Psy 230 Stats/Methods I

Chapter 11

Related (Paired) Samples t-test

I.  Compare Designs

A. Independent-measures design

Also called between subjects design

Two separate samples are used to obtain the two sets of data to be compared.

     B. Repeated-measures design 

Also called within subjects design

Two scores are obtained from the same sample of individuals.

Advantage—uses same subjects in all treatment conditions. No risk that Ss in one treatment are substantially different from the Ss in another. 

II. Related (Paired) Samples t-test

A. Logic

Analogous to single-sample t statistic

Based on difference scores rather than raw scores (X values).

How much change occurs as a result of the treatment?

The two scores for each subject are summarized as a single difference score.

       B. Example

At the .01 level of significance, can it be concluded that the course will result in a significant weight loss?

Name            Before             After    D

Wellman            155             154        -1

Gersten              228             207        -21

Tamayo              141             147        6

Miller                 162             157        -5

Ringman           211             196        -15

Garbe                 185             180        -5

Monk                 164             150        -14

Heilbrunn         172             165        -7

Difference score = D = X₂ – X₁

 _{For a two-tailed test:}

H ₀: µ_D = 0 

H ₁:µ_D ≠ 0 

What about for a one-tailed test?

       C. Formulas

III. Assumptions of the related samples t-test

A.  The observations within each treatment condition must be independent.

B.  The population distribution of difference scores (D values) must be normal.