Hypothesis Tests with Two Related Samples

1
Hypothesis Tests withTwo Related Samples

• Unit 9
• Ch 11 1-5, 7, 9, 11a, 13, 15 (pp. 307-309)

2
Related Samples

• Also called Dependent Samples
• 2 samples are statistically related
• repeated-measures
• matched-subjects
• Order of data in each sample important
• Not independent
• must modify hypothesis testing

3
Repeated-measures

• 2 measurements of same individual
• Pretest-posttest design
• measure each individual twice
• pretest ? treatment ? posttest
• compare scores

4
Matched-subjects

• Match individuals on important characteristic
• individuals that are related
• IQ, GPA, married, etc
• Assign to different treatment groups
• each group receives different levels of
  independent variable

5
Related-samples Designs

• Strength
• not affected by individual differences
• reduces s2
• repeated-measure needs fewer subjects
• Weaknesses
• carryover effects
• effects from1st test influence 2d test
• progressive error
• effects due only to repeated testing
• fatigue, practice, etc.

6
Difference Score

• D X2 - X1
• Requires n1 scores equal n2 scores
• Repeated-measures
• individuals 2d score minus 1st score
• Matched subjects
• subjects score in group 2 minus related score
  in group 1
• Get 1 sample of difference scores

7
Assumptions Related Samples

• Population of difference scores is normal
• Observations within each treatment independent
• scores for each subject in a group is independent
  of other subjects scores

8
Related-samples Hypotheses

• Nondirectional
• H0 m D 0
• H1 m D ? 0
• Directional
• H0 m D gt 0
• H1 m D lt 0
• Remember it depends on the direction of the
  prediction

9
Sample Statistics

• Mean difference

• Mean for single sample

10
Sample Statistics

• Standard deviation of differences

• n number of difference scores

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Sample Statistics

• Alternative formulas for s

Definitional formula
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Standard Deviation Related-samples
Single sample
13
Estimated Standard Error

• Calculate same as single sample
• use standard deviation of difference scores

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Test Statistic

• Related-samples t test

• Since mD 0

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Example

• Does drinking 3 oz of alcohol affect performance
  on an object recognition task?
• n 4
• pretest-posttest
• count number of errors
• 1. State Hypotheses
• H0 mD 0
• H1 mD ¹ 0

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Example

• 2. Set criterion for rejecting H0,
• a .05
• directionality?
• df
• tCV

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Example

• 3. Collect Sample, compute statistics
• X 2 X 1 D D2
• 6 1
• 7 1
• 7 2
• 4 2

5
25
36
6
5
25
4
2
90
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S D
S D2
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Example

• 3. compute standard deviation

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Example

• 3. compute estimated standard error

20
Example

• 3. compute test statistic

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Example

• 4. Interpret results
• Is tobs in critical region?
• decision
• Change directionality or a
• same as previous units