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M09.02.13 t-test
A t-test is a statistical method used to compare the means of two groups from a single nominal variable. By analyzing means from an interval variable, a t-test determines whether there is a significant difference between the two groups.
Key Components of the T-Test
- Objective: Compares the means of two groups.
- Output: Provides a t statistic, which reflects the size and direction of the difference between group means.
- Application: Suitable for comparing two groups only, using interval data to measure differences.
Example Scenario
Consider a clinical scenario: Do patients with myocardial infarction (MI) who participate in psychotherapy have a reduced convalescence period compared to those who do not undergo therapy?
Types of T-Tests
There are two main types of t-tests, each with specific applications:
| Type of T-Test | Description | Application Example |
|---|---|---|
| Pooled T-Test | Assumes equal variances between two groups. It’s a standard t-test for comparing two independent groups. | Comparing test scores between two classes taught differently. |
| Matched Pairs T-Test | Each person in one group is matched with a counterpart in the second group. It’s suitable for before-and-after studies and paired data. | Examining blood pressure before and after medication. |
Points to Remember
- Sample Size: T-tests are ideally conducted with sample sizes of 30 or more per group to meet assumptions of normality, though they can be used with smaller samples.
- Assumptions:
- The data is normally distributed.
- Interval or ratio data should be used for measuring differences.
- Independent vs. Paired Samples:
- Use a pooled t-test for comparing independent groups.
- Use a matched pairs t-test for paired or linked data, such as pre-and post-intervention measures.
Visual Comparison of T-Test Data
When analyzing data distributions between two groups, it’s useful to visualize their spread. For instance, the distribution of height could be compared between men and women, illustrating the difference in mean height.
| Frequency | Shorter Height | Taller Height |
|---|---|---|
| Women | Higher | Lower |
| Men | Lower | Higher |
Figure: Comparison of the distributions of two groups (e.g., men and women) on a characteristic like height.
Bibliography and Further Reading
- Statistics for Social Scientists: Offers insights into various statistical tests, including t-tests.
- Rumsey, D. J. (2016). Statistics For Dummies. Wiley.
- McDonald, J. H. (2014). Handbook of Biological Statistics (3rd ed.). Sparky House Publishing. Available at: www.biostathandbook.com