t-Tests of Hypotheses About Means

This course builds on the preceding course, Introducing Null Hypothesis Significance Testing With the z-Test, by applying the logic of Null Significance Hypothesis Testing (NHST) to research designs involving inferences about one or two sample means.

The course begins with coverage of one-sample t-tests that compare a single mean against another value. Practical examples are provided, as is demonstration of how to complete the test using the jamovi statistical program.

Next, the course considers paired-sample designs in which two measurements are taken from the same or related individuals and the means of these two measurements are compared. These paired-sample t-tests are similarly demonstrated through the use of multiple examples as well as within the jamovi statistical program.

Finally, the course covers independent-samples designs in which two means drawn from separate groups of individuals are compared. And once again, this research design is explained in the context of multiple, real-world examples and is also demonstrated in the jamovi statistical program.

In all three instances, the statement of null and alternative hypotheses, calculations of measures of effect size and confidence intervals are included. Statistical power as it relates to t-test designs is also covered. Additionally, the logic of NHST is explicitly and repeatedly articulated in the examples so as to reinforce the understanding of this statistical process.

Learning objectives

• Compare and contrast z- and t-distributions, and determine the appropriate test for various research situations.
• Develop and generate hypotheses for differences between means and conduct the corresponding tests.
• Calculate and interpret t-tests, effect sizes, and confidence intervals from raw data and summary statistics in both formal statistical terms and everyday language.
• Calculate effect sizes and required sample sizes to achieve desired statistical power, and interpret power curves for effect size and sample size.
• Generate and interpret confidence intervals for t-tests from raw data and summary statistics.