1. Statistics for the Social Sciences Psychology 340 Fall 2006 Using t-tests

2. Statistics for the Social Sciences Outline (for 2 weeks) Review t-tests –One sample, related samples, independent samples –Additional assumptions Levene’s test

3. Statistics for the Social Sciences Testing Hypotheses –Step 1: State your hypotheses –Step 2: Set your decision criteria –Step 3: Collect your data –Step 4: Compute your test statistics Compute your estimated standard error Compute your t-statistic Compute your degrees of freedom –Step 5: Make a decision about your null hypothesis Hypothesis testing: a five step program

4. Statistics for the Social Sciences t Test for Dependent Means Unknown population mean and variance Two situations –One sample, two scores for each person Repeated measures design –Two samples, but individuals in the samples are related Same procedure as t test for single sample, except –Use difference scores –Assume that the population mean is 0

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

6. 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 -

7. Statistics for the Social Sciences Performing your statistical test Diff. Expected by chance Estimated standard error of the differences Test statistic What are all of these “D’s” referring to? Mean of the differences Number of difference scores Difference scores –For each person, subtract one score from the other –Carry out hypothesis testing with the difference scores Population of difference scores with a mean of 0 –Population 2 has a mean of 0

8. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Difference scores 2 6 5 9 22 Person Pre-test Post-test 1 2 3 4 45 55 40 60 43 49 35 51 (Pre-test) - (Post-test) H0:H0: There is no difference between pre-test and post- test HA:HA: There is a difference between pre-test and post- test  D = 0  D ≠ 0

9. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Difference scores 2 6 5 9 22 = 5.5 Person Pre-test Post-test 1 2 3 4 45 55 40 60 43 49 35 51 (Pre-test) - (Post-test)

10. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person Pre-test Post-test Difference scores 1 2 3 4 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5

11. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person Difference scores 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 -3.5- 5.5 = 0.5- 5.5 = -0.5- 5.5 = 3.5- 5.5 = 12.25 0.25 12.25 25 = SS D D - D(D - D) 2

12. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 -3.5 0.5 -0.5 3.5 D - D Difference scores 12.25 0.25 12.25

13. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D -3.5 0.5 -0.5 3.5 D - D Difference scores 12.25 0.25 12.25

14. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D ? Think back to the null hypotheses -3.5 0.5 -0.5 3.5 D - D Difference scores 12.25 0.25 12.25

15. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D H 0 : Memory performance at the post-test are equal to memory performance at the pre-test. -3.5 0.5 -0.5 3.5 D - D Difference scores 12.25 0.25 12.25

16. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D This is our t obs -3.5 0.5 -0.5 3.5 D - D Difference scores 12.25 0.25 12.25

17. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D t obs  = 0.05 Two-tailed t crit -3.5 0.5 -0.5 3.5 D - D Difference scores 12.25 0.25 12.25

18. Statistics for the Social Sciences +3.18 = t crit - Reject H 0 Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D t obs  = 0.05 Two-tailed t crit -3.5 0.5 -0.5 3.5 D - D Difference scores 12.25 0.25 12.25 t obs =3.8

19. Statistics for the Social Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D t obs  = 0.05 Two-tailed t crit T obs > t crit so we reject the H 0 -3.5 0.5 -0.5 3.5 D - D Difference scores 12.25 0.25 12.25

20. Statistics for the Social Sciences Using SPSS Person Pre-test Post-test 1 2 3 4 45 55 40 60 43 49 35 51

21. Statistics for the Social Sciences Next time Independent samples t-tests