://www.gwern.net/docs/zeo/2011-zeo-melatonin.csv")

# "Melatonin" was formerly "SSCF 10";
# I also edited the CSV to convert all '3' to '1' (& so a binary)

l <- lm(cbind(ZQ, Total.Z, Time.to.Z, Time.in.Wake, Time.in.REM,
                 Time.in.Deep, Awakenings, Morning.Feel, Time.in.Light)
            ~ Melatonin, data=zeo)
summary(manova(l))
#           Df Pillai approx F num Df den Df Pr(>F)
# Melatonin    1  0.102    0.717      9     57   0.69
# Residuals 65
summary(l)
# Response ZQ :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)    83.52       4.13   20.21   <2e-16
# Melatonin      2.43       4.99    0.49     0.63
#
# Response Total.Z :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)   452.38      22.86   19.79   <2e-16
# Melatonin       9.68      27.59    0.35     0.73
#
# Response Time.to.Z :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)    19.48       2.59    7.52  2.1e-10
# Melatonin      -5.04       3.13   -1.61     0.11
#
# Response Time.in.Wake :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)    7.095      1.521    4.66  1.6e-05
# Melatonin     -0.247      1.836   -0.13     0.89
#
# Response Time.in.REM :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)   144.62       9.38   15.41   <2e-16
# Melatonin      -3.73      11.32   -0.33     0.74
#
# Response Time.in.Deep :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)    54.33       3.26   16.68   <2e-16
# Melatonin       5.56       3.93    1.41     0.16
#
# Response Awakenings :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)    3.095      0.524    5.90  1.4e-07
# Melatonin     -0.182      0.633   -0.29     0.77
#
# Response Morning.Feel :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)    2.952      0.142   20.78   <2e-16
# Melatonin      0.222      0.171    1.29      0.2
#
# Response Time.in.Light :
#
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)   253.86      13.59   18.68   <2e-16
# Melatonin       7.93      16.40    0.48     0.63

The in­di­cates no sta­tis­ti­cal­ly-sig­nifi­cant differ­ence be­tween the groups of days, tak­ing all vari­ables into ac­count (p = 0.69). To sum­ma­rize the re­gres­sion:

Vari­able Correlate/Effect p-value Co­effi­cien­t’s sign is…
Time.to.Z - 5.04 0.11 bet­ter
Awakenings - 0.18 0.77 bet­ter
Time.in.Wake - 0.25 0.89 bet­ter
Time.in.Deep 5 .56 0.16 bet­ter
Time.in.Light 7 .93 0.63 worse
Time.in.REM - 3.73 0.74 worse
Total.Z 9.68 0.73 bet­ter
ZQ 2.43 0.63 bet­ter
Morning.Feel 0 .22 0.20 bet­ter

Part of the prob­lem is that too many days wound up be­ing use­less, and each day costs us in­for­ma­tion and re­duces our true sam­ple size. (None of the met­rics are strong enough to sur­vive mul­ti­ple cor­rec­tion7, sad­ly.)

And also un­for­tu­nate­ly, this dataseries does­n’t dis­tin­guish be­tween ad­di­tion to mela­tonin or ben­e­fits from mela­ton­in—per­haps the 3.2 is my ‘nor­mal’ sleep qual­ity and the 2.9 comes from a ‘with­drawal’ of sorts. The re­search on mela­tonin does­n’t in­di­cate any ad­dic­tion effect, but who knows?

If I were to run fur­ther ex­per­i­ments, I would defi­nitely run it dou­ble-blind, and maybe even test <1.5mg doses as well to see if I’ve been tak­ing too much; 3mg turned out to be ex­ces­sive, and there are one or two stud­ies in­di­cat­ing that <1mg doses are best for nor­mal peo­ple. I wound up us­ing 1.5mg dos­es. (There could be 3 con­di­tions: place­bo, 0.75mg, and 1.5mg. For look­ing at mela­tonin effect in gen­er­al, the data on 2 dosages could be com­bined. Mela­tonin has a short half-life, so prob­a­bly there would be no point in ran­dom blocks of more than 2-3 days8: we can ran­dom­ize each day sep­a­rately and as­sume that days are in­de­pen­dent of each oth­er.)

Worth com­par­ing are Jayson Viris­si­mo’s pre­lim­i­nary re­sults:

Ac­cord­ing to the pre­lim­i­nary [Zeo] data, while on mela­ton­in, I seemed to get more to­tal sleep, more REM sleep, less deep sleep, and wake up about the same num­ber of times each night. Be­cause this is­n’t enough data to be very con­fi­dent in the re­sults, I plan on con­tin­u­ing this ex­per­i­ment for at least an­other 4 months (2 on and 2 off of mela­ton­in) and will an­a­lyze the re­sults for the [s­ta­tis­ti­cal] sig­nifi­cance and mag­ni­tude of the effects (if there re­ally are any) while throw­ing out the out­liers (s­ince my sleep sched­ule is so er­rat­ic).

Value of Information (VoI)

See also the dis­cus­sion as ap­plied to or­der­ing modafinil and test­ing nootrop­ics

We all know it’s pos­si­ble to spend more time fig­ur­ing out how to “save time” on a task than we would ac­tu­ally save time like re­ar­rang­ing books on a shelf or clean­ing up in the name of effi­ciency (xkcd even has a cute chart list­ing the break-even points for var­i­ous pos­si­bil­i­ties,“Is It Worth The Time?”), and sim­i­lar­ly, it’s pos­si­ble to spend more money try­ing to “save money” than one would ac­tu­ally save; less ap­pre­ci­ated is that the same thing is also pos­si­ble to do with gain­ing in­for­ma­tion.

The value of an ex­per­i­ment is the in­for­ma­tion it pro­duces. What is the value of in­for­ma­tion? Well, we can take the eco­nomic tack and say value of in­for­ma­tion is the value of the de­ci­sions it changes. (Would you pay for a weather fore­cast about some­where you are not go­ing to? No. Or a weather fore­cast about your trip where you have to make that trip, come hell or high wa­ter? Only to the ex­tent you can make prepa­ra­tions like bring­ing an um­brel­la.)

Wikipedia says that for a risk-neu­tral per­son, value of per­fect in­for­ma­tion is “value of de­ci­sion sit­u­a­tion with per­fect in­for­ma­tion”—“value of cur­rent de­ci­sion sit­u­a­tion”. (Im­per­fect in­for­ma­tion is just weak­ened per­fect in­for­ma­tion: if your in­for­ma­tion was not 100% re­li­able but 99% re­li­able, well, that’s still worth a lot.)

The de­ci­sion is the bi­nary take or not take. Mela­tonin costs ~$10 a year (if you buy in bulk dur­ing sales, as I did). Sup­pose I had per­fect in­for­ma­tion it worked; I would not change any­thing, so the value is $0. Sup­pose I had per­fect in­for­ma­tion it did not work; then I would stop us­ing it, sav­ing me $10 a year in per­pe­tu­ity, which has a net present value9 (at 5% dis­count­ing) of $205. So the best-case value of per­fect in­for­ma­tion—the case in which it changes my ac­tion­s—is $205, be­cause it would save me from blow­ing $10 every year for the rest of my life. My mela­tonin ex­per­i­ment is not per­fect since I did­n’t ran­dom­ize or dou­ble-blind it, but I had a lot of data and it was well pow­ered, with some­thing like a >90% chance of de­tect­ing the de­cent effect size I ex­pect­ed, so the im­per­fec­tion is just a loss of 10%, down to $184. From my pre­vi­ous re­search and per­sonal use over years, I am highly con­fi­dent it work­s—say, 80%10.

If the ex­per­i­ment says mela­tonin works, the in­for­ma­tion is use­less to me since I con­tinue us­ing mela­ton­in, and if the ex­per­i­ment says it does­n’t, then let’s as­sume I de­cide to quit mela­tonin11 and then save $10 a year or $184 to­tal. What’s the ex­pected value of ob­tain­ing the in­for­ma­tion, given these two out­comes? . Or an­other way, re­do­ing the net present val­ue: At min­i­mum wage op­por­tu­nity cost of $7 an hour, $36.8 is worth 5.25 hours of my time. I spent much time on screen­shots, sum­ma­riz­ing, and analy­sis, and I’d guess I spent closer to 10-15 hours all told.

This worked out ex­am­ple demon­strates that when a sub­stance is cheap and you are highly con­fi­dent it works, a long costly ex­per­i­ment may not be worth it. (Of course, I would have done it any­way due to fac­tors not in­cluded in the cal­cu­la­tion: to try out my Zeo, learn a bit about sleep ex­per­i­men­ta­tion, do some­thing cool, and have some­thing neat to show every­one.)

Melatonin data

The data looked much bet­ter than the first night, ex­cept for a big 2-hour gap where I vaguely re­call the sen­sor head­band hav­ing slipped off. (I don’t think it was be­cause it was un­com­fort­able but due to shift­ing po­si­tions or some­thing.) Judg­ing from the cy­cle of sleep phas­es, I think I lost data on a REM peak. The REM peaks in­ter­est me be­cause it’s a stan­dard the­ory of polypha­sic sleep­ing that thriv­ing on 2 or 3 hours of sleep a day is pos­si­ble be­cause REM (and deep sleep) is the only phase that truly mat­ters, and REM can dom­i­nate sleep time through and train­ing.

Sec­ond night

Be­sides that, I no­ticed that time to sleep was 19 min­utes that night. I also had for­got­ten to take my mela­tonin. Hmm…

Since I’ve be­gun this in­ad­ver­tent ex­per­i­ment, I’ll try con­tin­u­ing it, al­ter­nat­ing days of mela­tonin us­age. I claim in my mela­tonin ar­ti­cle that us­age seems to save about 1 hour of sleep/time, but there’s sev­eral pos­si­ble av­enues. One could be quicker to fall asleep; one could awake fewer times; and one could have greater per­cent­age of REM or deep sleep, re­duc­ing light sleep. (Light sleep does­n’t seem very use­ful; I some­times feel worse after light sleep.)

Dur­ing the after­noon, I took a quick nap. I’m not a very good nap­per, it seem­s—only the first 5 min­utes reg­is­tered as even light sleep.

A dose of mela­tonin (1.5mg) and off to bed a bit ear­ly. I’m a lit­tle more im­pressed with the smart alarm; since I’m hard-of-hear­ing and au­dio alarms rarely if ever work, I usu­ally use a Sonic Alert vi­brat­ing alarm clock. But in the morn­ing I woke up within a minute of the alarm, de­spite the lack of vi­bra­tion or flash­ing lights. (The chart does­n’t re­flect this, but as a pre­vi­ous link says, dis­tin­guish­ing wak­ing from sleep­ing can be diffi­cult and the tran­si­tions are the least trust­wor­thy parts of the da­ta.)

The data was es­pe­cially good to­day, with no big gaps:

2010-12-27 ZQ sleep logs

You can see an im­pres­sively reg­u­lar sleep cy­cle, cy­cling be­tween REM and light sleep. What’s dis­turb­ing is the rel­a­tive lack of deep sleep­—­down 4-5% (and there was­n’t a lot to be­gin with). I sus­pect that the lack of deep sleep in­di­cates I was­n’t sleep­ing very well, but not badly enough to wake up, and this is prob­a­bly due ei­ther to light from the Zeo it­self—I only fig­ured out how to turn it off a few days lat­er—or my lack of reg­u­lar blan­kets and use of a sleep­ing bag. But the awak­en­ings around 4-6 AM and on other days has made me sus­pi­cious that one of the cats is both­er­ing me around here and I’m just for­get­ting it as I fall asleep.

The next night is an­other no-me­la­tonin night. This time it took 79 min­utes to fall asleep. Very bad, but far from un­prece­dent­ed; this sort of thing is why I was in­ter­ested in mela­tonin in the first place. Deep sleep is again lim­ited in dis­per­sion, with a block at the be­gin­ning and end, but mostly a reg­u­lar cy­cle be­tween light and REM:

2010-12-28 ZQ sleep logs

Mela­tonin night, and 32 min­utes to sleep. (I’m start­ing to no­tice a trend here.) An­other fairly reg­u­lar cy­cle of phas­es, with some deep sleep at the be­gin­ning and end; 32 min­utes to fall asleep is­n’t great but much bet­ter than 79 min­utes.

2010-12-29 ZQ sleep logs

Per­haps I should try a bipha­sic sched­ule where I sleep for an hour at the be­gin­ning and end? That’d seem to pick up most of my deep sleep, and REM would hope­fully take care of it­self with REM re­bound. Need to sum my av­er­age REM & deep sleep times (that sum seems to differ quite a bit, eg one fel­low needs 4+ hours. My own need seems to be sim­i­lar) so I don’t try to pick a sched­ule doomed to fail.

An­other night, no mela­tonin. Time to sleep, just 18 min­utes and the ZQ sets a new record even though my cat Stormy woke me up in the morn­ing12:

2010-12-30 ZQ sleep logs

I per­son­ally blame this on be­ing ex­hausted from 10 hours work­ing on my tran­scrip­tion of . But a data point is a data point.

I spend New Year’s Eve pretty much fin­ish­ing The Notenki Mem­oirs (tran­scrib­ing the last of the bi­ogra­phies, the round-table dis­cus­sion, and edit­ing the im­ages for in­clu­sion), which ex­hausts me a fair bit as well; the cham­pagne does­n’t help, but be­tween that and the mela­ton­in, I fall asleep in a record-set­ting 7 min­utes. Un­for­tu­nate­ly, the head­band came off some­where around 5 AM:

2010-12-31 ZQ sleep logs

A cat? Wak­ing up? Dun­no.

An­other rel­a­tively quick falling asleep night at 20 min­utes. Which then gets screwed up as I sim­ply can’t stay asleep and then the cat be­gins both­er­ing the heck out of me in the early morn­ing:

2011-01-01 ZQ sleep logs

Mela­tonin night, which sub­jec­tively did­n’t go too bad­ly; 20 min­utes to sleep. But lots of wake time (long enough wakes that I re­mem­bered them) and 2 or 3 hours not recorded (prob­a­bly from ad­just­ing my scarf and the head­band):

2011-01-03 ZQ sleep logs

Ac­ci­den­tally did an­other mela­tonin night (thought Mon­day was a no-me­la­tonin night). Very good sleep­—set records for REM es­pe­cially to­wards the late morn­ing which is cu­ri­ous. (The dreams were also very cu­ri­ous. I was an Evan­ge­lion char­ac­ter (Ka­woru) tasked with rid­ing that kind of car­ni­val-like ride that goes up and drops straight down.) Also an­other quick falling asleep:

2011-01-04 ZQ sleep logs

Rather than 3 mela­tonin nights in a row, I skipped mela­tonin this night (and thus will have it the next one). Per­haps be­cause I went to sleep so very late, and de­spite some awak­en­ings, this was a record-set­ting night for ZQ and TODO deep sleep or REM sleep? :

2011-01-05 ZQ sleep logs

I also switched the alarm sounds 2 or 3 days ago to ‘for­est’ sounds; they seem some­what more pleas­ant than the beep­ing mu­si­cal tones. The next night, data is all screwed up. What hap­pened there? It did­n’t even record the start of the night, though it seemed to be ac­tive and work­ing when I checked right be­fore go­ing to sleep. Odd.

Next 2 days aren’t very in­ter­est­ing; first is no-me­la­ton­in, sec­ond is mela­ton­in:

2011-01-07 ZQ sleep logs
2011-01-08 ZQ sleep logs
Off
On
Off

One of my chief Zeo com­plaints was the bright blue-white LCD screen. I had re­sorted to turn­ing the base sta­tion over and sur­round­ing it with socks to block the light. Then I looked closer at the la­bels for the but­tons and learned that the up­-down but­tons changed the bright­ness and the LCD screen could be turned off. And I had read the part of the man­ual that ex­plained that. D’oh!

On
?
Off
Off (for­got)
On
Off
On
Off
On
Off

Off, but no data on the 22nd. No idea what the prob­lem is—the head­set seems to have been on all night.

On with a dou­ble-dose of mela­tonin be­cause I was go­ing to bed ear­ly; as you can see, did­n’t work:

2011-01-23 ZQ sleep logs

Off, no data on the 24th. On, no data on the 25th. I don’t know what went wrong on these two nights.

Off

The 27th (on for mela­ton­in) yielded no data be­cause, frus­trat­ing­ly, the Zeo was print­ing a ‘write-pro­tected’ er­ror on its screen; I as­sumed it had some­thing to do with up­load­ing ear­lier that day—per­haps I had yanked it out too quick­ly—and put it back in the com­put­er, un­mounted and went to eject it. But the mem­ory card splin­tered on me! It was stuck and the end was splin­ter­ing and lit­tle nee­dles of plas­tic break­ing off. I could­n’t get it out and gave up. The next day (I slept rea­son­ably well) I went back with a pair of needle-nose pli­ers. I had a backup mem­ory card. After much trial and er­ror, I fig­ured out the card had to be FAT-formatted and have a di­rec­tory struc­ture that looked like ZEO/ZEOSLEEP.DAT. So that’s that.

  • Off
  • On
  • 30: on
  • 31: off
  • 1: on
  • 2: off
  • 3: on

Un­for­tu­nate­ly, this night con­tin­ues a long run of no da­ta. Look­ing back, it does­n’t seem to have been the fault of the new mem­ory card, since some nights did have enough data for the Zeo web­site to gen­er­ate graphs. I sus­pect that the is­sue is the pad get­ting dirty after more than a month of use. I hope so, any­way. I’ll look around for rub­bing al­co­hol to clean it. That night ini­tially starts bad­ly—the rub­bing al­co­hol seemed to do noth­ing. After some mess­ing around, I fig­ure out that the head­band seems to have loos­ened over the weeks and so while the sen­sor felt rea­son­ably snug and tight and was trans­mit­ting, it was­n’t snug enough. I tighten it con­sid­er­ably and ac­tu­ally get some de­cent data:

  • Off
  • 5: on
  • Off
  • 7: on
  • 8: off
  • 9: on
  • Off
  • 11: on?

The pre­vi­ous night, I be­gan pay­ing closer at­ten­tion to when it was and was not read­ing me (usu­ally the lat­ter). Push­ing hard on it made it even­tu­ally read me, but tight­en­ing the head­band had­n’t helped the pre­vi­ous sev­eral nights. Push­ing and not push­ing, I no­ticed a sub­tle click. Ap­par­ently the band part with the metal sen­sor pad con­nects to the wire­less unit by 3 lit­tle black metal nubs; 2 were solidly in place, but the third was com­pletely loose. Sus­pi­cious, I try pulling on the band with­out push­ing on the wire­less unit—leav­ing the loose con­nec­tion loose. Sure enough, no con­nec­tion was reg­is­tered. I push on the unit while loos­ing the head­band—and the con­nec­tion worked. I felt I fi­nally had solved it. It was­n’t a loose head­band or me pulling it off at night or oils on the metal sen­sors or a prob­lem with the SD card. I was too tired to fix it when I had the re­al­iza­tion, but re­solved the next morn­ing to fix it by wrap­ping a rub­ber band around the wire­less unit and band. This turned out to not in­ter­fere with recharg­ing, and when I took a short nap, the data looked fine and gap­less. So! The long data drought is hope­fully over.

2011-02-11 ZQ sleep logs
Off
On
Off

On the 15th of Feb­ru­ary, I had a very early flight to San Fran­cis­co. That night and every night from then on, I was us­ing mela­ton­in, so we’ll just in­clude all the nights for which any sen­si­ble data was gath­ered. Oddly enough, the data and ZQs seem bad (as one would ex­pect from sleep­ing on a couch), but I wake up feel­ing fairly re­freshed. By this point we have the idea how the sleep charts work, so I will sim­ply link them rather than dis­play them.

Then I took a long break on up­dat­ing this page; when I had a month or two of data, I up­loaded to Zeo again, and buck­led down and fig­ured out how to have crop pages. The shell script (for screen­shots of my browser, YMMV) is for file in *.png; do mogrify +repage -crop 700x350+350+285 $file; done;

Gen­eral ob­ser­va­tions: al­most all these nights were on mela­tonin. Not far into this pe­ri­od, I re­al­ized that the lit­tle rub­ber band was not work­ing, and I hauled out my red and tight­ened it but good; and again, you can see the tran­si­tion from crappy record­ings to much cleaner record­ings. The rest of Feb­ru­ary:

March:

April:

April 4th was one of the few nights that I was not on mela­tonin dur­ing this times­pan; I oc­ca­sion­ally take a week­end and try to drop all sup­ple­ments and nootrop­ics be­sides the mul­ti­vi­t­a­mins and fish oil, which in­cludes my mela­tonin pills. This night (or more pre­cise­ly, that Sun­day evening) I also stayed up late work­ing on my com­put­er, get­ting in to bed at 12:25 AM. You can see how well that worked out. Dur­ing the 2 AM wake pe­ri­od, it oc­curred to me that I did­n’t es­pe­cially want to sac­ri­fice a day to show that com­puter work can make for bad sleep (which I al­ready have plenty of ci­ta­tions for in the Mela­tonin es­say), and I gave in, tak­ing a pill. That worked out much bet­ter, with a rel­a­tively nor­mal num­ber of wak­ings after 2 AM and a rea­son­able amount of deep & REM sleep.

Exercise

One-legged standing

Seth Roberts found that for him, stand­ing a lot helped him sleep. This seems very plau­si­ble to me—­more fa­tigue to re­pair, closer to an­ces­tral con­di­tions of con­stant walk­ing—and tal­lied with my own ex­pe­ri­ence. (One sum­mer I worked at a sum­mer camp, where I spent the en­tire day on my feet; I al­ways slept very well though my bunk was un­com­fort­able.) He also found that stress­ing his legs by stand­ing on one at a time for a few min­utes also helped him sleep. That did not seem as plau­si­ble to me. But still worth try­ing: stand­ing is free, and if it does noth­ing, at least I got a lit­tle more ex­er­cise.

Roberts tried a fairly com­pli­cated ran­dom­ized rou­tine. I am sim­ply al­ter­nat­ing days as with mela­tonin (note that I have re­sumed tak­ing mela­tonin every day). My stand­ing method is also sim­ple; for 5 min­utes, I stand on one leg, rise up onto the ball of my foot (be­cause my calves are in good shape), and then sink down a foot or two and hold it un­til the burn­ing sen­sa­tion in my thigh forces me to switch to the other leg. (I seem to al­ter­nate every minute.) I walk my dog most every day, so the effect is not as sim­ple as ‘some mod­er­ate ex­er­cise that day’; in the next ex­per­i­ment, I might try 5 min­utes of dumb­bell bi­cep curls in­stead.

One-legged standing analysis

The ini­tial re­sults were promis­ing. Of the first 5 days, 3 are ‘on’ and 2 are off; all 3 on-days had higher ZQs than the 2 off-days. Un­for­tu­nate­ly, the full time se­ries did not seem to bear this out. Look­ing at the ~70 recorded days be­tween 2011-06-11 and 2011-08-27 (raw CSV data), the raw un­cor­rected av­er­ages looked like this (as be­fore, the ‘3’ means the in­ter­ven­tion was used, ‘0’ that it was not):

Stand­ing ZQ vs non-s­tand­ing
Morn­ing feel rat­ing
To­tal sleep time
To­tal deep sleep time
To­tal REM sleep time
Num­ber of times woken
To­tal time awake

R analy­sis, us­ing mul­ti­vari­ate lin­ear re­gres­sion13 turns in a non-sig­nifi­cant value for one-legged­ness in gen­eral (p = 0.23); by vari­able:

Vari­able Effect p-value Co­effi­cien­t’s sign is…
ZQ -1.24 0.16 worse
Total.Z -4.09 0.37 worse
Time.to.Z 0.47 0.51 worse
Time.in.Wake -0.37 0.80 bet­ter
Time.in.REM -5.33 0.02 worse
Time.in.Light 2.76 0.38 worse
Time.in.Deep -1.56 0.10 worse
Awakenings -0.05 0.79 bet­ter
Morning.Feel -0.05 0.32 worse

No p-val­ues sur­vived mul­ti­ple-cor­rec­tion14:.

While I did not repli­cate Robert­s’s setup ex­actly in the in­ter­est of time and ease, and it was not blind­ed, I tried to com­pen­sate with an un­usu­ally large sam­ple: 69 nights of da­ta. This was a mixed ex­per­i­ment: there seems to be an neg­a­tive effect, but none of the changes seem to have large effect sizes or strong p-val­ues.

The one-legged stand­ing was not in ex­clu­sion to mela­tonin use, but I had used it most every night. I thought I might go on us­ing one-legged stand­ing, per­haps skip­ping it on nights when I am up par­tic­u­larly late or lack the willpow­er, but I’ve aban­doned it be­cause it is a lot of work to use and the re­sult looked weak. In the fu­ture, I should look into whether walks be­fore bed­time help.

Vitamin D

Vi­t­a­min D is a hor­mone en­doge­nously cre­ated by ex­po­sure to sun­light; due to his­tor­i­cally low out­doors ac­tiv­ity lev­els, it has be­come a pop­u­lar sup­ple­ment and I use it. Some anec­dotes sug­gest that vi­t­a­min D may have cir­ca­dian and zeit­ge­ber effects due to its orig­in, and is harm­ful to sleep when taken at night. I ran a blinded ran­dom­ized self­-ex­per­i­ment on tak­ing vi­t­a­min D pills at bed­time. The vi­t­a­min D dam­aged my sleep and es­pe­cially how rested I felt upon wak­en­ing, sug­gest­ing vi­t­a­min D did have a stim­u­lat­ing effect which ob­structed sleep. I con­ducted a fol­lowup blinded ran­dom­ized self­-ex­per­i­ment on the log­i­cal next ques­tion: if vi­t­a­min D is a day­time cue, then would vi­t­a­min D taken in the morn­ing show some ben­e­fi­cial effects? The re­sults were in­con­clu­sive (but slightly in fa­vor of ben­e­fit­s). Given the asym­me­try, I sug­gest that vi­t­a­min D sup­ple­ments should be taken only in the morn­ing.

Main ar­ti­cle: .

Potassium

Potas­sium and mag­ne­sium are min­er­als that many Amer­i­cans are de­fi­cient in. I tried us­ing potas­sium cit­rate and im­me­di­ately no­ticed diffi­culty sleep­ing. A short ran­dom­ized (but not blind­ed) self­-ex­per­i­ment of ~4g potas­sium taken through­out the day con­firmed large neg­a­tive effects on my sleep. A longer fol­lowup ran­dom­ized and blinded self­-ex­per­i­ment used stan­dard­ized doses taken once a day early in the morn­ing, and also found some harm to sleep, and I dis­con­tin­ued potas­sium use en­tire­ly.

Main ar­ti­cle: .

LSD microdosing

In the mid­dle of the five-fold ex­per­i­ment, I paused part of it to run ; I in­cluded sleep met­rics to check for dis­tur­bances. It did not seem to affect la­ten­cy, to­tal sleep, or awak­en­ings, but did im­prove (d = 0.42) the “morn­ing feel” non-s­ta­tis­ti­cal­ly-sig­nifi­cantly (due to the mul­ti­ple cor­rec­tion). Un­for­tu­nate­ly, given that it seemed to neg­a­tively affect more im­por­tant met­rics like the self­-rat­ing of mood/productivity & cre­ativ­i­ty, this is not nearly enough to be­gin to jus­tify fur­ther use of LSD mi­cro­dos­ing for me.

Alcohol

Sus­pi­cious that al­co­hol was de­lay­ing my sleep and wors­en­ing my sleep when I did fi­nally go to bed, I recorded my al­co­hol con­sump­tion for a year. Cor­re­lat­ing al­co­hol use against when I go to bed shows no in­ter­est­ing cor­re­la­tion, nor with any of the other sleep vari­ables Zeo records, even after cor­rect­ing for a shift in my sleep pat­terns over that year. So it would seem I was wrong.

In May 2013, I be­gan to won­der if al­co­hol was dam­ag­ing my sleep; I don’t drink al­co­hol too often and never more than a glass or two, so I don’t have any tol­er­ance built up. I no­ticed that on nights when I drank some red wine or had some of my mead, it seemed to take me much longer to fall asleep and I would reg­u­larly wake up in the mid­dle of the night. So I be­gan not­ing down days on which I drank any al­co­hol, to see if it cor­re­lated with sleep prob­lems (and prob­a­bly then just re­frain from al­co­hol in the evening, since I don’t care enough to run a ran­dom­ized ex­per­i­men­t).

In May 2014, I ran out of all my mead and also a gal­lon of bur­gundy wine I had bought to make beef bour­guignon with, so that marked a nat­ural close to the data col­lec­tion. I com­piled the al­co­hol data along with the Zeo data in the rel­e­vant time pe­ri­od, and looked at the key met­rics with a mul­ti­vari­ate mul­ti­ple re­gres­sion. The main com­plex­ity here is that I ear­lier dis­cov­ered that I had grad­u­ally shifted my sleep down and now Start.of.Night looks like a sig­moid, so to con­trol for that, I fit a sig­moid to the Date us­ing non­lin­ear least squares, and then plugged the es­ti­mated val­ues in. The code, show­ing only the re­sults for the Alcohol boolean:

drink <- read.csv("https://www.gwern.net/docs/zeo/2014-gwern-alcohol.csv")
library(minpack.lm)
summary(nlsLM(Start.of.Night ~ Alcohol + as.integer(Date) + (a / (1 + exp(-b * (as.integer(Date) - c)))),
              start = list(a = 6.15e+05, b = -1.18e-04, c = -5.15e+04),
              control=(nls.lm.control(ftol = sqrt(.Machine$double.eps)/4.9, maxfev=1024, maxiter=1024)),
              data=drink))
# Parameters:
#    Estimate Std. Error t value Pr(>|t|)
# a  5.61e+06   6.49e+09    0.00     1.00
# b -1.00e-03   2.44e-04   -4.10  4.8e-05
# c -8.26e+03   1.16e+06   -0.01     0.99
summary(lm(cbind(Start.of.Night, Time.to.Z, Time.in.Wake, Awakenings, Morning.Feel, Total.Z, Time.in.REM, Time.in.Deep) ~
                  Alcohol +
                  as.integer(Date) + I(5.61e+06 / (1 + exp(-(1.00e-03) * (as.integer(Date) - (-8.26e+03))))),
                 data=drink))
# Response Start.of.Night :
# Coefficients:
#                                                                Estimate Std. Error t value Pr(>|t|)
# AlcoholTRUE                                                   -8.96e-01   4.75e+00   -0.19     0.85
#
# Response Time.to.Z :
# Coefficients:
#                                                                Estimate Std. Error t value Pr(>|t|)
# AlcoholTRUE                                                   -2.50e+00   1.41e+00   -1.77    0.077
#
# Response Time.in.Wake :
# Coefficients:
#                                                                Estimate Std. Error t value Pr(>|t|)
# AlcoholTRUE                                                   -2.04e+00   2.40e+00   -0.85   0.3956
#
# Response Awakenings :
# Coefficients:
#                                                                Estimate Std. Error t value Pr(>|t|)
# AlcoholTRUE                                                   -2.03e-01   2.85e-01   -0.71     0.48
#
# Response Morning.Feel :
# Coefficients:
#                                                                Estimate Std. Error t value Pr(>|t|)
# AlcoholTRUE                                                   -5.03e-02   9.16e-02   -0.55   0.5836
#
# Response Total.Z :
# Coefficients:
#                                                                Estimate Std. Error t value Pr(>|t|)
# AlcoholTRUE                                                    1.04e+01   7.89e+00    1.32     0.19
#
# Response Time.in.REM :
# Coefficients:
#                                                                Estimate Std. Error t value Pr(>|t|)
# (Intercept)                                                    7.59e+05   9.83e+05    0.77     0.44
# AlcoholTRUE                                                    1.84e+00   3.58e+00    0.51     0.61
#
# Response Time.in.Deep :
# Coefficients:
#                                                                Estimate Std. Error t value Pr(>|t|)
# AlcoholTRUE                                                    1.14e+00   1.41e+00    0.80     0.42

Zilch. No cor­re­la­tion is at all in­ter­est­ing.

So it looks like al­co­hol—at least in the small quan­ti­ties I con­sume—­makes no differ­ence.

Timing

Bed time for better sleep

Some­one asked if I could turn up a bet­ter bed­time us­ing their Zeo da­ta. I ac­cept­ed, but the sleep data comes with quite a few vari­ables and it’s not clear which vari­able is the ‘best’—for ex­am­ple, I don’t think much of the ZQ vari­able, so it’s not as sim­ple as re­gress­ing ZQ ~ Bedtime and find­ing what value of Bed­time max­i­mizes ZQ. I de­cided that I could try find­ing the op­ti­mal bed­time by two strate­gies:

  1. look for some un­der­ly­ing fac­tor of good sleep us­ing —I’d ex­pect maybe 2 or 3 fac­tors, one for to­tal sleep, one for in­som­nia, and maybe one for REM sleep­—and max­i­mize the good ones and min­i­mize the bad ones, equally weighted
  2. just do a mul­ti­vari­ate re­gres­sion and weight each vari­able equally

So, se­tup:

zeo <- read.csv("https://www.gwern.net/docs/zeo/gwern-zeodata.csv")
zeo$Sleep.Date <- as.Date(zeo$Sleep.Date, format="%m/%d/%Y")
## convert "05/12/2014 06:45" to "06:45"
zeo$Start.of.Night <- sapply(strsplit(as.character(zeo$Start.of.Night), " "), function(x) { x[2] })
## convert "06:45" to 24300
interval <- function(x) { if (!is.na(x)) { if (grepl(" s",x)) as.integer(sub(" s","",x))
                                           else { y <- unlist(strsplit(x, ":")); as.integer(y[[1]])*60 + as.integer(y[[2]]); }
                                         }
                          else NA
                        }
zeo$Start.of.Night <- sapply(zeo$Start.of.Night, interval)
## correct for the switch to new unencrypted firmware in March 2013;
## I don't know why the new firmware subtracts 15 hours
zeo[(zeo$Sleep.Date >= as.Date("2013-03-11")),]$Start.of.Night
 <- (zeo[(zeo$Sleep.Date >= as.Date("2013-03-11")),]$Start.of.Night + 900) %% (24*60)

## after midnight (24*60=1440), Start.of.Night wraps around to 0, which obscures any trends,
## so we'll map anything before 7AM to time+1440
zeo[zeo$Start.of.Night<420 & !is.na(zeo$Start.of.Night),]$Start.of.Night
 <- (zeo[zeo$Start.of.Night<420 & !is.na(zeo$Start.of.Night),]$Start.of.Night + (24*60))

## keep only the variables we're interested in:
zeo <- zeo[,c(2:10, 23)]
## define naps or nights with bad data as total sleep time under ~1.5 hours (100m) & delete
zeo <- zeo[zeo$Total.Z>100,]
write.csv(zeo, file="bedtime-factoranalysis.csv", row.names=FALSE)

Let’s be­gin with a sim­ple fac­tor analy­sis, look­ing for a ‘good sleep’ fac­tor. Zeo Inc ap­par­ently was try­ing for this with the ZQ vari­able but I’ve al­ways been sus­pi­cious of it be­cause it does­n’t seem to track Morning.Feel or Awakenings very well but sim­ply be how long you slept (Total.Z):

zeo <- read.csv("https://www.gwern.net/docs/zeo/2014-07-26-bedtime-factoranalysis.csv")
library(psych)
nfactors(zeo)
# VSS complexity 1 achieves a maximimum of 0.8  with  6  factors
# VSS complexity 2 achieves a maximimum of 0.94  with  6  factors
# The Velicer MAP achieves a minimum of 0.09  with  1  factors
# Empirical BIC achieves a minimum of  466.5  with  5  factors
# Sample Size adjusted BIC achieves a minimum of  39396  with  5  factors
#
# Statistics by number of factors
#    vss1 vss2   map dof chisq prob sqresid  fit RMSEA   BIC SABIC complex  eChisq    eRMS eCRMS eBIC
# 1  0.71 0.00 0.090  35 41394    0  6.4648 0.71  0.99 41145 41256     1.0 1.8e+03 0.12926  0.15 1577
# 2  0.77 0.85 0.099  26 40264    0  3.3366 0.85  1.13 40079 40162     1.2 9.4e+02 0.09275  0.12  755
# 3  0.78 0.89 0.139  18 40323    0  2.1333 0.91  1.36 40195 40253     1.4 9.0e+02 0.09075  0.14  772
# 4  0.75 0.89 0.216  11 39886    0  1.3401 0.94  1.73 39808 39843     1.5 8.0e+02 0.08560  0.17  722
# 5  0.78 0.89 0.280   5 39415    0  0.7267 0.97  2.56 39380 39396     1.4 5.0e+02 0.06779  0.20  467
# 6  0.80 0.94 0.450   0 38640   NA  0.3194 0.99    NA    NA    NA     1.2 2.2e+02 0.04479    NA   NA
# 7  0.80 0.92 0.807  -4 37435   NA  0.1418 0.99    NA    NA    NA     1.2 1.0e+02 0.03075    NA   NA
# 8  0.78 0.91 4.640  -7 30474   NA  0.0002 1.00    NA    NA    NA     1.3 2.5e-02 0.00048    NA   NA
# 9  0.78 0.91   NaN  -9 30457   NA  0.0002 1.00    NA    NA    NA     1.3 2.5e-02 0.00048    NA   NA
# 10 0.78 0.91    NA -10 30440   NA  0.0002 1.00    NA    NA    NA     1.3 2.5e-02 0.00048    NA   NA

## BIC says 5 factors, so we'll go with that:
factorization <- fa(zeo, nfactors=5); factorization
# Standardized loadings (pattern matrix) based upon correlation matrix
#                  MR1   MR2   MR5   MR4   MR3   h2    u2 com
# ZQ              0.87 -0.14 -0.01  0.25 -0.04 0.99 0.013 1.2
# Total.Z         0.96  0.04 -0.01  0.07 -0.04 0.99 0.011 1.0
# Time.to.Z       0.05 -0.03  0.92  0.03  0.10 0.84 0.159 1.0
# Time.in.Wake   -0.18  0.90 -0.02  0.04 -0.15 0.83 0.168 1.1
# Time.in.REM     0.87  0.05  0.03  0.05  0.09 0.78 0.215 1.0
# Time.in.Light   0.94  0.02 -0.04 -0.20 -0.14 0.84 0.158 1.1
# Time.in.Deep    0.02  0.03  0.01  0.99 -0.02 0.98 0.023 1.0
# Awakenings      0.35  0.75  0.08 -0.03  0.26 0.79 0.209 1.7
# Start.of.Night -0.21  0.00  0.10 -0.05  0.86 0.84 0.162 1.2
# Morning.Feel    0.22 -0.13 -0.55  0.11  0.46 0.66 0.343 2.5
#
#                        MR1  MR2  MR5  MR4  MR3
# SS loadings           3.65 1.44 1.21 1.16 1.08
# Proportion Var        0.37 0.14 0.12 0.12 0.11
# Cumulative Var        0.37 0.51 0.63 0.75 0.85
# Proportion Explained  0.43 0.17 0.14 0.14 0.13
# Cumulative Proportion 0.43 0.60 0.74 0.87 1.00
#
#  With factor correlations of
#       MR1   MR2   MR5   MR4   MR3
# MR1  1.00  0.03 -0.18  0.34 -0.03
# MR2  0.03  1.00  0.27 -0.09  0.00
# MR5 -0.18  0.27  1.00 -0.09  0.09
# MR4  0.34 -0.09 -0.09  1.00  0.03
# MR3 -0.03  0.00  0.09  0.03  1.00
#
# Mean item complexity =  1.3
# Test of the hypothesis that 5 factors are sufficient.
#
# The degrees of freedom for the null model are  45  and the objective function was  40.02 with Chi Square of  48376
# The degrees of freedom for the model are 5  and the objective function was  32.69
#
# The root mean square of the residuals (RMSR) is  0.07
# The df corrected root mean square of the residuals is  0.2
#
# The harmonic number of observations is  1152 with the empirical chi square  473.1  with prob <  5.1e-100
# The total number of observations was  1214  with MLE Chi Square =  39412  with prob <  0
#
# Tucker Lewis Index of factoring reliability =  -6.359
# RMSEA index =  2.557  and the 90 % confidence intervals are  2.527 2.569
# BIC =  39377
# Fit based upon off diagonal values = 0.97

This looks like MR1=over­all sleep; MR2=insomnia/bad-sleep; MR5=d­iffi­cul­ty-falling-asleep?; MR4=deep­-sleep­-(not part of MR1!); MR3=­dun­no. MR1 and MR4 cor­re­late 0.34, and MR2/MR5 0.27, which makes sense. I want to max­i­mize over­all sleep and deep sleep (deep sleep seems con­nected to health), so MR1 and M4.

Now that we have our fac­tors, we can ex­tract them and plot them over time for a graph­i­cal look:

MR1 <- predict(factorization, data=zeo)[,1]
MR4 <- predict(factorization, data=zeo)[,4]

par(mfrow=c(2,1), mar=c(4,4.5,1,1))
plot(MR1 ~ I(Start.of.Night/60), xlab="",        ylab="Total sleep (MR1)", data=zeo)
plot(MR4 ~ I(Start.of.Night/60), xlab="Bedtime", ylab="Deep sleep (MR4)",  data=zeo)
To­tal & deep sleep fac­tors vs bed­time

looks like a over­all lin­ear de­cline (later=­worse), but pos­si­bly with a peak some­where look­ing like a qua­drat­ic.

So we’ll try fit­ting qua­drat­ics:

factorModel <- lm(cbind(MR1, MR4) ~ Start.of.Night + I(Start.of.Night^2), data=zeo); summary(factorModel)
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -6.63e+01   7.65e+00   -8.67   <2e-16
# Start.of.Night       9.74e-02   1.07e-02    9.13   <2e-16
# I(Start.of.Night^2) -3.56e-05   3.72e-06   -9.57   <2e-16
#
# Residual standard error: 0.829 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.152,   Adjusted R-squared:  0.15
# F-statistic:  101 on 2 and 1127 DF,  p-value: <2e-16
#
#
# Response MR4 :
#
# Call:
# lm(formula = MR4 ~ Start.of.Night + I(Start.of.Night^2), data = zeo)
#
# Residuals:
#    Min     1Q Median     3Q    Max
# -3.057 -0.651 -0.017  0.600  4.329
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -5.06e+01   8.97e+00   -5.64  2.1e-08
# Start.of.Night       7.23e-02   1.25e-02    5.79  9.3e-09
# I(Start.of.Night^2) -2.58e-05   4.36e-06   -5.92  4.2e-09
#
# Residual standard error: 0.971 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.0384,  Adjusted R-squared:  0.0367
# F-statistic: 22.5 on 2 and 1127 DF,  p-value: 2.57e-10

## on the other hand, if we had ignored the quadratic term, we'd
## get a much worse fit
summary(lm(cbind(MR1, MR4) ~ Start.of.Night, data=zeo))
# Coefficients:
#                 Estimate Std. Error t value Pr(>|t|)
# (Intercept)     6.643744   0.653047    10.2   <2e-16
# Start.of.Night -0.004613   0.000457   -10.1   <2e-16
#
# Residual standard error: 0.861 on 1128 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.0829,  Adjusted R-squared:  0.0821
# F-statistic:  102 on 1 and 1128 DF,  p-value: <2e-16
#
# Response MR4 :
#
# Coefficients:
#                 Estimate Std. Error t value Pr(>|t|)
# (Intercept)     2.337279   0.747401    3.13   0.0018
# Start.of.Night -0.001627   0.000523   -3.11   0.0019
#
# Residual standard error: 0.986 on 1128 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.00851, Adjusted R-squared:  0.00764
# F-statistic: 9.69 on 1 and 1128 DF,  p-value: 0.0019

So we want to use the qua­drat­ic. Given this qua­dratic mod­el, what’s the op­ti­mal bed­time?

estimatedFactorValues <- predict(factorModel, newdata=data.frame(Start.of.Night=1:max(zeo$Start.of.Night, na.rm=TRUE)))
## when is MR1 maximized?
which(estimatedFactorValues[,1] == max(estimatedFactorValues[,1]))
# 1368
1368 / 60
# [1] 22.8
## 10:48 PM seems reasonable
## when is MR3 maximized?
which(estimatedFactorValues[,2] == max(estimatedFactorValues[,2]))
# 1401
## 11:21 PM seems reasonable

## summing the factors isn't quite the average of the two time, but it's close:
combinedFactorSums <- rowSums(estimatedFactorValues)
which(combinedFactorSums == max(combinedFactorSums))
# 1382
## 11:02PM

Maybe us­ing fac­tors was­n’t a good idea? We can try a mul­ti­vari­ate re­gres­sion on the vari­ables di­rect­ly:

quadraticModel <- lm(cbind(ZQ, Total.Z, Time.to.Z, Time.in.Wake, Time.in.REM,
                           Time.in.Light, Time.in.Deep, Awakenings, Morning.Feel)
                       ~ Start.of.Night + I(Start.of.Night^2), data=zeo)
summary(quadraticModel)
# Response ZQ :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -7.84e+02   1.06e+02   -7.38  3.1e-13
# Start.of.Night       1.29e+00   1.48e-01    8.68  < 2e-16
# I(Start.of.Night^2) -4.70e-04   5.16e-05   -9.10  < 2e-16
#
# Residual standard error: 11.5 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.139,   Adjusted R-squared:  0.137
# F-statistic: 90.9 on 2 and 1127 DF,  p-value: <2e-16
#
# Response Total.Z :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -4.48e+03   5.54e+02   -8.08  1.7e-15
# Start.of.Night       7.32e+00   7.73e-01    9.47  < 2e-16
# I(Start.of.Night^2) -2.67e-03   2.69e-04   -9.91  < 2e-16
#
# Residual standard error: 60 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.158,   Adjusted R-squared:  0.156
# F-statistic:  106 on 2 and 1127 DF,  p-value: <2e-16
#
# Response Time.to.Z :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -6.09e+02   1.22e+02   -4.98  7.3e-07
# Start.of.Night       8.43e-01   1.71e-01    4.94  8.8e-07
# I(Start.of.Night^2) -2.81e-04   5.95e-05   -4.73  2.6e-06
#
# Residual standard error: 13.2 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.0431,  Adjusted R-squared:  0.0415
# F-statistic: 25.4 on 2 and 1127 DF,  p-value: 1.61e-11
#
# Response Time.in.Wake :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -1.26e+02   1.76e+02   -0.72     0.47
# Start.of.Night       2.15e-01   2.45e-01    0.88     0.38
# I(Start.of.Night^2) -7.83e-05   8.55e-05   -0.92     0.36
#
# Residual standard error: 19.1 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.00149, Adjusted R-squared:  -0.000283
# F-statistic: 0.84 on 2 and 1127 DF,  p-value: 0.432
#
# Response Time.in.REM :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -1.43e+03   2.69e+02   -5.32  1.2e-07
# Start.of.Night       2.32e+00   3.75e-01    6.19  8.6e-10
# I(Start.of.Night^2) -8.39e-04   1.31e-04   -6.42  2.0e-10
#
# Residual standard error: 29.1 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.0608,  Adjusted R-squared:  0.0592
# F-statistic: 36.5 on 2 and 1127 DF,  p-value: 4.37e-16
#
# Response Time.in.Light :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -2.45e+03   3.43e+02   -7.15  1.5e-12
# Start.of.Night       4.07e+00   4.78e-01    8.50  < 2e-16
# I(Start.of.Night^2) -1.50e-03   1.67e-04   -9.00  < 2e-16
#
# Residual standard error: 37.2 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.164,   Adjusted R-squared:  0.162
# F-statistic:  110 on 2 and 1127 DF,  p-value: <2e-16
#
# Response Time.in.Deep :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -5.88e+02   1.10e+02   -5.34  1.1e-07
# Start.of.Night       9.27e-01   1.53e-01    6.04  2.1e-09
# I(Start.of.Night^2) -3.30e-04   5.35e-05   -6.17  9.5e-10
#
# Residual standard error: 11.9 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.0398,  Adjusted R-squared:  0.0381
# F-statistic: 23.4 on 2 and 1127 DF,  p-value: 1.12e-10
#
# Response Awakenings :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -1.18e+02   2.71e+01   -4.36  1.4e-05
# Start.of.Night       1.68e-01   3.77e-02    4.46  9.0e-06
# I(Start.of.Night^2) -5.67e-05   1.32e-05   -4.31  1.7e-05
#
# Residual standard error: 2.93 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.0274,  Adjusted R-squared:  0.0256
# F-statistic: 15.9 on 2 and 1127 DF,  p-value: 1.62e-07
#
# Response Morning.Feel :
#
# Coefficients:
#                      Estimate Std. Error t value Pr(>|t|)
# (Intercept)         -2.12e+01   7.02e+00   -3.01  0.00266
# Start.of.Night       3.32e-02   9.79e-03    3.39  0.00073
# I(Start.of.Night^2) -1.15e-05   3.41e-06   -3.37  0.00079
#
# Residual standard error: 0.761 on 1127 degrees of freedom
#   (84 observations deleted due to missingness)
# Multiple R-squared:  0.0103,  Adjusted R-squared:  0.0085
# F-statistic: 5.84 on 2 and 1127 DF,  p-value: 0.00301

## Likewise, what's the optimal predicted time?
estimatedValues <- predict(quadraticModel, newdata=data.frame(Start.of.Night=1:max(zeo$Start.of.Night, na.rm=TRUE)))
# but what time is best? we have so many choices of variable to optimize.
# Let's simply sum them all and say bigger is better
# first, we need to negate 'Time.in.Wake', 'Time.to.Z', 'Awakenings',
# as for those, bigger is worse
estimatedValues[,3] <- -estimatedValues[,3] # Time.to.Z
estimatedValues[,4] <- -estimatedValues[,4] # Time.in.Wake
estimatedValues[,8] <- -estimatedValues[,8] # Awakenings
combinedSums <- rowSums(estimatedValues)
which(combinedSums == max(combinedSums))
# 1362

Or 10:42PM, which is al­most iden­ti­cal to the MR1 es­ti­mate. So just like be­fore.

Both ap­proaches sug­gest that I go to bed some­what ear­lier than I do now. This has the same cor­re­la­tion ≠ causal­ity is­sue as the rise-time analy­sis does (per­haps I am es­pe­cially sleepy on the days I go to bed a bit early and so nat­u­rally sleep more), but on the other hand, it’s not sug­gest­ing I go to bed at 7PM or any­thing crazy, so I am more in­clined to take a chance on it.

Rise time for productivity

I no­ticed a claim that for one per­son, ris­ing at 3-5AM (!) seemed to im­prove their days “be­cause the morn­ing hours have no dis­trac­tions” and I won­dered whether there might be any such cor­re­la­tion for my­self, so I took my usual MP daily self­-rat­ing and plot­ted against rise-time that day:

Self­-rat­ing vs rise time, n = 841

It looks like a cu­bic sug­gest­ing one peak around 8:30AM and then a later peak, but that’s based on so lit­tle I ig­nore it. The causal re­la­tion­ship is also un­clear: maybe get­ting up ear­lier re­ally does cause higher MP self­-rat­ings, but per­haps on days I don’t feel like do­ing any­thing I am more likely to sleep in, or some other com­mon cause. The avail­able sam­ples sug­gest that ear­lier than that is worse, pos­si­bly much worse, so I am not in­clined to try out some­thing I ex­pect to make me mis­er­able.

The source code of the graph & analy­sis; pre­pro­cess­ing:

mp <- read.csv("~/selfexperiment/mp.csv", colClasses=c("Date","integer"))
zeo <- read.csv("https://www.gwern.net/docs/zeo/gwern-zeodata.csv")
## we want the date of the day sleep ended, not started, so we ignore the usual 'Sleep.Date' and construct our own 'Date':
zeo$Date <- as.Date(sapply(strsplit(as.character(zeo$Rise.Time), " "), function(x) { x[1] }), format="%m/%d/%Y")
## convert "05/12/2014 06:45" to "06:45"
zeo$Rise.Time <- sapply(strsplit(as.character(zeo$Rise.Time), " "), function(x) { x[2] })
## convert "06:45" to the integer 24300
interval <- function(x) { if (!is.na(x)) { if (grepl(" s",x)) as.integer(sub(" s","",x))
                                           else { y <- unlist(strsplit(x, ":")); as.integer(y[[1]])*60 + as.integer(y[[2]]); }
                                         }
                          else NA
                        }
zeo$Rise.Time <- sapply(zeo$Rise.Time, interval)
## doesn't always work, so delete missing data:
zeo <- zeo[!is.na(zeo$Date),]

## correct for the switch to new unencrypted firmware in March 2013;
## I don't know why the new firmware changed things; adjustment of 226 minutes was estimated using:
# library(changepoint); cpt.mean(na.omit(zeo$Rise.Time)); '$mean [1] 566.7 340.2';  566.7 - 340.2 = 226
zeo[(zeo$Date >= as.Date("2013-03-11")),]$Rise.Time  <-
 (zeo[(zeo$Date >= as.Date("2013-03-11")),]$Rise.Time + 226) %% (24*60)

allData <- merge(mp,zeo)
morning <- data.frame(MP=allData$MP, Rise.Time=allData$Rise.Time)
morning$Rise.Time.Hour <- morning$Rise.Time / 60
write.csv(morning, file="morning.csv", row.names=FALSE)

Graph­ing and fit­ting:

morning <- read.csv("https://www.gwern.net/docs/zeo/2014-07-26-risetime-mp.csv")
library(ggplot2)
ggplot(data = morning, aes(x=Rise.Time.Hour, y=jitter(MP, factor=0.2)))
 + xlab("Wake time (24H)")
 + ylab("Mood/productivity self-rating (2/3/4)")
 + geom_point(size=I(4))
 ## cross-validation suggests 0.8397 but looks identical to auto-LOESS span choice
 + stat_smooth(span=0.8397)

## looks 100% like a cubic function
linear <- lm(MP ~ Rise.Time,         data=morning)
cubic  <- lm(MP ~ poly(Rise.Time,3), data=morning)
anova(linear,cubic)
# Model 1: MP ~ Rise.Time
# Model 2: MP ~ poly(Rise.Time, 3)
#   Res.Df RSS Df Sum of Sq    F Pr(>F)
# 1    839 442
# 2    837 437  2      5.36 5.14 0.0061
AIC(linear,cubic)
#        df  AIC
# linear  3 1852
# cubic   5 1846
summary(cubic)
# ...Coefficients:
#                     Estimate Std. Error t value Pr(>|t|)
# (Intercept)           3.0571     0.0249  122.70   <2e-16
# poly(Rise.Time, 3)1  -0.9627     0.7225   -1.33    0.183
# poly(Rise.Time, 3)2  -1.4818     0.7225   -2.05    0.041
# poly(Rise.Time, 3)3   1.7795     0.7225    2.46    0.014
#
# Residual standard error: 0.723 on 837 degrees of freedom
# Multiple R-squared:  0.0142,    Adjusted R-squared:  0.0107
# F-statistic: 4.02 on 3 and 837 DF,  p-value: 0.00749

# plot(morning$Rise.Time,morning$MP); points(morning$Rise.Time,fitted(cubic),pch=19)
which(fitted(cubic) == max(fitted(cubic))) / 60
#  516   631   762
# 8.60 10.52 12.70

Magnesium citrate

Re-an­a­lyz­ing data from a mag­ne­sium self­-ex­per­i­ment, I find both pos­i­tive and neg­a­tive effects of the mag­ne­sium on my sleep. It’s not clear what the net effect is.

I be­came after not­ing a pos­si­ble effect on my pro­duc­tiv­ity from TruBrain (which among other things in­cluded a mag­ne­sium tablet), and then a clear cor­re­la­tion from some mag­ne­sium l-thre­onate. I’d also long heard of mag­ne­sium help­ing sleep, and was cu­ri­ous about that too. So I be­gan a large (~207 days) RCT try­ing out 136mg then 800mg of el­e­men­tal mag­ne­sium per day in late 2013—early 2014. (This was not a large enough ex­per­i­ment to de­fin­i­tively an­swer ques­tions about both pro­duc­tiv­ity and sleep, but since I have all the data on hand, I thought I’d look.)

The re­sults of the main were sur­pris­ing: it seemed that the mag­ne­sium caused an ini­tial large boost to my pro­duc­tiv­i­ty, but the boost be­gan to fade and after 20 days or so, the effect be­came neg­a­tive, and the pe­riod with the larger dose had a worse effect, sug­gest­ing a cu­mu­la­tive over­dose.

With the differ­ing effect of the doses in mind, I looked at the effect on my sleep da­ta.

Analysis

Prep:

magnesium <- read.csv("https://www.gwern.net/docs/nootropics/2013-2014-magnesium.csv")
magnesium$Date <- as.Date(magnesium$Date)

zeo <- read.csv("https://www.gwern.net/docs/zeo/gwern-zeodata.csv")
zeo$Sleep.Date <- as.Date(zeo$Sleep.Date, format="%m/%d/%Y")
zeo$Date <- zeo$Sleep.Date
rm(zeo$Sleep.Date)
# create a equally-weighted index of bad sleep: a z-score of the 3 bad things
zeo$Disturbance <- scale(zeo$Time.to.Z) + scale(zeo$Awakenings) + scale(zeo$Time.in.Wake)

magnesiumSleep <- merge(zeo, magnesium)
write.csv(magnesiumSleep, file="2014-07-27-magnesium-sleep.csv", row.names=FALSE)

(I then hand-edited the CSV to delete un­used column­s.)

Graph­ing Dis­tur­bance:

Sleep dis­tur­bance over time, col­ored by mag­ne­sium dose, with LOESS-smoothed trend-lines
magnesiumSleep <- read.csv("https://www.gwern.net/docs/zeo/2014-07-27-magnesium-sleep.csv")
magnesiumSleep$Date <- as.Date(magnesiumSleep$Date)
## historical baseline:
magnesiumSleep[is.na(magnesiumSleep$Magnesium.citrate),]$Magnesium.citrate <- -1
library(ggplot2)
ggplot(data = magnesiumSleep, aes(x=Date, y=Disturbance, col=as.factor(magnesiumSleep$Magnesium.citrate))) +
 ylab("Disturbance z-score (lower=better)") +
 geom_point(size=I(4)) +
 stat_smooth() +
 scale_colour_manual(values=c("gray49", "grey35", "red1", "red2" ),
                     name = "Magnesium")

Analy­sis (first dis­tur­bances, then all vari­ables):

magnesiumSleep <- read.csv("https://www.gwern.net/docs/zeo/2014-07-27-magnesium-sleep.csv")
l0 <- lm(Disturbance ~ as.factor(Magnesium.citrate), data=magnesiumSleep)
summary(l0)
# ...Coefficients:
#                                   Estimate Std. Error  t value  Pr(>|t|)
# (Intercept)                     -0.5020571  0.1862795 -2.69518 0.0076218
# as.factor(Magnesium.citrate)136 -0.0566556  0.3101388 -0.18268 0.8552318
# as.factor(Magnesium.citrate)800 -0.5394708  0.3259212 -1.65522 0.0994178

So it seems that mag­ne­sium cit­rate may de­crease sleep prob­lems.

l1 <- lm(cbind(ZQ, Total.Z, Time.to.Z, Time.in.Wake, Time.in.REM, Time.in.Light,
               Time.in.Deep, Awakenings, Morning.Feel)
               ~ as.factor(Magnesium.citrate),
         data=magnesiumSleep)
summary(l1)
# Response ZQ : ...Coefficients:
#                                 Estimate Std. Error  t value Pr(>|t|)
# (Intercept)                     95.85149    1.29336 74.11065  < 2e-16
# as.factor(Magnesium.citrate)136 -3.27254    2.15332 -1.51976  0.13012
# as.factor(Magnesium.citrate)800  1.49545    2.26290  0.66086  0.50945
#
# Response Total.Z : ...Coefficients:
#                                  Estimate Std. Error  t value Pr(>|t|)
# (Intercept)                     536.35644    6.59166 81.36898  < 2e-16
# as.factor(Magnesium.citrate)136 -27.37398   10.97453 -2.49432 0.013414
# as.factor(Magnesium.citrate)800  15.86805   11.53300  1.37588 0.170367
#
# Response Time.to.Z : ...Coefficients:
#                                 Estimate Std. Error  t value Pr(>|t|)
# (Intercept)                     12.59406    1.24108 10.14766  < 2e-16
# as.factor(Magnesium.citrate)136  4.26559    2.06629  2.06437 0.040247
# as.factor(Magnesium.citrate)800 -2.43079    2.17144 -1.11944 0.264269
#
# Response Time.in.Wake : ...Coefficients:
#                                 Estimate Std. Error  t value Pr(>|t|)
# (Intercept)                     24.09901    1.87720 12.83776  < 2e-16
# as.factor(Magnesium.citrate)136 -3.66041    3.12537 -1.17119  0.24289
# as.factor(Magnesium.citrate)800 -4.16023    3.28441 -1.26666  0.20672
#
# Response Time.in.REM : ...Coefficients:
#                                  Estimate Std. Error  t value Pr(>|t|)
# (Intercept)                     171.45545    2.99387 57.26889  < 2e-16
# as.factor(Magnesium.citrate)136  -6.45545    4.98452 -1.29510  0.19675
# as.factor(Magnesium.citrate)800   2.27925    5.23818  0.43512  0.66393
#
# Response Time.in.Light : ...Coefficients:
#                                  Estimate Std. Error  t value   Pr(>|t|)
# (Intercept)                     304.54455    4.08746 74.50709 < 2.22e-16
# as.factor(Magnesium.citrate)136 -23.33403    6.80525 -3.42883 0.00073338
# as.factor(Magnesium.citrate)800  20.51667    7.15156  2.86884 0.00455323
#
# Response Time.in.Deep : ...Coefficients:
#                                 Estimate Std. Error  t value Pr(>|t|)
# (Intercept)                     60.88119    1.20888 50.36152  < 2e-16
# as.factor(Magnesium.citrate)136  2.48723    2.01268  1.23578  0.21796
# as.factor(Magnesium.citrate)800 -6.81996    2.11510 -3.22441  0.00147
#
# Response Awakenings : ...Coefficients:
#                                  Estimate Std. Error  t value Pr(>|t|)
# (Intercept)                      6.039604   0.238675 25.30475  < 2e-16
# as.factor(Magnesium.citrate)136 -0.548376   0.397372 -1.38001  0.16910
# as.factor(Magnesium.citrate)800 -0.427359   0.417594 -1.02338  0.30734
#
# Response Morning.Feel : ...Coefficients:
#                                   Estimate Std. Error  t value Pr(>|t|)
# (Intercept)                      2.7227723  0.0762575 35.70497  < 2e-16
# as.factor(Magnesium.citrate)136  0.1193330  0.1269620  0.93991  0.34837
# as.factor(Magnesium.citrate)800 -0.1513437  0.1334229 -1.13432  0.25799
l2 <- lm(cbind(ZQ, Total.Z, Time.to.Z, Time.in.Wake, Time.in.REM, Time.in.Light,
               Time.in.Deep, Awakenings, Morning.Feel) ~ Magnesium.citrate,
         data=magnesiumSleep)
summary(manova(l1))
#                              Df    Pillai approx F num Df den Df     Pr(>F)
# as.factor(Magnesium.citrate)  2 0.3265357 4.271083     18    394 2.3902e-08
# Residuals                    204
summary(manova(l2))
#                              Df    Pillai approx F num Df den Df     Pr(>F)
# Magnesium.citrate            1 0.1815233  4.85456      9    197  7.1454e-06
# Residuals         205
which(p.adjust(c(0.3483,0.2579,0.1752,0.1301,0.5094,0.3344,0.0134,0.1703,0.0632,0.1967,
                 0.6639,0.4895,0.0007,0.0045,0.0005,0.2179,0.0014,0.0004,0.0402,0.2642,
                 0.1262,0.2428,0.2067,0.2673,0.1691,0.3073,0.4144),
               method="BH")
      < 0.05)
# [1] 13 14 15 17 18

A ta­ble sum­ma­riz­ing the re­sults by dose (‘all’ is the net effect from the non-fac­tor ver­sion):

Vari­able Dose (mg) Coef p Effect
Morning.Feel 136 0.11933 0.3483 bet­ter
Morning.Feel 800 -0.15134 0.2579 worse
Morning.Feel all -0.00022 0.1752 worse
ZQ 136 -3.27254 0.1301 worse
ZQ 800 1.49545 0.5094 bet­ter
ZQ all 0.00270 0.3344 bet­ter
Total.Z 136 -27.3739 0.0134 worse
Total.Z 800 15.8680 0.1703 bet­ter
Total.Z all 0.02698 0.0632 bet­ter
Time.in.REM 136 -6.45545 0.1967 worse
Time.in.REM 800 2.27925 0.6639 bet­ter
Time.in.REM all 0.00447 0.4895 bet­ter
Time.in.Light 136 -23.3340 0.0007 worse
Time.in.Light 800 20.5166 0.0045 bet­ter
Time.in.Light all 0.03202 0.0005 bet­ter
Time.in.Deep 136 2.48723 0.2179 bet­ter
Time.in.Deep 800 -6.81996 0.0014 worse
Time.in.Deep all -0.00939 0.0004 worse
Time.to.Z 136 4.26559 0.0402 worse
Time.to.Z 800 -2.43079 0.2642 bet­ter
Time.to.Z all -0.00415 0.1262 bet­ter
Time.in.Wake 136 -3.66041 0.2428 bet­ter
Time.in.Wake 800 -4.16023 0.2067 bet­ter
Time.in.Wake all -0.00449 0.2673 bet­ter
Awakenings 136 -0.54837 0.1691 bet­ter
Awakenings 800 -0.42735 0.3073 bet­ter
Awakenings all -0.00042 0.4144 bet­ter

For the low dose, 4⁄9 were bet­ter; for the high dose, 7⁄9 were bet­ter. Ad­just­ing for mul­ti­ple-com­par­i­son at p < 0.05: the sur­viv­ing effects are:

Vari­able Dose (mg) Coef p Effect
Time.in.Light 136 -23.3340 0.0007 worse
Time.in.Light 800 20.5166 0.0045 bet­ter
Time.in.Light all 0.03202 0.0005 bet­ter
Time.in.Deep 800 -6.81996 0.0014 worse
Time.in.Deep all -0.00939 0.0004 worse

Redshift/f.lux

I ran a ran­dom­ized ex­per­i­ment with a free pro­gram (Red­shift) which red­dens screens at night to avoid tam­per­ing with mela­tonin se­cre­tion & the sleep from 2012-2013, mea­sur­ing sleep changes with my Zeo. With 533 days of data, the main re­sult is that Red­shift causes me to go to sleep half an hour ear­lier but oth­er­wise does not im­prove sleep qual­i­ty.

Main ar­ti­cle: .

Lithium

As part of a self­-ex­per­i­ment in­volv­ing low doses of lithium oro­tate blinded & ran­dom­ized in 7-day paired blocks, I checked for effects on Zeo sleep data dur­ing the self­-ex­per­i­ment. No vari­ables reached sta­tis­ti­cal-sig­nifi­cance in that ex­per­i­ment, in­clud­ing the sleep ones.

Main ar­ti­cle: Nootrop­ics page.

ZMA

I ran a blinded ran­dom­ized self­-ex­per­i­ment of 2.5g nightly ZMA pow­der effect on Zeo-recorded sleep data dur­ing March-Oc­to­ber 2017 (n = 127). The lin­ear model and SEM model show no sta­tis­ti­cal­ly-sig­nifi­cant effects or high pos­te­rior prob­a­bil­ity of ben­e­fits, al­though all point-es­ti­mates were in the di­rec­tion of ben­e­fits. Data qual­ity is­sues re­duced the avail­able dataset, ren­der­ing the ex­per­i­ment par­tic­u­larly un­der­pow­ered and the re­sults more in­con­clu­sive. I de­cided to not con­tinue use of ZMA after run­ning out; ZMA may help my sleep but I need to im­prove data qual­ity be­fore at­tempt­ing any fur­ther sleep self­-ex­per­i­ments on it.

Main ar­ti­cle: .

Hammock

Ever since I was a lit­tle kid watch­ing on & then , I had one burn­ing ques­tion about the an­tics of the cast and their is­land idyll/prison: what was it like to sleep in a , any­way‽ Skip­per and Gilli­gan slept in ham­mocks all the time, but the show stub­bornly re­fused to go into any de­tails about the na­ture of ham­mock sleep­ing. Was it bet­ter than beds? Worse? Hot­ter? Cold­er? Did it hurt the neck?

While my beds usu­ally are good as far as beds go, I’ve never been com­pletely happy with them: as a side sleep­er, it’s all too easy for me to wake up with a par­a­lyzed arm or a crick in the neck. (It is ir­ri­tat­ing to like a sheet of bub­ble-wrap in the morn­ing.) And any­time I have to move a bed, I can’t help won­der­ing if beds re­ally have to be as bulky and heavy as they are. But it seemed to me that a ham­mock, en­furl­ing & en­clos­ing one as they do, might re­solve that prob­lem. What does the sci­en­tific lit­er­a­ture say about this? The topic seems to be al­most com­pletely un­re­searched. For ex­am­ple, al­most every hit for the word “ham­mock” on Pubmed is due to the au­thor B.D. Ham­mock. Google Scholar does a lit­tle bit bet­ter, as the first few pages of hits, be­sides turn­ing up B.D. Ham­mock again, points at a short ex­per­i­ment “Rock­ing syn­chro­nizes brain waves dur­ing a short nap” which com­pared 12 men nap­ping on a sway­ing bed, and sug­gests some lit­er­a­ture on the effect of spinal an­gle on sleep. This si­lence is a lit­tle sur­pris­ing, con­sider that a non­triv­ial frac­tion of hu­man­ity sleeps in ham­mocks or ham­mock­-like things—y­ou’d think navies, at the very least, would be in­ter­ested in the sub­ject of whether ham­mocks were bet­ter than bed­s—but so it goes.

The ques­tions, at ir­reg­u­lar in­ter­vals over the years, con­tin­ued to prey on my mind, oc­ca­sion­ally prompted by men­tion of sailors. Of course I pe­ri­od­i­cally would run into lawn/garden ham­mocks, but those wretched con­trap­tions were no an­swer: the cord made for an un­com­fort­able rest, and the enor­mous spreader bars lead to se­vere in­sta­bil­ity (although they made for great pranks). Fi­nally in 2014, it dawned on me that I had ac­cess to an un­used stand for a lawn ham­mock; I had room to set it up in my bed­room; and from idly brows­ing Ama­zon, I knew I could get a ham­mock for un­der $50, which seemed rea­son­able for an ex­per­i­ment. Why cunc­tate and re­pine fur­ther? I could­n’t think of any rea­son why not, so after some more brows­ing, the cheap­est ham­mock seemed to be the Army Green Ul­tra Light Ham­mocks with Tree Strap for $22.50, and I or­dered it in Sep­tem­ber.

I was a lit­tle sur­prised how small and light­weight the hunter-green ny­lon ham­mock turns out to be (the whole pack­age fits in a padded en­ve­lope mailer and weighs un­der a pound), and quickly set it up.

The frame creaked alarm­ingly un­der my 200 pounds, but it held up. It feels very differ­ent from a bed, more like a slide at an amuse­ment park in how one is lay­ing back into a tube. Lay­ing in a ham­mock is also much more sta­ble than a lawn ham­mock, at least once you get into it suc­cess­ful­ly. An­other is­sue was the grad­ual dis­com­fort of hav­ing my feet el­e­vated due to the V-shape of the ham­mock as it sagged un­der my weight. This seemed mostly re­solved by tight­en­ing the ropes and lay­ing at more of a di­ag­o­nal.

I found it easy to take a brief nap or rest in it, but it felt like it was squeez­ing my shoul­ders into my chest and my first at­tempt to sleep overnight failed. The sec­ond & third nights went bet­ter, but still not as good as the bed.

The prob­lem seems to be the arms/chest squeez­ing, caused by noth­ing ‘push­ing apart’ the two walls of the ham­mock at the top. The Wikipedia ar­ti­cle on ham­mocks men­tions sailors us­ing a “spreader bar”, which sounds like a so­lu­tion to my prob­lem. So I need to find a piece of wood and tweak it into a suit­able form, while avoid­ing any sharp cor­ners which might cut the ny­lon ma­te­r­ial of the ham­mock.

My first ap­proach was to take a short nar­row plank about the width of my shoul­ders and saw V-shaped notches in each end, then bevel and sand the edges of the notches so they would­n’t fray the ny­lon cords. This was easy enough, and then one sim­ply sticks it in be­tween the two cords on one end. It turns out that the plank slips out very eas­i­ly, and the pres­sure causes it to slide up halfway to form a di­a­mond con­fig­u­ra­tion, which does­n’t ac­com­plish the goal of spread­ing the ham­mock, since the ham­mock is still dan­gling from a point where one wants a per­pen­dic­u­lar line. I could force it down the strings to­wards the end of the ham­mock, spread­ing out the ham­mock, but the in­stant any pres­sure was placed on the sys­tem (such as by get­ting in), the plank would ei­ther col­lapse or re­vert to a di­a­mond+­point.

So if it kept slip­ping, I’d force it to stay. This time, I drilled two holes through op­po­site ends of the plan, fed the two ends of the ny­lon cord through the two holes, drew the cord as tight as pos­si­ble, then put a knot behind/above each hole in the plank. Now they could­n’t slip be­cause the knots would not pass through the drilled holes, and I had left no slack, so when weight was put, a point was not formed but more of a tri­an­gle. (I did wind up adding ex­tra knots as slack slowly grew.)

That worked. Now I could lie back and my chest was not be­ing com­pressed. Com­bined with an in­ter­me­di­ate loose­ness of hang (it turns out tighter is not al­ways bet­ter once the squeeze prob­lem is re­solved and you’re sleep­ing slightly di­ag­o­nal­ly), the ham­mock was now very pleas­ant for nap­ping, and pretty good for sleep­ing.

I gave sleep­ing in ham­mock a few more nights of try­ing, and ran into a new prob­lem: the same fea­ture that makes ham­mocks so good for hot cli­mates also makes them prob­lem­atic in the win­ter, ie you’re ex­posed to the air. The chill woke me up early in the morn­ing twice, even after I added in a fuzzy blan­ket to sleep on top of. Prob­a­bly I could fix this by adding a thicker blan­ket un­der­neath, but I de­cided to pack up the ham­mock (which takes very lit­tle space) and retry again in spring when my room starts get­ting warm again.

In May 2015, after it be­came warm enough again that I needed air con­di­tion­ing on at night, I set the ham­mock back up and gave it an­other try. After 3 failed nights, I gave up: the cold­ness was great, but no po­si­tion or ten­sion seemed to give my shoul­ders enough room to move and let me roll over. I con­cluded that I’m too used to sleep­ing in a bed to adapt to a ham­mock in the ab­sence of trop­i­cal in­cen­tives.

So I moved the ham­mock out­side—what­ever its prob­lems for sleep­ing in, it’s great for nap­ping and in­fi­nitely more com­fort­able than the com­mon rope lawn ham­mock.

A par­tial so­lu­tion to the cold is foam earplugs; an­other in­ter­est­ing pos­si­bil­ity is a , a hol­low pil­low or frame­work which re­duces the need for a thick blanket/pillow to clutch and sup­port one while lay­ing on one’s side. (I don’t know what to do about the neck is­sues. Prob­a­bly just put up with it as I al­ways have.) The hol­low kind don’t seem eas­ily avail­able with­out or­der­ing from sketchy sites, so I took an old com­forter blan­ket, rolled it up roughly the width of my stom­ach to my chin, and tied it tightly into a bun­dle with ny­lon line, which works for now.

In progress

Some­one sug­gested that in­stead of run­ning ex­per­i­ments se­ri­al­ly, with lim­ited sam­ple sizes (be­cause I am im­pa­tient to try the next in­ter­est­ing sug­ges­tion), I could in­stead take a step up in sta­tis­ti­cal so­phis­ti­ca­tion and use a de­sign: use mul­ti­ple ex­per­i­men­tal in­ter­ven­tions si­mul­ta­ne­ously for a much larger sam­ple size, and then run analy­ses rather than sim­pler two-sam­ple t-tests. No less than praises mul­ti­fac­to­r­ial ex­per­i­ments as be­ing more effi­cient: squeez­ing more data out of a given sam­ple. Hence, I thought a crazy thought: my lithium ex­per­i­ment was go­ing to run for ~360 days, and so I kept putting it off. But what if I ran mul­ti­ple ex­per­i­ments for 360 days? If I had 4 or 5, then by the end of the year, I would have 5 re­sults to show, and I would have the sta­tis­ti­cal equiv­a­lent of more than n = 72 (360⁄5) for each ex­per­i­ment. Win-win.

Clas­sic mul­ti­fac­to­r­ial de­signs arrange to have every pos­si­ble com­bi­na­tion of the n ex­per­i­ments hap­pen on some day or other (such an arrange­ment is called a ). How­ev­er, with 5 ex­per­i­ments, each of which has 2 states (on and off), that means I only have 25=32 pos­si­ble arrange­ments, all of which ought to be cov­ered over 360 days, ter­mi­nat­ing in March 2013. (It ac­tu­ally will take much longer, as I paused the lithium sub­-ex­per­i­ment for sev­eral months to run the X self­-ex­per­i­ment.) So I will be lazy and will in­de­pen­dently ran­dom­ize each ex­per­i­ment.

As it wound up, I had bit­ten off too much in try­ing to run in­ter­con­nected ex­per­i­ments: while the Red­shift ex­per­i­ment ran with­out too much prob­lem, an un­ex­pected and abrupt move in July 2012 com­pletely dis­rupted my daily rou­tine and I was un­able to main­tain my habit of ran­dom­iz­ing my med­i­ta­tion ses­sions. So I will be an­a­lyz­ing the ex­per­i­ments sep­a­rate­ly.

Push-ups

Rather than dumb­bells (might be hard to find in the dark), I de­cided to try out push-ups since I rou­tinely do 25 push-ups after show­er­ing and it ought to be men­tally easy to shift those push-ups to before/after bed­time. As be­fore, al­ter­nate-day, but with a twist: on-days, I do the push-ups im­me­di­ately be­fore go­ing to bed, but off-days en­tail im­me­di­ately upon awak­en­ing. (I don’t ex­er­cise enough in gen­er­al.) I be­gan 2011-09-21.

I in­ter­rupted the ex­per­i­ment for a long pe­riod to run the vi­t­a­min D ex­per­i­ments; when I re­sumed on 2012-05-08, I de­cided to avoid the al­ter­nate-day pro­ce­dure and in­stead ran­dom­ize morn­ing vs evening push ups with a coin. Non-blind­ed.

On 2012-11-13, I de­cided I was suffi­ciently con­vinced that ex­er­cise im­me­di­ately be­fore bed was dam­ag­ing my sleep la­tency that I did­n’t want to con­tinue to pay the price of worse sleep, and I dis­con­tin­ued this vari­able. Hope­fully the pre­vi­ous data will be suffi­cient to con­firm or dis­con­firm any effect.

Meditation

The prac­tice of med­i­ta­tion can be time-in­ten­sive; a claimed anec­do­tal ben­e­fit is that one sleeps less and so the time re­quire­ment is­n’t as bad as it may seem.

Med­i­ta­tion has been linked with sleep changes mul­ti­ple times; see . In par­tic­u­lar, found a cor­re­la­tion be­tween long med­i­ta­tion and re­duced sleep need. The gen­eral link seems plau­si­ble—that de­lib­er­ate re­lax­ation may re­duce the need for an­other kind of re­lax­ation (although I doubt med­i­ta­tion is go­ing as far as re­duc­ing synap­tic weights as the “synap­tic home­osta­sis” hy­poth­e­sis pre­dicts which I dis­cuss in )—but I can think of at least 2 plau­si­ble ways the cor­re­la­tion would not be cau­sa­tion (1. those with less sleep need can afford to spend time on med­i­ta­tion; 2. med­i­ta­tion is par­tially sleep so there’s no cor­re­la­tion or cau­sa­tion to ex­plain).

Ran­dom­ized on a daily ba­sis: ei­ther 20-3015 min­utes of med­i­ta­tion or none. (I am not sure what a good placebo would be so I will omit it.) Non-blind­ed. My med­i­ta­tion is noth­ing fan­cy: sim­ple breath-fol­low­ing (based on early chap­ters of Mind­ful­ness in Plain Eng­lish).

Plau­si­bly, any de­crease in sleep need could be due to long-term changes in the brain it­self, as med­i­ta­tion is ar­eas like the . Kaul et al 2010 above did not ran­dom­ize the long-term med­i­ta­tors’ use of med­i­ta­tion or ap­par­ently in­ves­ti­gate whether sleep time av­er­ages cor­re­lated with med­i­ta­tion. If the changes are long-term, then there will be rel­a­tively lit­tle vari­a­tion dur­ing the 360 days and in­stead a grad­ual trend of less sleep. If no clear effect shows up in the analy­sis, I’ll try a be­fore-after com­par­ison: com­pare n days be­fore the ex­per­i­ment started to n days after the ex­per­i­ment and see if there is a differ­ence in the av­er­ages.

Power calculation

Kaul et al 2010 de­scribes the long-term med­i­ta­tors as spend­ing “2-3 hrs/day” in med­i­ta­tion. (Their ex­per­i­ment used novices who med­i­tated for 1 hour.) If med­i­ta­tion in­deed re­duces sleep time, but I am med­i­tat­ing for only 1⁄3 an hour, can I de­tect any effect?

The differ­ence be­tween the long-term med­i­ta­tors and their nor­mal In­dian coun­ter­parts was 5.2 hours of sleep per day ver­sus 7.8. As­sume the worst case of 3 hours, this im­plies that med­i­ta­tion is in­deed a net cost in time (8.2 > 7.8), but also that each hour of med­i­ta­tion is equiv­a­lent to al­most an hour of sleep (). So at that con­ver­sion rate, 20 min­utes of med­i­ta­tion trans­lates to 17.32 min­utes less sleep. We will steal code and data from the pre­vi­ous Red­shift power cal­cu­la­tion: as­sume the same con­trol sleep, same stan­dard de­vi­a­tion, and sub­tract 17.32 from the con­trol to get the true mean of the in­ter­ven­tion

# install.packages("pwr")
library(pwr)
pwr.t.test(d=(456.4783 - (456.4783 - 17.32))/131.4656,power=0.5,type="paired",alternative="greater")

     Paired t test power calculation
              n = 157.237

# we're getting 360 days or 180 pairs; let's ask for more than 50-50 power;
# what does n = 180 buy us? Not much!
pwr.t.test(d=(456.4783 - (456.4783 - 17.32))/131.4656,power=0.55,type="paired",alternative="greater")

     Paired t test power calculation

              n = 181.9631

# how many pairs *do* we need for good results?
pwr.t.test(d=(456.4783 - (456.4783 - 17.32))/131.4656,power=0.75,
  sig.level=0.01,type="paired",alternative="greater")

     Paired t test power calculation
              n = 521.5252

pwr.t.test(d=(456.4783 - (456.4783 - 17.32))/131.4656,power=0.56
 sig.level=0.01,type="paired",alternative="greater")

     Paired t test power calculation
              n = 356.2923

This is dis­cour­ag­ing. With 180 pairs, we only have a 55% chance of see­ing any­thing at p = 0.05? That’s aw­ful! But there’s no point in look­ing fur­ther into this power cal­cu­la­tion: I’m not go­ing to be do­ing a paired t-test, after all, but some sort of ANOVA, and I’m not sure how much power the in­ter­fer­ing ex­per­i­ments cost me. The first cal­cu­la­tion is the most im­por­tant: to sat­isfy some­what rea­son­able cri­te­ria, I need less than half the data I will get, which ought to be an ad­e­quate mar­gin of safe­ty.

VoI

For back­ground on “value of in­for­ma­tion” cal­cu­la­tions, see the first cal­cu­la­tion.

I find med­i­ta­tion use­ful when I am screw­ing around and can’t fo­cus on any­thing, but I don’t med­i­tate as much as I might be­cause I lose half an hour. Hence, I am in­ter­ested in the sug­ges­tion that med­i­ta­tion may not be as ex­pen­sive as it seems be­cause it re­duces sleep need to some de­gree: if for every two min­utes I med­i­tate, I need one less minute of sleep, that halves the time cost—I spend 30 min­utes med­i­tat­ing, gain back 15 min­utes from sleep, for a net time loss of 15 min­utes. So if I med­i­tate reg­u­larly but there is no sub­sti­tu­tion, I lose out on 15 min­utes a day. Fig­ure I skip every 2 days, that’s a to­tal lost time of hours a year or $427 at min­i­mum wage. I find the the­ory some­what plau­si­ble (60%), and my year-long ex­per­i­ment has roughly a 55% chance of de­tect­ing the effect size (es­ti­mated based on the sleep re­duc­tion in a In­dian sam­ple of med­i­ta­tors). So . The ex­per­i­ment it­self is un­usu­ally time-in­ten­sive, since it in­volve ~180 ses­sions of med­i­ta­tion, which if I am “over­pay­ing” trans­lates to 45 hours () of wasted time or $315. But even in­clud­ing the de­sign and analy­sis, that’s less than the cal­cu­lated value of in­for­ma­tion.

This ex­am­ple demon­strates that drugs aren’t the only ex­pen­sive things for which you should do ex­ten­sive test­ing.

Masturbation

Or­gasm has been linked oc­ca­sion­ally with changes in sleep la­ten­cy, al­though one 1985 ex­per­i­men­tal study found no changes. cov­ers some in­con­clu­sive fol­lowup stud­ies on re­lated mat­ters like whether arousal or brief view­ing of porn in­ter­feres with sleep (no).

Ran­dom­ized on a daily ba­sis be­fore go­ing to bed; no place­bo, but ab­sti­nence. Non-blind­ed. Since the the­ory has al­ways been about a very short­-term effect, there’s no need to worry about day­time ac­tiv­i­ties. (This would only mat­ter if I were test­ing some­thing like the folk wis­dom that mas­tur­ba­tion re­duces testos­terone lev­els, where the tim­ing is not as im­por­tant as the quan­ti­ty.)

Treadmill / walking desk

In June 2012, I ac­quire a free tread­mill. I be­came in­ter­ested in us­ing it as a tread­mill desk, rea­son­ing that it was an easy way to get more ex­er­cise. My ini­tial days of use led me to sus­pect that the tread­mill desk’s ex­er­cise might come at the ex­pense of some con­cen­tra­tion or pro­duc­tiv­i­ty. While I was able to quickly rule out any no­tice­able neg­a­tive cor­re­la­tion of tread­mill use with typ­ing speed/accuracy, that still leaves other pos­si­ble neg­a­tive effects.

Power

Start­ing it part way, I lose po­ten­tial pow­er: there are only ~330 days left. The effect of most in­ter­est is pro­duc­tiv­i­ty, where I ex­pect a neg­a­tive effect, but we also need a more strin­gent p-value since we’re look­ing at so many vari­ables; so 330 sam­ples gives a floor on de­tectable effect size of

pwr.t.test(n=(330/2),power=0.75,sig.level=0.01,type="paired",alternative="less")

     Paired t test power calculation

              n = 165
              d = -0.2355713

Not that great. We may wind up be­ing able to con­clude lit­tle about the effect on pro­duc­tiv­i­ty; sim­i­larly for sleep­—the effect would have to be com­pa­ra­ble to vi­t­a­min D or mela­tonin to be de­tectable.

VoI

The VoI cal­cu­la­tion for this in­ves­ti­ga­tion is very diffi­cult: it may im­prove sleep and it may im­prove or worsen pro­duc­tiv­ity but re­gard­less is good for very valu­able ex­er­cise, scrap­ping the prac­tice has im­me­di­ate cash val­ue, but none of this is cer­tain and there are few guides from ex­per­i­men­tal stud­ies.

If it turns out the tread­mill is not help­ful, I can prob­a­bly sell it for ~$100 based on prices listed in Craigslist. (I wound up sell­ing it for $70.) If it’s help­ful, I gain con­sid­er­able ex­er­cise (1MPH im­plies an 8-hour day could be 8 miles of ex­er­cise a day!) with the re­lated ben­e­fits. I strongly sus­pect that this much ex­er­cise would in­flu­ence my sleep for the bet­ter, but I’m not sure the tread­mill desk re­ally does al­low for pro­duc­tiv­ity like reg­u­lar sit­ting does. If it does re­duce pro­duc­tiv­ity some­what but I oth­er­wise can adapt, it’s prob­a­bly still a net gain be­cause of the ex­tra ex­er­cise. How­ev­er, a smal­l­-to-medium de­crease—let’s say an effect size of d<=-0.4—­would be enough to cause me to scrap the tread­mill. This is highly un­like­ly. The large sam­ple gives a very good shot at de­tect­ing it. Run­ning the ex­per­i­ment is rel­a­tively easy since the tread­mill desk can be set up and put away in ~5 min­utes. With­out run­ning num­bers on this one, my best guess is that the VoI is neg­a­tive; so this is an­other ex­per­i­ment I am do­ing be­cause it is in­ter­est­ing and other peo­ple may find it in­ter­est­ing, rather than be­cause run­ning the ex­per­i­ment makes eco­nomic sense.

Morning caffeine pills

One trick to com­bat morn­ing slug­gish­ness is to get caffeine ex­tra-early by us­ing caffeine pills shortly be­fore or upon try­ing to get up. From 2013-2014 I ran a blinded & place­bo-con­trolled ran­dom­ized ex­per­i­ment mea­sur­ing the effect of caffeine pills in the morn­ing upon awak­en­ing time and daily pro­duc­tiv­i­ty. The es­ti­mated effect is small and the pos­te­rior prob­a­bil­ity rel­a­tively low, but a de­ci­sion analy­sis sug­gests that since caffeine pills are so cheap, it would be worth­while to con­duct an­other ex­per­i­ment.

Main ar­ti­cle: .

CO2/Bedroom ventilation experiment

Some psy­chol­ogy stud­ies find that CO2 im­pairs cog­ni­tion, and some sleep stud­ies find that bet­ter ven­ti­la­tion may im­prove sleep qual­i­ty. Use of a Ne­tatmo air qual­ity sen­sor re­veals that clos­ing my bed­room tightly to re­duce morn­ing light also causes CO2 lev­els to spike overnight to 7x day­time lev­els. To in­ves­ti­gate the pos­si­ble harm­ful effects, in 2016 I run a non-blind self­-ex­per­i­ment ran­dom­iz­ing an open bed­room door and a bed­room box fan (2x2) and an­a­lyze the data us­ing a struc­tural equa­tion model of air qual­ity effects on a la­tent sleep fac­tor with mea­sure­ment er­ror.

Main ar­ti­cle: .

Appendix

Inverse correlation of sleep quality with productivity?

Cu­ri­ous­ly, play­ing around with the full potas­sium data after the 2013 morn­ing ex­per­i­ment, poor sleep qual­ity seemed to cor­re­late with higher mood/productivity rat­ings.

cor.test(pot$Disturbance, pot$MP)
#     Pearson`s product-moment correlation
#
# data:  pot$Disturbance and pot$MP
# t = 1.224, df = 49, p-value = 0.2269
# alternative hypothesis: true correlation is not equal to 0
# 95% confidence interval:
#  -0.1085  0.4275
# sample estimates:
#    cor
# 0.1722

Hypotheses

While not sta­tis­ti­cal­ly-sig­nifi­cant, this in­verse cor­re­la­tion comes as a sur­prise and I thought worth think­ing about more. I have a cou­ple the­o­ries on what could be go­ing on:

  1. it could be an ar­ti­fact and ac­tu­ally bet­ter sleep means bet­ter per­for­mance: I’ve al­ways been con­cerned about the pos­si­bil­ity of off-by-one er­rors in my data or analy­ses. If bet­ter sleep meant bet­ter per­for­mance (as one would naively sus­pec­t), and ei­ther sleep data or per­for­mance data was ‘shifted’ by one day, then you would ob­serve the ex­act op­po­site.

    One would have to care­fully check the data and make sure every field is re­fer­ring to the time it should. If a en­try records 10hrs sleep for 2012-02-03, does that re­fer to sleep that morn­ing which is nec­es­sary be­cause you were awake dur­ing 2012-02-02, or does it re­fer to the sleep you en­gage in that evening (you go to bed at 11pm 2012-02-03 and that is the sleep data be­ing used).

    This seems un­like­ly, since such an er­ror should screw up all sorts of other analy­ses (for ex­am­ple such a flip ought to have claimed that potas­sium would help sleep, if days were be­ing re­versed).

  2. it could be that on pro­duc­tive days, you leap out of bed; but if you are de­pressed, un­mo­ti­vat­ed, ap­a­thet­ic, you might hang around in bed for a while after the alarm rings. De­pressed peo­ple some­times sleep more than reg­u­lar peo­ple; for pretty much this rea­son, I’d guess.

    This could be checked by look­ing at sleep qual­ity in­di­ca­tors in the be­gin­ning or mid­dle of the night. For ex­am­ple time to fall asleep (higher on more pro­duc­tive days in this sam­ple), or per­cent­age in deep sleep (mostly done to­wards the be­gin­ning and mid­dle of a sleep; seemed to be lower for pro­duc­tive days). One could try to test the slug­gard hy­poth­e­sis: how much past an alarm one snoozed.

  3. it’s a tem­po­rary cor­re­la­tion of this time pe­ri­od, per­haps re­lated to the potas­si­um, per­haps not.

    This is testable: with more data, does the cor­re­la­tion shrink or go away?

  4. I have some­times won­dered if I am de­pressed. One of the cu­ri­ous facts about de­pres­sion is that the symp­toms of de­pres­sion in peo­ple who pre­fer evenings (owl­s), and I am in­deed an owl. What does this im­ply?

    We can do some back­-of-the-en­ve­lope es­ti­mates. re­ports a very high de­pres­sion in­ci­dence; we’ll call it a 25% life­time risk. But pre­sum­ably the treat­ment only works if one is ac­tu­ally in a de­pres­sive episode, and while it’s un­clear what the dis­tri­b­u­tion or length of de­pres­sion pe­riod (as op­posed to in­di­vid­ual episodes) might be, it seems to be closer to years than months or decades, so we’ll put it at ~3 years out of an adult lifes­pan of ~60 years or a per-year risk of . On closer ex­am­i­na­tion of Selvi et al 2006, the morning/evening split only ap­pears with the to­tal sleep de­pri­va­tion pro­ce­dure (morn­ing types see their mood wors­en, evening sees it im­prove) while with par­tial sleep de­pri­va­tion both groups seem to see an im­prove­ment in their mood; since I rarely skip sleep en­tirely and such nights are dropped from the Zeo data, the to­tal sleep de­pri­va­tion re­sults are ir­rel­e­vant, but then my chrono­type be­ing evening does­n’t mat­ter. Fi­nal­ly, the sleep de­pri­va­tion pa­pers es­ti­mate <60% effec­tive­ness in the de­pressed, so that knocks the pos­si­bil­ity that both I am de­pressed and par­tial sleep de­pri­va­tion helps me to <0.025. 2.5% is not a large pos­si­bil­i­ty; and my vague spec­u­la­tion and a small in­verse cor­re­la­tion do not seem like they would in­crease that pos­si­bil­ity a lot.

(If it’s not the­se, I don’t have any sug­ges­tion on why it might be. Why would poor sleep ei­ther cause pro­duc­tiv­ity or be caused by some­thing that later also causes pro­duc­tiv­i­ty?)

Analysis

But be­fore rashly as­sum­ing I am de­pres­sive or en­gag­ing in per­son­ally costly self­-ex­per­i­ments like sleep de­pri­va­tion, I de­cided on 2013-04-26 to check the cor­re­la­tion on a larger dataset.

Typ­ing up my full self­-rat­ing dataset of 416 days and clean­ing up all the data16, I rechecked the cor­re­la­tion: r = 0.06617 This is no­tice­ably smaller (hence, less prac­ti­cally rel­e­vant) than the pre­vi­ous cor­re­la­tion, is also not sta­tis­ti­cal­ly-sig­nifi­cant, and shrink­ing is what one would ex­pect from a spu­ri­ous re­la­tion­ship.

To be more sure, I reused some of the tech­niques from my (specifi­cal­ly, ) and looked for a re­la­tion­ship; the re­sult was sim­i­lar, an odds which was in­verse but close to no effect (1.05718). More im­por­tant­ly, when all the other vari­ables are taken into ac­count in the lo­gis­tic re­gres­sion, things change19: with other data to con­di­tion on, the in­verse re­la­tion­ship of sleep qual­ity with mood/productivity re­verses and be­comes the ex­pected re­la­tion­ship (an in­crease in sleep dis­tur­bances pre­dicts lower mood/productivity); many of the other vari­ables turn out to be far stronger pre­dic­tors (big­ger odd­s); and some of the signs look odd (how can to­tal sleep time pre­dict in­creased mood/productivity, yet in­creas­ing all forms of sleep—REM/light/deep—predicts de­creased mood/productivity‽). I at­tempted to con­struct a sim­pler mod­el, which wound up ig­nor­ing any met­ric of sleep dis­tur­bance and ig­nor­ing all but 3 vari­ables, and con­clud­ing that “Morn­ing Feel” was the most im­por­tant pre­dic­tor20—which makes a lot of sense to me, and con­firms my pre­vi­ous ex­per­i­ments’ fo­cus­ing on the “Morn­ing Feel” vari­able.

Given this weak­en­ing and in the ab­sence of any cor­rob­o­rat­ing in­for­ma­tion, I con­sider it highly un­likely that the orig­i­nal cor­re­la­tion is re­flect­ing an an­ti-de­pres­sant effect due to sleep de­pri­va­tion. A fol­lowup in a few years may be war­ranted to see if a larger still dataset will shrink the cor­re­la­tion closer to ze­ro.

Phases of the moon

I at­tempt to repli­cate, us­ing pub­lic Zeo-recorded sleep datasets, a find­ing of a monthly cir­ca­dian rhythm affect­ing sleep in a small sleep lab. I find only small non-s­ta­tis­ti­cal­ly-sig­nifi­cant cor­re­la­tions, de­spite be­ing well-pow­ered.

Main ar­ti­cle: .

SDr lucid dreaming: exploratory data analysis

In Oc­to­ber 2012, an ac­quain­tance offered me an ex­tract from his free-form data on which he had been com­pil­ing since 2004, to see what in­sights I could ex­tract. In May 2013, I aug­mented it with an­other 60 en­tries

Data cleaning

The orig­i­nal text was a se­ri­ous mess, and I put sev­eral hours into clean­ing it up and or­ga­niz­ing it into some­thing more sen­si­ble. This was­n’t enough, so I wrote an ugly Haskell pro­gram to parse it into a quasi-CSV file:

import Data.List (isInfixOf, isPrefixOf, intercalate)
import Data.List.Split (splitOn) -- http://hackage.haskell.org/package/split

main :: IO ()
main = do txt <- readFile "2012-sdr-dream.txt"
          let txt' = filter (not . isPrefixOf "#") $ lines txt
          let header = drop 2 $ head $ filter (isPrefixOf "# Sleep Date,") $ lines txt
          let fields = map (splitOn ",") txt'
          let csvs = map convert fields
          putStrLn $ unlines (header : map show csvs)

data CSVEntry = CSVEntry { sleepDate :: String, totalZ :: Int,
                           wakeTime :: String, intensity :: String, recall :: String,
                           emotion :: String, interrupted :: Bool, melatonin :: Bool, lucid :: String }
instance Show CSVEntry where
 show a = intercalate "," [sleepDate a, if totalZ a == 0 then "" else show (totalZ a),
                           wakeTime a, intensity a, recall a, emotion a,
                           if interrupted a then "1" else "0", if melatonin a then "1" else "0", lucid a]

convert :: [String] -> CSVEntry
convert xs = CSVEntry { sleepDate = safeHead $ filter (\x -> isInfixOf "." x || isInfixOf "20" x) xs,
                        totalZ = timeToMinutes $ drop 12 $ safeHead $ filter (isInfixOf "dreamtime: ") xs,
                        wakeTime = drop 7 $ safeHead $ filter (isInfixOf "wake: ") xs,
                        intensity = drop 6 $ safeHead $ filter (isInfixOf "int: ") xs,
                        recall = drop 9 $ safeHead $ filter (isInfixOf "recall: ") xs,
                        emotion = drop 6 $ safeHead $ filter (isInfixOf "emo: ") xs,
                        lucid =  drop 8 $ safeHead $ filter (isInfixOf "lucid: ") xs,
                        interrupted = any (isInfixOf "interrupted") xs,
                        melatonin = any (isInfixOf "melatonin") xs }
                        where
                                safeHead :: [String] -> String
                                safeHead ys = if null ys then "" else head ys

                                -- clock hour:minute to total minutes: timeToMinutes "4:30" → 270
                                timeToMinutes :: String -> Int
                                timeToMinutes a = if null a then 0 else let (x,y) = break (==':') a
                                                     in read x * 60 + read (tail y)

Analysis

This was us­able. My next ques­tion was: since none of his rou­tines were ran­dom­ized and cor­re­la­tions were all that one could ex­tract, what cor­re­la­tions were in his data?

table <- read.csv("https://www.gwern.net/docs/zeo/2013-sdr-dream.csv")
summary(table)
      Sleep.Date     Total.Z        Wake.Time     Intensity        Recall         Emotion
 2011.10.02:  2   Min.   : 120           :217   Min.   :0.10   Min.   :0.000   Min.   :-0.50
 2011.11.26:  2   1st Qu.: 480   16:00   :  3   1st Qu.:0.30   1st Qu.:0.200   1st Qu.: 0.00
 2012.02.28:  2   Median : 600   11:00   :  2   Median :0.40   Median :0.300   Median : 0.20
 2012.04.15:  2   Mean   : 613   13:23:00:  2   Mean   :0.44   Mean   :0.367   Mean   : 0.18
 2012.06.21:  2   3rd Qu.: 720   19:17:00:  2   3rd Qu.:0.50   3rd Qu.:0.500   3rd Qu.: 0.40
 2013.01.23:  2   Max.   :1320   4:55:00 :  2   Max.   :7.00   Max.   :1.000   Max.   : 0.70
 (Other)   :316   NA's   :8      (Other) :100   NA's   :94     NA's   :26      NA's   :296
  Interrupted     Melatonin          Lucid      Day.quality
 Min.   :0.00   Min.   :0.0000   Min.   :0.0   Min.   :0.10
 1st Qu.:0.00   1st Qu.:0.0000   1st Qu.:0.1   1st Qu.:0.30
 Median :0.00   Median :0.0000   Median :0.2   Median :0.40
 Mean   :0.07   Mean   :0.0762   Mean   :0.2   Mean   :0.42
 3rd Qu.:0.00   3rd Qu.:0.0000   3rd Qu.:0.2   3rd Qu.:0.52
 Max.   :1.00   Max.   :1.0000   Max.   :0.6   Max.   :0.70
 NA's   :76                      NA's   :319   NA's   :312

# These 2 date fields haven't been turned into anything useful, so we'll just delete them:
rm(table$Wake.Time, table$Sleep.Date)

# Warning: 'Lucid' has just 9 datapoints, and 'Melatonin' just 6!
# Table cleaned up heavily by hand from default R output:
# deleted duplicates, censored any correlation -0.1<x<0.1 etc.
cor(table,use="pairwise.complete.obs")
             Recall  Emotion Interrupted Melatonin  Lucid  Day.quality
Total.Z                                    -0.12    -0.43  0.56
Intensity    0.35     0.37                           0.79
Recall                0.16      -0.16       0.14    -0.15
Emotion                          0.28      -0.14
Interrupted                                          0.91
Melatonin                                                  0.25

Much of the data is too im­pov­er­ished to draw any sug­ges­tions from. The re­main­ing cor­re­la­tions are:

  • ‘In­ten­sity’/‘Re­call’: r = 0.35

    The causal­ity is likely ‘In­ten­sity’->‘Re­call’; ei­ther one is prob­a­bly im­pos­si­ble to ex­per­i­men­tally ma­nip­u­late.

  • ‘In­ten­sity’/‘Emo­tion’: r = 0.37

    Causal­ity could go ei­ther way or to a third fac­tor; ‘Emo­tion’ might be ma­nip­u­la­ble by in­tend­ing to dream of dis­turb­ing top­ics, but might not.

  • ‘In­ter­rupted’/‘Re­call’: r=-0.16

  • ‘In­ter­rupted’/‘Emo­tion’: r = 0.28

    ‘In­ter­rup­tion’ is ex­per­i­men­tally ma­nip­u­la­ble by eg. an alarm clock or room­mate. ‘Re­call’ might be im­proved by some change in jour­nal­ing, for ex­am­ple do­ing at your bed in­stead of wait­ing un­til you’re on your com­put­er. The pos­i­tive cor­re­la­tion with ‘Emo­tion’ sug­gests that, per the WILD method­ol­ogy of lu­cid dream­ing (see & , Ex­plor­ing the World of Lu­cid Dream­ing), a tem­po­rary awak­en­ing does in­crease the chance of a lu­cid dream (laden with emo­tion).

  • ‘Mela­tonin’ in­ter­est­ingly cor­re­lates with both day qual­ity and with re­duced sleep; this is in­ter­est­ing be­cause Total.Z in­creas­ing also in­creased Day.quality so it’s not clear how mela­tonin could do both at the same time if more sleep is oth­er­wise bet­ter. The cor­re­la­tions may be sta­tis­ti­cal­ly-sig­nifi­cant but the data is too wretched and the melatonin/day-quality vari­ables too few to say any­thing fur­ther.

(One ob­ser­va­tion that came to mind work­ing on clean­ing the data was that col­lec­tion was very sparse, spo­radic, and ac­ci­den­tal-look­ing.)

So these gen­eral points sug­gest 3 fu­ture over­lap­ping ap­proach­es:

  1. de­lib­er­ate use of in­ter­rup­tions (maybe ran­dom­ized), to in­ves­ti­gate effect on lu­cid dream­ing
  2. more sys­tem­atic us­age (per­haps ran­dom­ized or blind­ed) of mela­ton­in, to al­low cor­re­la­tions or causal in­fer­ences to other vari­ables
  3. at­tack­ing the un­sys­tem­atic data col­lec­tion (per­haps it’s too much trou­ble to do all those vari­ables each day?) by get­ting a Zeo to han­dle part of the data col­lec­tion for you.

  1. Rel­e­vant pa­pers:

    Also rel­e­vant: “Com­par­ing 10 Sleep Track­ers (2017): How well do they track your sleep? A 9-day min­ute-by-minute com­par­i­son”.↩︎

  2. The cheaper al­ter­na­tive to the Zeo would be the , the most pop­u­lar of the many ac­celerom­e­ters on the mar­ket. There aren’t many com­par­isons; Di­ana Sher­man com­pared one night, Joe Betts-LaCroix com­pared ~38 nights of data, and Christo­pher Win­ter com­pared one night of polysomnog­ra­phy, Philips Ac­ti­watch Spec­trum (actig­ra­phy), Ba­sis Chrome (move­ment, heart-rate, oth­er­s), and the Jaw­bone Up & Fit­Bit Flex & iPhone+“24/7” (actig­ra­phy). In the pre­vi­ous cas­es, the Fit­bit seemed to be pretty sim­i­lar to the Zeo at es­ti­mat­ing to­tal sleep time (the only thing it can mea­sure). Betts-LaCroix ex­plic­itly rec­om­mends the Zeo, but I’m not clear on whether that is due to the bet­ter data qual­ity or be­cause Fit­bit made it hard to im­pos­si­ble for him to ex­tract the de­tailed Fit­bit data while Zeo offers easy ex­port­ing. Sim­i­lar­ly, in her 2013 Am­s­ter­dam talk, Chris­tel De Maeyer presents her sleep data sum­maries (means) from two dis­joint time pe­ri­ods us­ing the Zeo and the ac­celerom­e­ter band which were com­pa­ra­ble for to­tal sleep es­ti­mates. In any case, I al­ready have the Zeo and I’ve come to like the de­tailed in­for­ma­tion.↩︎

  3. I had pre­vi­ously tried hu­perzine-A and sub­jec­tively no­ticed no effect from it, but I had no way of re­ally notic­ing any effect on sleep, and in his The Four-hour Body claims:

    Tak­ing 200 mil­ligrams of hu­perzine-A 30 min­utes be­fore bed can in­crease to­tal REM by 20-30%. Hu­perzine-A, an ex­tract of Hu­perzia ser­rata, slows the break­down of the neu­ro­trans­mit­ter acetyl­choline. It is a pop­u­lar nootropic (s­mart drug), and I have used it in the past to ac­cel­er­ate learn­ing and in­crease the in­ci­dence of lu­cid dream­ing. I now only use hu­perzine-A for the first few weeks of lan­guage ac­qui­si­tion, and no more than three days per week to avoid side effects. Iron­i­cal­ly, one doc­u­mented side effect of overuse is in­som­nia. The brain is a sen­si­tive in­stru­ment, and while gen­er­ally well tol­er­at­ed, this drug is con­traindi­cated with some classes of med­ica­tions. Speak with your doc­tor be­fore us­ing.

    ↩︎
  4. My own sus­pi­cion is that given the ex­is­tence of neu­ron-level sleep in mice, poor self­-mon­i­tor­ing in hu­mans, and anec­do­tal re­ports about polypha­sic sleep, is that polypha­sic sleep is a real & work­able phe­nom­e­non but that it comes at the price of a large chunk of men­tal per­for­mance.↩︎

  5. ar­gues that there is no need for peo­ple to use the old frame­work of p-val­ues and null hy­pothe­ses etc, with their many well-known philo­soph­i­cal diffi­cul­ties and mis­lead­ing in­ter­pre­ta­tion­s—in­ter­pre­ta­tions I, alas, per­pet­u­ate in my analy­ses with my use of sta­tis­ti­cal sig­nifi­cance:

    Nev­er­the­less, some peo­ple have the im­pres­sion that con­clu­sions from NHST and Bayesian meth­ods tend to agree in sim­ple sit­u­a­tions such as com­par­i­son of two groups: “Thus, if your pri­mary ques­tion of in­ter­est can be sim­ply ex­pressed in a form amenable to a t-test, say, there re­ally is no need to try and ap­ply the full Bayesian ma­chin­ery to so sim­ple a prob­lem.” (Brooks, 2003, p. 2694) This ar­ti­cle shows, to the con­trary, that Bayesian pa­ra­me­ter es­ti­ma­tion pro­vides much richer in­for­ma­tion than the NHST t-test, and that its con­clu­sions can differ from those of the NHST t-test. De­ci­sions based on Bayesian pa­ra­me­ter es­ti­ma­tion are bet­ter founded than NHST, whether the de­ci­sions of the two meth­ods agree or not. The con­clu­sion is bold but sim­ple: Bayesian pa­ra­me­ter es­ti­ma­tion su­per­sedes the NHST t-test.

    Un­for­tu­nate­ly, while I have no love for NHST, I did find it much eas­ier to use the NHST con­cepts & code when learn­ing how to do these analy­ses. In the fu­ture, hope­fully I can switch to Bayesian tech­niques.↩︎

  6. The usual way to cor­rect for the is­sue of mul­ti­ple com­par­isons in­flat­ing re­sults (a big prob­lem in epi­demi­ol­ogy and why their re­sults are so often false) is to use a Bon­fer­roni cor­rec­tion—if I look at the p-val­ues for 7 Zeo met­rics, I would­n’t con­sider any to be sta­tis­ti­cal­ly-sig­nifi­cant at ‘p = 0.05’ un­less they were ac­tu­ally sta­tis­ti­cal­ly-sig­nifi­cant at , which is even more strin­gent than the rarer ‘p = 0.01’ cri­te­ri­on. With the even stronger cri­te­rion ‘p = 0.007’, it’s a safe bet than none of my tests give sta­tis­ti­cal­ly-sig­nifi­cant re­sults. Which may be the right thing to con­clude, since all my data is just n = 1 and un­re­li­able in many ways, but still, the Bon­fer­roni cor­rec­tion is not be­ing very help­ful here.

    The caveat is that the Bon­fer­roni cor­rec­tion is in­tended for use on ‘in­de­pen­dent’ data, while the Zeo met­rics are all very de­pen­dent, some by de­fi­n­i­tion (eg. ZQ is de­fined partly as what the REM sleep length was, AFAIK). So while the Bon­fer­roni cor­rec­tion will still do the job of only let­ting through re­ally sta­tis­ti­cal­ly-sig­nifi­cant data, it’ll do so by throw­ing out way more po­ten­tially good re­sults than one has to. (It’ll avoid some false pos­i­tives by mak­ing many false neg­a­tives.) So what should we do?

    Andy McKen­zie sug­gested lim­it­ing our by us­ing the method of Ben­jamin & Hochberg 1995:

    …let’s say that you test 6 hy­pothe­ses, cor­re­spond­ing to differ­ent fea­tures of your Zeo da­ta. You could use a t-test for each, as above. Then ag­gre­gate and sort all the p-val­ues in as­cend­ing or­der. Let’s say that they are 0.001, 0.013, 0.021, 0.030, 0.067, and 0.134.

    As­sume, ar­bi­trar­i­ly, that you want the over­all false dis­cov­ery rate to be 0.05, which is in this con­text called the q-val­ue. You would then se­quen­tially test, from the last value to the first, whether the cur­rent p-value is less than . You stop when you get to the first true in­equal­ity and call the p-val­ues of the rest of the hy­pothe­ses [s­ta­tis­ti­cal­ly-]sig­nifi­cant.

    So in this ex­am­ple, you would stop when you cor­rectly call , and only the hy­pothe­ses cor­re­spond­ing to the first four [s­mall­est] p-val­ues would be called [s­ta­tis­ti­cal­ly-]sig­nifi­cant.

    ↩︎
  7. If we cor­rect for mul­ti­ple com­par­isons (see pre­vi­ous foot­note) at q-val­ue=0.05, none of them sur­vive:

    p.adjust(c(0.11,0.77,0.89,0.16,0.63,0.74,0.73,0.63,0.20), method="BH") < 0.05
    # [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

    Oh well.↩︎

  8. “Block­ing” is a style of vari­a­tion on a sim­ple ran­dom­ized de­sign where in­stead of con­sid­er­ing each day sep­a­rate and ran­dom­iz­ing a sin­gle day, we in­stead ran­dom­ize pairs of days, or more; so in­stead of flip­ping our coin to de­cide whether ‘this week’ is place­bo, we flip our coin to de­cide whether ‘this week will be placebo & next ac­tive’ or ‘this week ac­tive & next placebo’. This has 2 big ad­van­tages which jus­tify the com­plex­i­ty:

    1. Often, I’m wor­ried about sim­ple ran­dom­iza­tion lead­ing to an im­bal­ance in sam­ple vs ex­per­i­men­tal; if I’m only get­ting 20 to­tal dat­a­points on some­thing, then ran­dom­iza­tion could eas­ily lead to some­thing like 14 con­trol and 6 ex­per­i­men­tal dat­a­points—throw­ing out a lot of sta­tis­ti­cal power com­pared to 10 con­trol and 10 ex­per­i­men­tal! Why am I los­ing pow­er? Be­cause data is sub­ject to : each new point re­duces the stan­dard er­ror of your es­ti­mates less than the pre­vi­ous one did (s­ince the to­tal er­ror shrinks as, rough­ly, in­verse of the square root of the to­tal sam­ple size; the differ­ence be­tween √1 and √2 is big­ger and shrinks er­ror more than √2 vs √3, etc) . So the ex­tra 4 con­trol dat­a­points re­duce the er­ror less than the lost 4 ex­per­i­men­tal dat­a­points would have, and this leaves me with a fi­nal an­swer less pre­cise than if it had been ex­actly 10:10. (If di­min­ish­ing re­turns is­n’t in­tu­itive, imag­ine tak­ing it to an ex­treme: is 10:10 just as good as 5:15? As good as 2:18? How about 0:20?) But if I pair days like this, then I know I will get ex­actly 10:10.
    2. Block­ing is the nat­ural way to han­dle mul­ti­ple-day effects or trends: if I think lithium op­er­ates slow­ly, I will pair en­tire weeks or months, rather than days and hop­ing enough ex­per­i­men­tal and con­trol days form runs which will re­veal any trend rather than wash it out in av­er­ag­ing.
    ↩︎
  9. The net present value for­mula is the an­nual sav­ings di­vided by the nat­ural log of the dis­count rate, out to eter­ni­ty. Ex­po­nen­tial dis­count­ing means that a bond that ex­pires in 50 years is worth a sur­pris­ingly sim­i­lar amount to one that con­tin­ues pay­ing out for­ev­er. For ex­am­ple, a 50 year bond pay­ing $10 a year at a dis­count rate of 5% is worth sum (map (\t -> 10 / (1 + 0.05)^t) [1..50]) → 182.5 but if that same bond never ex­pires, it’s worth 10 / log 1.05 = 204.9 or just $22.4 more! My own ex­pected longevity is ~50 more years, but I pre­fer to use the sim­ple nat­ural log for­mula rather than the more ac­cu­rate sum­ma­tion. Ei­ther way is in­ter­est­ing; Vaniver:

    …pos­si­bly a way to drive it home is to talk about di­vid­ing by log 1.05, which is es­sen­tially mul­ti­ply­ing by 20.5. If you can make a one-time in­vest­ment that pays off an­nu­ally un­til you die, that’s worth 20.5 times the an­nual re­turn, and mul­ti­ply­ing the value of some­thing by 20 can often move it from not worth think­ing about to worth think­ing about.

    ↩︎
  10. Vaniver notes that one rea­son I might be less con­fi­dent than you would ex­pect is that many sub­stances or sup­ple­ments lose effect over time as one’s body re­gains home­osta­sis and com­pen­sates for the sub­stance, build­ing tol­er­ance. Which is quite true, and a ma­jor rea­son I tested mela­ton­in—I was sure it worked for me in the past, but did it still work?↩︎

  11. For sim­plic­i­ty, in all my VoI cal­cu­la­tions I as­sume that I’ll stop buy­ing the sup­ple­ment (or do­ing the ac­tiv­i­ty) if I hit a neg­a­tive re­sult. The proper way a real an­a­lyst would do this value of in­for­ma­tion ques­tion would be to say that the neg­a­tive re­sult gives us ad­di­tional in­for­ma­tion which changes the ex­pect­ed-value of mela­tonin use.

    In my mela­tonin ar­ti­cle ar­ti­cle, I cal­cu­lated that since mela­tonin saved me close to an hour while each dose cost lit­er­ally a penny or two, the value was as­tro­nom­i­cal—$2350.60 a year! By Bayes’ for­mu­la, if I started with 80% con­fi­dence and had a 95% ac­cu­rate test, a neg­a­tive re­sult drops my 80% all the way down to 17%. We get this by us­ing a de­riva­tion of Bayes’s the­o­rem:

    But iron­i­cally if I now be­lieved that mela­tonin only had a 17% chance of do­ing some­thing help­ful rather than noth­ing at all (as com­pared to my orig­i­nal 80% be­lief), well, 17% of $2350 ($117) is still way more money than the mela­tonin cost ($10), so I’d use it any­way!

    Would it make sense to it­er­ate again and test mela­tonin a sec­ond time? Well, what does the cal­cu­la­tion say? We have a new prior of 17; what hap­pens if we get a neg­a­tive re­sult again? and then the ex­pected value is , which is not much more than the cost of $10, and given the diffi­cult-to-quan­tify pos­si­bil­ity of neg­a­tive long-term health effects, is not enough of a profit to re­ally en­tice me.↩︎

  12. Tech­nol­ogy Re­view ed­i­tor Emily Singer no­ticed the same prob­lem when us­ing her Zeo.↩︎

  13. The R in­ter­preter ses­sion, load­ing a CSV as be­fore:

    zeo <- read.csv("https://www.gwern.net/docs/zeo/2011-zeo-oneleg.csv")
    colnames(zeo)[24] <- "OneLeg"
    l <- lm(cbind(ZQ, Total.Z, Time.to.Z, Time.in.Wake, Time.in.REM,
                  Time.in.Light, Time.in.Deep, Awakenings, Morning.Feel)
             ~ OneLeg, data=zeo)
    summary(manova(l))
    #           Df Pillai approx F num Df den Df Pr(>F)
    # OneLeg     1  0.177     1.37      9     57   0.23
    # Residuals 65
    summary(l)
    # Response ZQ :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   96.231      1.712   56.22   <2e-16
    # OneLeg        -1.244      0.883   -1.41     0.16
    #
    # Response Total.Z :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   514.67       8.84    58.2   <2e-16
    # OneLeg         -4.09       4.56    -0.9     0.37
    #
    # Response Time.to.Z :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   14.949      1.373   10.89  2.7e-16
    # OneLeg         0.469      0.708    0.66     0.51
    #
    # Response Time.in.Wake :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   12.821      2.786    4.60    2e-05
    # OneLeg        -0.369      1.436   -0.26      0.8
    #
    # Response Time.in.REM :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   168.72       4.25   39.70   <2e-16
    # OneLeg         -5.33       2.19   -2.43    0.018
    #
    # Response Time.in.Light :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   277.15       6.06   45.75   <2e-16
    # OneLeg          2.76       3.12    0.88     0.38
    #
    # Response Time.in.Deep :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   69.282      1.802   38.44   <2e-16
    # OneLeg        -1.558      0.929   -1.68    0.098
    #
    # Response Awakenings :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   4.1538     0.3690   11.26   <2e-16
    # OneLeg       -0.0513     0.1902   -0.27     0.79
    #
    # Response Morning.Feel :
    #
    # Coefficients:
    #             Estimate Std. Error t value Pr(>|t|)
    # (Intercept)   2.8718     0.1014    28.3   <2e-16
    # OneLeg       -0.0525     0.0523    -1.0     0.32
    ↩︎
  14. If we cor­rect for mul­ti­ple com­par­isons (see pre­vi­ous foot­note on the Bon­fer­roni cor­rec­tion) at q-val­ue=0.05, none of them sur­vive:

    p.adjust(c(0.16,0.37,0.51,0.80,0.02,0.38,0.10,0.79,0.32), method="BH") < 0.05
    # [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

    Oh well! Sta­tis­tics is a harsh mis­tress in­deed.↩︎

  15. I don’t use a timer, but in­stead count 400 full breaths. De­pend­ing on how fast and shal­lowly I breathe, this runs from 20-35 min­utes (eg. 2012-05-16’s med­i­ta­tion ran 33 min­utes long). To be con­ser­v­a­tive, I will as­sume the med­i­ta­tion is only 20 min­utes. In mid-Oc­to­ber, I bought and be­gan us­ing in­stead a timer which could be set to 15 min­utes.↩︎

  16. The ex­act pro­cess­ing steps, for those cu­ri­ous:

    zeo <- read.csv("https://www.gwern.net/docs/zeo/gwern-zeodata.csv")
    zeo$Sleep.Date <- as.Date(zeo$Sleep.Date, format="%m/%d/%Y")
    mp <- read.csv("mp.csv", colClasses=c("Date","factor"))
    zeo$MP <- ordered(mp[mp$Date %in% zeo$Sleep.Date,]$MP)
    zeo$Disturbance <- scale(zeo$Time.to.Z) + scale(zeo$Awakenings) + scale(zeo$Time.in.Wake)
    zeo <- zeo[!is.na(zeo$Disturbance) & !is.na(zeo$Morning.Feel),]
    ↩︎
  17. Load & cor­re­late:

    zeo <- read.csv("https://www.gwern.net/docs/zeo/2013-gwern-sleepdisturbances-productivity.csv")
    cor.test(zeo$Disturbance, as.integer(zeo$MP))
    
        Pearson`s product-moment correlation
    
    data:  zeo$Disturbance and as.integer(zeo$MP)
    t = 1.344, df = 414, p-value = 0.1798
    alternative hypothesis: true correlation is not equal to 0
    95% confidence interval:
     -0.03045  0.16102
    sample estimates:
        cor
    0.06589
    ↩︎
  18. We regress a con­tin­u­ous pre­dic­tor onto a cat­e­gor­i­cal out­come:

    # turn into an ordinal variable
    zeo$MP <- ordered(zeo$MP)
    
    library(MASS)
    lmodel <- polr(MP ~ Disturbance, data = zeo); summary(lmodel)
    ...
    Coefficients:
                 Value Std. Error t value
    Disturbance 0.0553     0.0429    1.29
    
    Intercepts:
        Value  Std. Error t value
    1|2 -4.413  0.450     -9.808
    2|3 -0.990  0.110     -8.965
    3|4  1.101  0.113      9.711
    
    Residual Deviance: 915.66
    AIC: 923.66
    
    exp(lmodel$coefficients)
    Disturbance
           1.057
    ↩︎
  19. Try out more vari­ables:

    almodel <- polr(MP ~ Disturbance + ZQ + Total.Z + Time.to.Z + Time.in.Wake + Time.in.REM +
                         Time.in.Light + Time.in.Deep + Awakenings + Morning.Feel, data = zeo); almodel
    
    Coefficients:
      Disturbance            ZQ       Total.Z     Time.to.Z  Time.in.Wake   Time.in.REM Time.in.Light
        -0.431623     -0.276236      0.307941      0.045819      0.003266     -0.246901     -0.272593
     Time.in.Deep  Morning.Feel
        -0.227003      0.205541
    
    Intercepts:
        1|2     2|3     3|4
    -2.9105  0.5465  2.6902
    
    Residual Deviance: 903.01
    AIC: 927.01
    ↩︎
  20. Re­duced by cut­ting out ex­tra­ne­ous vari­ables us­ing :

    salmodel <- step(almodel); summary(salmodel)
    ...
    Coefficients:
                   Value Std. Error t value
    Time.to.Z     0.0163    0.00713    2.29
    Time.in.Deep -0.0152    0.00823   -1.85
    Morning.Feel  0.1906    0.12683    1.50
    
    Intercepts:
        Value  Std. Error t value
    1|2 -4.457  0.785     -5.675
    2|3 -1.011  0.649     -1.557
    3|4  1.113  0.649      1.713
    
    Residual Deviance: 907.60
    AIC: 919.60
    ↩︎