2 Sample TTests Independent ttest Dependent ttest Picking

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

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 Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2 t 2

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. Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2 t 3

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…. – – μv. games = μno games μv. games - μno games = 0 [Expect diff. bet means to equal zero] • With sorority study – – μv. sorority = μnon-sorority μv. sorority - μnon-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 Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2 t 4

Indep t-test: formula Actual difference observed. (For our purposes, always zero) 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 Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2 t 5

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

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

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

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 tcritical = 2. 306 4. (not needed if using SPSS) tobtained = -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. . Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2 t 9

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)… number in one group • then d… Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2 t 10

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 Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2 t 11

Hypothesis Testing Steps (Dep. t) 1. Comparing xbar 1 and xbar 2, μ and σ unknown. 2. H 0: μD = 0 H A: μ D ≠ 0 3. α =. 05, df=npairs – 1 = 7 -1 = 6, tcritical = 2. 447 4. tobtained = -3. 074 Get off SPSS print-out 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. Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2 t 12