Hypothesis Tests: Two Related Samples

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Chapter 11 Hypothesis 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
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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 difference

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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 (n9) 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
• a.05, two tailed

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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 PTSD
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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
Compute t test for related samples
df n - 1 9 - 1 8
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Step 4

• The critical value with 8 df, a.05, two-tailed
  2.306
• We calculated t 6.85
• Since 6.85 gt 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
• Cohens d
• r2

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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 mD 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?