• Probability & Statistics
    Open & Free

    Statistics presented with a full treatment of probability
    Free for independent learners

Probability & Statistics — Open & Free

Introductory-level course teaches students the basic concepts of statistics and the logic of statistical reasoning. Designed for students with no prior knowledge in statistics, its only prerequisite is basic algebra. Includes a classical treatment of probability.
Learn about Open & Free OLI courses by visiting the “Open & Free features” tab below.

Description

Probability & Statistics introduces students to the basic concepts and logic of statistical reasoning and gives the students introductory-level practical ability to choose, generate, and properly interpret appropriate descriptive and inferential methods. In addition, the course helps students gain an appreciation for the diverse applications of statistics and its relevance to their lives and fields of study. The course does not assume any prior knowledge in statistics and its only prerequisite is basic algebra.

We offer two versions of statistics, each with a different emphasis: Probability and Statistics and Statistical Reasoning. The Open & Free versions of the courses includes all expository text, simulations, case studies, interactive learning exercises, and the StatTutor labs, but they omit the scored tests and instructor tools. Both Probability & Statistics and Statistical Reasoning contain all of the instructions for the five statistics packages options we support. To do the activities, students will need their own copy of Microsoft Excel, Minitab, the open source R software, TI calculator, or StatCrunch.

One of the main differences between the courses is the path through probability. Probability and Statistics includes the classical treatment of probability as it is in the earlier versions of the OLI Statistics course, while Statistical Reasoning gives a more abbreviated treatment of probability, using it primarily to set up the inference unit that follows it.

Throughout the course there are many interactive elements. These include: simulations, “walk-throughs” that integrate voice and graphics to explain an example of a procedure or a difficult concept, and, most prominently, computer tutors in which students practice problem solving, with hints and immediate and targeted feedback. The most elaborate of such activities is the “StatTutor,” a tool that supports students as they go through the processes of data analysis while emphasizing the big picture of statistics.

The course is built around a series of carefully devised learning objectives that are independently assessed. Most of the interactive tutors are tagged by learning objective and skill, and so student work can be tracked by the system and reported to the instructor via the Learning Dashboard. These give the instructor insight into mastery of learning objectives and skills, both for the class as a whole and for individual students.

In-Depth Description

Topics Covered:

Exploratory Data Analysis, Producing Data, Probability, and Inference.

Both Probability and Statistics and Statistical Reasoning include four units, with different Probability units (Unit 3), as outlined below.

Unit 1

Exploratory Data Analysis. This is organized into two modules – Examining Distributions and Examining Relationships. The general approach is to provide students with a framework that will help them choose the appropriate descriptive methods in various data analysis situations.

Unit 2

Producing Data. This unit is organized into two modules – Sampling and Study Design.

Unit 3

Probability. As stated above, this is the unit where the two versions of the course differ. In the Probability and Statistics course the unit is a classical treatment of probability and includes basic probability principles, conditional probability, discrete random variables (including the Binomial distribution) and continuous random variables (with emphasis on the normal distribution). The probability unit of the Statistical Reasoning version of the course essentially acts as a “bridge” to the inference section and includes only those concepts necessary to support a conceptual understanding of the role of probability as the “machinery” behind inference. Both probability units culminate in a discussion of sampling distributions that is grounded in simulation.

Unit 4

Inference. This unit introduces students to the logic as well as the technical side of the main forms of inference: point estimation, interval estimation and hypothesis testing. The unit covers inferential methods for the population mean and population proportion, Inferential methods for comparing the means of two groups and of more than two groups (ANOVA), the Chi-Square test for independence and linear regression. The unit reinforces the framework that the students were introduced to in the Exploratory Data Analysis for choosing the appropriate, in this case, inferential method in various data analysis scenarios.

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