1

2-Sample T-Tests

•Independent t-test

•Dependent t-test

•Picking the correct test

Dr. Sinn, PSYC 301 Unit 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

Dr. Sinn, PSYC 301 Unit 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.

x

21 xx

games nov.games xx

sorority-nonsorority xx

Dr. Sinn, PSYC 301 Unit 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….– 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 μ1 – μ2 = 0

• Sampling distribution centered on this– some observed differences bigger– some observed differences smaller

Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2t p. 5

Indep t-test: formula

21ˆ

)()( 2121

xxobs s

xxt

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.

Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2t p. 6

Sampling Distribution of the Difference Between Means

Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2t p. 7

Ind. t-test: Example

Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2t p. 8

Ind. t-test: Example

Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2t p. 9

Hypothesis Testing Steps (Ind. t)

1. Comparing xbar1 and xbar2, μ and σ unknown.

2. H0: μ1 – μ2 = 0; HA: μ1 – μ2 ≠ 0

3. α = .05, df = n1+n2–2 = 5 + 5 - 2 = 8

tcritical = 2.306

4. tobtained = -1.947

5. RETAIN the H0 .

• 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)

Dr. Sinn, PSYC 301 Unit 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…

8705.3805.18

127111

ˆ21

s

xxd

380.18ˆ

22.8*5ˆ

ˆ*ˆ21

s

s

sns xx

number in one group

Dr. Sinn, PSYC 301 Unit 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

D

D

s

Dt

ˆ

Dr. Sinn, PSYC 301 Unit 2: z, t, hyp, 2t p. 12

Hypothesis Testing Steps (Dep. t)

1. Comparing xbar1 and xbar2, μ and σ unknown.

2. H0: μD = 0 HA: μD ≠ 0

3. α = .05, df=npairs –1 = 7-1 = 6, tcritical = 2.447

4. tobtained = -3.074

5. REJECT the H0 • 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.

1619.191.12

57.20357.188

ˆ21

s

xxd

Get off SPSS print-out