Hypothesis Tests: Two Related Samples
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Hypothesis Tests: Two Related Samples. 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.

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Hypothesis Tests: Two Related Samples

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Hypothesis tests two related samples

Hypothesis Tests: Two Related Samples


Related samples

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.


Related samples cont

Related Samples--cont.

  • Correlation between before and after scores

    • Causes a change in the statistic we can use

  • Sometimes called matched samples or repeated measures


Difference scores

Difference Scores

  • Calculate difference between first and second score

    • e. g. Difference = Before - After

  • Base subsequent analysis on difference scores

    • Ignoring Before and After data


An example

An Example

  • Therapy for rape victims

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

  • One group received Supportive Counseling

  • Measured post-traumatic stress disorder symptoms before and after therapy


Therapy for ptsd

Therapy for PTSD


Results

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.

    • See raw data

    • r = .64

Cont.


Results cont

Results--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


T test

t test

D and sD = mean and standard deviation of differences.

df = n - 1 = 9 - 1 = 8

Cont.


T test cont

t test--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.


Advantages of related samples

Advantages of Related Samples

  • Eliminate subject-to-subject variability

  • Control for extraneous variables

  • Need fewer subjects


Disadvantages of related samples

Disadvantages of Related Samples

  • Order effects

  • Carry-over effects

  • Subjects no longer naive

  • Change may just be a function of time

  • Sometimes not logically possible


Effect size again

Effect Size Again

  • 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.


Effect size cont

Effect Size, cont.

Cont.


Effect size cont1

Effect Size, 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.


Iq pill

IQ Pill


Iq pill1

IQ Pill


Computing t

Computing t


Interpreting t

Interpreting t

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.


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