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, 2t
p. 2
Ind. t-test: 2 sample means
• Compares two sample means:
x1  x2
• Both σ & μ unknown – only sample info
– Compare average aggression level of 20 kids that play violent
computer games to 20 kidsx that don’t.
xv.games  xno games
– Study impact of peer pressure on eating disorders. Compare
average weight of sorority women vs. non-sorority women.
xsorority  xnon-sorority
Dr. Sinn, PSYC 301
Unit 2: z, t, hyp, 2t
p. 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 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. 4
Indep t-test: formula
Actual difference
observed.
tobs
(For our
purposes,
always zero)
( x1  x2 )  ( 1   2 )

sˆx1  x2
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, 2t
p. 5
Sampling Distribution of the Difference
Between Means
Dr. Sinn, PSYC 301
Unit 2: z, t, hyp, 2t
p. 6
Ind. t-test: Example
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
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
(not needed if using SPSS)
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..
Dr. Sinn, PSYC 301
Unit 2: z, t, hyp, 2t
p. 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
sˆ  n * sˆx1  x2
• then d…
sˆ  5 * 8.22
sˆ  18.380
x1  x2 111  127
d

 .8705
sˆ
18.3805
Dr. Sinn, PSYC 301
Unit 2: z, t, hyp, 2t
p. 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
D  D
t
Dr. Sinn, PSYC 301
Unit 2: z, t, hyp, 2t
sˆD
p. 11
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
x1  x2 188.57  203.57
d

 1.1619
sˆ
12.91
Get off SPSS print-out
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.
Dr. Sinn, PSYC 301
Unit 2: z, t, hyp, 2t
p. 12