Introduction to t-tests: Comparing Group Means

1. An Introduction to t tests By Del Siegle, PhD del.siegle@uconn.edu www.delsiegle.info (This presentation may be used for instructional purposes) Press the space bar or your mouse button to work through this introduction on t tests.

2. Suppose we conducted a study to compare two strategies for teaching spelling. 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores Group A had a mean score of 19. The range of scores was 16 to 22, and the standard deviation was 1.5. Group B had a mean score of 20. The range of scores was 17 to 23, and the standard deviation was 1.5. and Group B occurred because of differences in our reading strategies, rather than by chance? How confident can we be that the difference we found between the means of Group A

3. A t test allows us to compare the means of two groups and determine how likely the difference between the two means occurred by chance when there was no difference in population from which the sample was drawn. The calculations for a t test requires three pieces of information: - the difference between the means (mean difference) - the standard deviation for each group - and the number of subjects in each group. 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores

4. 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores All other factors being equal, large differences between means are less likely to occur by chance than small differences.

5. The size of the standard deviation also influences the outcome of a t test. 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores Spelling Test Scores Given the same difference in means, groups with smaller standard deviations are more likely to report a significant difference than groups with larger standard deviations.

6. 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores Spelling Test Scores Less overlap would indicate that the groups are more different from each other. than larger standard deviations. From a practical standpoint, we can see that smaller standard deviations produce less overlap between the groups

7. 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores The size of our sample is also important. The more subjects that are involved in a study, the more confident we can be that the differences we find between our groups did not occur by chance.

8. Once we calculate the outcome of the t test (which produces a t-value), we check that value (with the appropriate degrees of freedom) on a critical value table (a process similar to what we did for correlations) to determine how likely the difference between the means occurred by chance. The above process can be accomplished with a computer statistical package which calculates the means and standard deviations of both groups, the mean difference, the standard error of the mean difference, and a p-value (probability of the mean difference occurring by chance). I have created an excel spreadsheet which does these calculations and provides this information. I have also created a PowerPoint presentation that demonstrates how to use the Excel spreadsheet.

9. There are three types of t tests and each is calculated slightly differently. A correlated (or paired) t test is concerned with the difference between the average scores of a single sample of individuals who is assessed at two different times (such as before treatment and after treatment) or on two different measures. It can also compare average scores of samples of individuals who are paired in some way (such as siblings, mothers and daughters, persons who are matched in terms of a particular characteristics). An independent t test compares the averages of two samples that are selected independently of each other (the subjects in the two groups are not the same people). There are two types of independent t tests: equal variance and unequal variance.

10. An equal variance (pooled variance) t test is used when the number of subjects in the two groups is the same OR the variance of the two groups is similar. An unequal variance (separate variance) t test is used when the number of subjects in the two groups is different AND the variance of the two groups is different.

11. Yes No Are there the same number of people in the two groups? Paired t test (Dependent t-test; Correlated t-test) No Yes Equal Variance Independent t test (Pooled Variance Independent t-test) Are the variances of the two groups different? Yes(Significance Level for Levene (or F-Max) is p <.05 No(Significance Level for Levene (or F-Max) is p >.05 Equal Variance Independent t test (Pooled Variance Independent t test) Unequal Variance Independent t-test (Separate Variance Independent t test) How do we determine which t test to use… Are the scores for the two means from the same subject (or related subjects)?