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

2. Statistics for the Social Sciences Outline Review t-tests –One sample, related samples, independent samples

3. Statistics for the Social Sciences Statistical analysis follows design The related-samples t- test can be used when: –1 sample –Two scores per subject

4. Statistics for the Social Sciences Statistical analysis follows design The related-samples t- test can be used when: –1 sample –Two scores per subject –2 samples –Scores are related - OR -

5. Statistics for the Social Sciences Performing your statistical test Test statistic Diff. Expected by chance One sample z One sample tRelated samples t

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

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

8. Statistics for the Social Sciences Independent samples What are we doing when we test the hypotheses? –Consider a new variation of our memory experiment example Memory treatment Memory patients Memory Test 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:H0: HA:HA: Memory placebo Memory Test Compare these two means

9. Statistics for the Social Sciences Statistical analysis follows design The independent samples t-test can be used when: –2 samples –Samples are independent

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

11. Statistics for the Social Sciences Performing your statistical test Test statistic One-sample t Independent-samples t Sample means

12. Statistics for the Social Sciences Performing your statistical test Test statistic One-sample t Independent-samples t Population means from the hypotheses

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

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

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

16. Statistics for the Social Sciences variance Performing your statistical test “pooled variance” We combine the variance from the two samples Recall “weighted means,” need to use “weighted variances” here Variance (s 2 ) * degrees of freedom (df)

17. Statistics for the Social Sciences Performing your statistical test Independent-samples t Compute your estimated standard error Compute your t-statistic Compute your degrees of freedom This is the one you use to look up your t crit

18. Statistics for the Social Sciences Performing your statistical test Person Exp. group Control group 1 2 3 4 45 55 40 60 43 49 35 51 Need to compute the mean and variability for each sample 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.

19. Statistics for the Social Sciences Performing your statistical test Person Exp. group Control group 1 2 3 4 45 55 40 60 43 49 35 51 Need to compute the mean and variability for each sample Control group = 50 (45-50) 2 + (55-50) 2 + (40-50) 2 + (60-50) 2 = 250 SS = A 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.

20. Statistics for the Social Sciences Performing your statistical test Exp. group (43-44.5) 2 + (49- 44.5) 2 + (35- 44.5) 2 + (51- 44.5) 2 = 155 SS = B Person Exp. group Control group 1 2 3 4 45 55 40 60 43 49 35 51 Need to compute the mean and variability for each sample 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. = 44.5

21. Statistics for the Social Sciences Performing your statistical test Person Exp. group Control group 1 2 3 4 45 55 40 60 43 49 35 51 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. = 0.95

22. Statistics for the Social Sciences Performing your statistical test T obs = 0.95 T crit = ±2.447  = 0.05 Two-tailed Person Exp. group Control group 1 2 3 4 45 55 40 60 43 49 35 51 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. = 0.95

23. Statistics for the Social Sciences Performing your statistical test T obs = 0.95  = 0.05 Two-tailed T crit = ±2.447 Person Exp. group Control group 1 2 3 4 45 55 40 60 43 49 35 51 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. +2.45 = t crit - Fail to Reject H 0 t obs =0.95 = 0.95

24. Statistics for the Social Sciences Performing your statistical test T obs = 0.95  = 0.05 Two-tailed T crit = ±2.447 T obs T crit Compare < Fail to reject the H 0 Person Exp. group Control group 1 2 3 4 45 55 40 60 43 49 35 51 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. = 0.95

25. Statistics for the Social Sciences 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. Statistics for the Social Sciences Effect Size for the t Test for Independent Means Estimated effect size after a completed study

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

28. Statistics for the Social Sciences Approximate Sample Size Needed for 80% Power (.05 significance level)

29. Statistics for the Social Sciences Statistical Tests Summary DesignStatistical test (Estimated) Standard error One sample,  known One sample,  unknown Two related samples,  unknown Two independent samples,  unknown