Statistics for the Social Sciences

1. Statistics for the Social Sciences Psychology 340 Spring 2005 Using t-tests

2. Outline • Review t-tests • One sample, related samples, independent samples

3. 1 sample • Two scores per subject • The related-samples t-test can be used when: Statistical analysis follows design

4. 2 samples • Scores are related • The related-samples t-test can be used when: Statistical analysis follows design • 1 sample • Two scores per subject - OR -

5. Performing your statistical test One sample t Related samples t One sample z Test statistic Diff. Expected by chance

6. Effect Sizes & Power for t Test for Dependent Means Remember we don’t know these

7. Approximate Sample Size Needed for 80% Power (.05 significance level) • Using Power and effect sizes to determine how many participants you need

8. Compare these two means Independent samples • What are we doing when we test the hypotheses? • Consider a new variation of our memory experiment example Memory Test Memory placebo Memory patients Memory Test Memory treatment • the memory treatment sample are the same as those in the population of memory patients. • they aren’t the same as those in the population of memory patients H0: HA:

9. 2 samples • Samples are independent • The independent samples t-test can be used when: Statistical analysis follows design

10. Estimate of the standard error based on the variability of both samples Performing your statistical test

11. Sample means Performing your statistical test Independent-samples t One-sample t Test statistic

12. Population means • from the hypotheses Performing your statistical test Independent-samples t One-sample t Test statistic

13. H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. So: Performing your statistical test Independent-samples t One-sample t Test statistic • Population means • from the hypotheses

14. We have two samples, so the estimate is based on two samples estimate is based on one sample Estimated standard error (difference expected by chance) Performing your statistical test One-sample t Test statistic

15. “pooled variance” Number of subjects in group A Number of subjects in group B Performing your statistical test We combine the variance from the two samples

16. “pooled variance” Variance (s2) * degrees of freedom (df) variance Performing your statistical test We combine the variance from the two samples Recall “weighted means,” need to use “weighted variances” here

17. This is the one you use to look up your tcrit Performing your statistical test Independent-samples t • Compute your estimated standard error • Compute your t-statistic • Compute your degrees of freedom

18. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05. Control group Exp. group Person 1 45 43 2 55 49 3 40 35 4 60 51 Performing your statistical test Need to compute the mean and variability for each sample

19. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05. Control group Exp. group Person 1 45 43 2 55 49 SS = (45-50)2 + (55-50)2 + (40-50)2 + (60-50)2 3 40 35 A 4 60 51 = 250 Performing your statistical test Need to compute the mean and variability for each sample Control group = 50

20. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05. Control group Exp. group Person 1 45 43 2 55 49 SS = (43-44.5)2 + (49- 44.5)2 + (35- 44.5)2 + (51- 44.5)2 3 40 35 B 4 60 51 = 155 Performing your statistical test Need to compute the mean and variability for each sample Exp. group = 44.5

21. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05. Control group Exp. group Person 1 45 43 2 55 49 3 40 35 4 60 51 Performing your statistical test = 0.95

22. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05. Control group Exp. group Person 1 45 43 2 55 49 Two-tailed • = 0.05 3 40 35 4 60 51 Performing your statistical test = 0.95 Tobs= 0.95 Tcrit=±2.447

23. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05. Control group Exp. group Person 1 45 43 2 55 49 3 40 35 tobs=0.95 4 60 51 +2.45 = tcrit Performing your statistical test = 0.95 Tobs= 0.95 Tcrit=±2.447 Two-tailed • = 0.05 - Fail to Reject H0

24. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05. Control group Exp. group Person 1 45 43 2 55 49 3 40 35 4 60 51 Performing your statistical test = 0.95 Tobs= 0.95 Tcrit=±2.447 Two-tailed • = 0.05 Compare Tobs < Tcrit Fail to reject the H0

25. Assumptions • Each of the population distributions follows a normal curve • The two populations have the same variance • We’ll return to this next time

26. Effect Size for the t Test for Independent Means • Estimated effect size after a completed study

27. Power for the t Test for Independent Means (.05 significance level)

28. Approximate Sample Size Needed for 80% Power(.05 significance level)

29. Statistical Tests Summary (Estimated) Standard error Design Statistical test One sample,  known One sample,  unknown Two related samples,  unknown Two independent samples,  unknown