By Del Siegle, PhD [email protected] www.delsiegle.info Press the space bar or your mouse button to work through this introduction on t tests. c. 2002 Del Siegle (This presentation may be used for instructional purposes) Suppose we conducted a study to compare two strategies for teaching spelling. 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. 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 c. 2002 Del Siegle How confident can we be that the difference we found between the means of Group A and Group B occurred because of differences in our reading strategies, rather than by chance? 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. 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 c. 2002 Del Siegle 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. All other factors being equal, large differences between means are less likely to occur by chance than small differences. 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25

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 c. 2002 Del Siegle Spelling Test Scores The size of the standard deviation also influences the outcome of a t test. 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. 10 9 8 7 6

5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 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 c. 2002 Del Siegle Spelling Test Scores From a practical standpoint, we can see that smaller standard deviations produce less overlap between the groups than larger standard deviations. Less overlap

would indicate that the groups are more different from each other. 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 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

c. 2002 Del Siegle 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. 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 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 c. 2002 Del Siegle Spelling Test Scores 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. 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. c. 2002 Del Siegle

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). There are three types of t tests and each is calculated slightly differently. 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. c. 2002 Del Siegle 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 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.

c. 2002 Del Siegle 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. How do we determine which t test to use Paired t test (Dependent t-test; Correlated t-test) Are the scores for the two means from the same subject (or related subjects)? Yes No Are there the same number of people in the two groups? No No Equal Variance Independent t test (Pooled Variance

Independent t test) (Significance Level for Levene (or F-Max) is p >.05 Are the variances of the two groups different? Yes (Significance Level for Levene (or F-Max) is p <.05 Unequal Variance Independent t-test (Separate Variance Independent t test) c. 2002 Del Siegle Yes Equal Variance Independent t test (Pooled Variance Independent t-test)