1. 1 2-Sample T-Tests Independent t-test Dependent t-test Picking the correct test

2. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 2 Overview z-tests with distributions; z-tests with sample means t-tests with sample means New Stuff –t-tests with two independent samples e.g., Boys vs. Girls on reading ability test “Independent t-test” –t-tests with two dependent samples e.g., Hipness level Before and After “Queer Eye for a Straight Guy” “Dependent t-test” Later on: ANOVAs – 3+ samples

3. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 3 Ind. t-test: 2 sample means Compares two sample means: Both σ & μ unknown – only sample info –Compare average aggression level of 20 kids that play violent computer games to 20 kids that don’t. –Study impact of peer pressure on eating disorders. Compare average weight of sorority women vs. non-sorority women.

4. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 4 Ind. t-test: Ho What do we expect if there’s no treatment effect? What would Ho be? If video games don’t affect aggression…. – μ v. games = μ no games – μ v. games - μ no games = 0 [Expect diff. bet means to equal zero] With sorority study – μ v. sorority = μ non-sorority – μ v. sorority - μ non-sorority = 0 So, we define the Ho as μ 1 – μ 2 = 0 Sampling distribution centered on this –some observed differences bigger –some observed differences smaller

5. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 5 Indep t-test: formula Standard Error of the Difference (between the means) -difference expected between sample means -how much we expect the sample means to differ purely by chance (For our purposes, always zero) Actual difference observed.

6. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 6 Sampling Distribution of the Difference Between Means

7. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 7 Ind. t-test: Example

8. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 8 Ind. t-test: Example

9. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 9 Hypothesis Testing Steps (Ind. t) 1. Comparing xbar 1 and xbar 2, μ and σ unknown. 2. H 0 : μ 1 – μ 2 = 0;H A : μ 1 – μ 2 ≠ 0 3.α =.05, df = n 1 +n 2 –2 = 5 + 5 - 2 = 8 t critical =  2.306 4.t obtained = -1.947 5. RETAIN the H 0. The research hypothesis was not supported. The weight of women in sororities (M=111) does not differ significantly from that of other women (M=127), t(8)= -1.947, n.s.. (not needed if using SPSS)

10. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 10 Effect Size (Ind. t) Since we retained the Ho, we don’t need an effect size statistics. However, if we did, it would work like this… first calculate ŝ (standard deviation of all the scores combined) … then d… number in one group

11. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 11 Dependent T-test 2 samples – two groups are matched in some way (e.g., pairs of twins are divided between two groups) –typically the same people are in both groups (e.g., before & after design) –Example: The North American Bacon Council tests if participants change weight after 6 months of an all bacon diet. IV: Diet (normal, all-bacon); DV: Weight Standard Error of the Mean Difference

12. Dr. Sinn, PSYC 301Unit 2: z, t, hyp, 2t p. 12 Hypothesis Testing Steps (Dep. t) 1. Comparing xbar 1 and xbar 2, μ and σ unknown. 2. H 0 : μ D = 0 H A : μ D ≠ 0 3. α =.05, df=n pairs –1 = 7-1 = 6, t critical =  2.447 4.t obtained = -3.074 5. REJECT the H 0 The research hypothesis was supported. The weight of subjects before the all bacon diet (M=188.57) was significantly less than the weight after (M=203.57), t(6)= -3.074, p≤.05. The effect of the diet on weight was large, d=1.1619. Get off SPSS print-out