Chapter 11Hypothesis Tests: Two

Related Samples

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Overview Learning objectives Vocabulary lesson again Introduce t test for related samples Advantages and disadvantages An example Review questions

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Learning Objectives Difference between independent-measures

& related-samples experimental design Difference between repeated-measures &

matched-subjects experimental design Compute t test for dependent groups Advantages and disadvantages Measures of effect size

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Vocabulary Related-samples t statistic Repeated-

measures design Matched-samples design Difference scores (estimated standard error

of D-bar) Individual differences Carry-over effects

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Related-samples t statistic Two forms

• Repeated-measures design

• Matched-samples design Use difference scores between two

measurement points rather than means

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Repeated-measures The same participants give us data on two

measures (e. g. Before and After treatment)

• Aggressive responses before video and aggressive responses after

Accounts for the fact that if someone is high on one measure probably high on other.

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Matched-samples Individuals in one group are matched to

individuals in a second sample

• Matching based on variables thought to be relevant to the study

• Not always perfect match Also called matched pairs or pairwise t test

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Difference Scores Calculate difference between first and

second score (between individual scores or matched pairs)

• e. g. Difference = Before – After

• D = X2-X1

Base subsequent analysis on difference scores

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The Formulas

1,

ndfs

Dt

D

D

n

s

n

ssD

2

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Hypothesis Testing Null states that

• The population of difference scores has a mean of zero

• No systematic or consistent difference between the conditions

Alternative states that

• There is a real difference0:

0:

1

0

D

D

H

H

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Advantages of Related Samples

Eliminate subject-to-subject variability

• Makes the test more powerful Control for extraneous variables Need fewer subjects

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Disadvantages of Related Samples

Order effects Carry-over effects Subjects no longer naïve Change may just be a function of time Sometimes not logically possible

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An Example Therapy for rape victims

• Foa, Rothbaum, Riggs, & Murdock (1991)

A group (n=9) received Supportive Counseling

Measured post-traumatic stress disorder symptoms before and after therapy

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Step 1 Null: there is no difference in symptoms in

individuals after treatment Alternative: there is a difference in

symptoms α=.05, two tailed

0:

0:

1

0

D

D

H

H

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Step 2 With a sample of 9

• df = n-1 = 9-1 = 8

• Critical value = +2.306 Sketch

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The Data: Therapy for PTSDBefore After Diff.

212421263227212518

1515172017208

1910

6946

157

1368

MeanSt. Dev.

23.844.20

15.674.24

8.173.60

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Eye test of Results The Supportive Counseling group

decreased number of symptoms Was this enough of a change to be

significant? Before and After scores are not

independent; use related-samples t test

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Step 3

85.62.1

22.8

9

6.3022.8

n

sD

s

Dt

D

D

D

D

df = n - 1 = 9 - 1 = 8

Compute t test for related samples

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Step 4 The critical value with 8 df, α=.05, two-

tailed = +2.306 We calculated t = 6.85 Since 6.85 > 2.306, reject H0

Conclude that the mean number of symptoms after therapy was less than mean number before therapy.

Supportive counseling seems to work.

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SPSS Next slide shows SPSS Printout

• Similar printout from other software

• Results match ours

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Magnitude of difference by computing effect size

Two methods for computing effect size

Cohen’s d

r2

s

DdsCohen _'

dft

tr

2

22

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Review Questions Why do we say that the two sets of measures

are not independent? What are other names for “related samples?” How do we calculate difference scores?

• What happens if we subtract before from after instead of after from before?

Cont.

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Review Questions--cont. Why do we usually test H0: D = 0?

Why do we have 8 df in our sample when we actually have 18 observations?

What are the advantages and disadvantages of related samples?