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Hypothesis Tests: Two Related Samples

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Hypothesis Tests: Two Related Samples

- The same participants give us data on two measures
- e. g. Before and After treatment
- Aggressive responses before video and aggressive responses after

- With related samples, someone high on one measure is probably high on other.

Cont.

- Correlation between before and after scores
- Causes a change in the statistic we can use

- Sometimes called matched samples or repeated measures

- Calculate difference between first and second score
- e. g. Difference = Before - After

- Base subsequent analysis on difference scores
- Ignoring Before and After data

- Therapy for rape victims
- Foa, Rothbaum, Riggs, & Murdock (1991)

- One group received Supportive Counseling
- Measured post-traumatic stress disorder symptoms before and after therapy

- The Supportive Counseling group decreased number of symptoms
- Was this enough of a change to be significant?
- Before and After scores are not independent.
- See raw data
- r = .64

Cont.

- If no change, mean of differences should be zero
- So, test the obtained mean of difference scores against m = 0.
- Use same test as in Chapter 12.

- We don’t know s, so use s and solve for t

D and sD = mean and standard deviation of differences.

df = n - 1 = 9 - 1 = 8

Cont.

- With 8 df, t.025 = +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.

- Eliminate subject-to-subject variability
- Control for extraneous variables
- Need fewer subjects

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

- We could simply report the difference in means.
- Diff = 8.22
- But the units of measurement have no particular meaning to us—Is 8.22 large?

- We could “scale” the difference by the size of the standard deviation.

Cont.

Cont.

- The difference is approximately 2 standard deviations, which is very large.
- Why use standard deviation of Before scores?
- Notice that we substituted statistics for parameters.

t(4) = 1.236, p > .05.

Do not reject null hypothesis

Sample came from population in which mean difference score = 0

IQ scores after taking the pill (M = 102.4) were not significantly higher than IQ scores before taking the pill (M = 99.4), t(4) = 1.24, p > .05.