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