Repeated Measures

1

Repeated Measures or Matched Subjects Designs Two Related Samples t-test

I. Assumptions for t-test

A. Populations 1. population from which the sample is selected is normal 2. two populations must have equal variances (i.e. are the same population)

B. One random sample (each tested twice) with each subject experiencing two conditions 1. Individuals in one treatment are directly related (one-to-one) to individuals in

the other treatment a. Repeated measures (same person does both treatments)

(1) danger of order effect (i.e. carryover, practice, fatigue) (2) must counterbalance to erase order effect

b. Matched subjects (matched twins substitute for same person’s scores) C. Data values

1. Sample values known (mean, standard deviation) 2. Difference (D) values between two treatments utilized (mean, standard dev) 3. Populational values (mean, standard deviation) not known

II. Diagramming your research (shows the whole logic and process of hypothesis testing) a. Draw a picture of your research design (see diagramming your research handout). b. There are always two explanations (i.e. hypotheses) of your research results, the

wording of which depends on whether the research question is directional (one-tailed) or non-directional (two-tailed). State them as logical opposites.

c. For statistical testing, ignore the alternative hypothesis and focus on the null hypothesis, since the null hypothesis claims that the research results happened by chance through sampling error.

d. Assuming that the null is true (i.e. that the research results occurred by chance through sampling error) allows one to do a probability calculation (i.e. all statistical tests are nothing more than calculating the probability of getting your research results by chance through sampling error).

e. Observe that there are two outcomes which may occur from the results of the probability calculation (high or low probability of getting your research results by chance, depending on the alpha (α) level).

f. Each outcome will lead to a decision about the null hypothesis, whether the null is probably true (i.e. we then accept the null to be true) or probably not true (i.e. we then reject the null as false).

III. Hypotheses

A. Two-tailed (non-directional research question) 1. Alternative hypothesis (H1): The independent variable causes a difference in

performance between the two treatments. 2. Null hypothesis (H0): The independent variable does not cause a difference in

performance between the two treatments other than by sampling error. B. One-tailed (directional research question)

1. Alternative hypothesis (H1): The independent variable causes one treatment to perform better or less than the other.

2. Null hypothesis (H0): The independent variable causes the one treatment to

2

perform in an opposite effect than expected or no change in performance.

IV. Determine critical regions (i.e. critical t value between high & low probability) using table A-27 A. Significance level (should be given or decided prior to experiment)

1. α or p = .05, .01, or .001 B. One- or two-tailed test

1. One-tailed: use the first row across the top 2. Two-tailed: use the second row across the top

C. Degrees of freedom 1. df = n - 1

D. With degrees of freedom and one- or two-tailed p values, find the critical t value 1. If two-tailed, then critical t value is ± t value 2. If one-tailed, then determine if critical t value is + or - t

V. Calculate t-test statistic A. t-test formula for two related samples (note: D is the difference of the two raw scores

per person or per paired person)

t = DM where D = x1 - x2 & DM = ∑D standard error n

B. Calculations

1. Compute variance

s 2 =

∑𝐷2 − (∑𝐷)2

𝑛

𝑛−1 or

𝑆𝑆𝐷

𝑑𝑓

2. Compute standard error (Note: standard error is simply an estimate of the

average sampling error which may occur by chance, since a sample can never give a totally accurate picture of a population

𝑠𝐷 = √ 𝑠2

𝑛

3. Compute t-test statistic

t = 𝐷𝑀

𝑠𝐷

B. Compare calculated t-statistic to critical t-value & make decision

1. Reject null and accept alternative or 2. Accept null

VI. Reporting the results of a related samples (repeated measures) t test

“The group performed better after experiencing treatment (M = 25, SD = 4.22) than before experiencing treatment (M = 19, SD = 4.71). This difference was significant, t(18) = 3.00, p < .05, two-tailed.”