Ch. 14--Student's T test for correlated, independent samples

1. Introduction













2.Student's T for correlated groups.

A. Correlated groups defined

i. one sample, two observations





ii. Two samples









B. Hypothesis generation for correlated group designs





















C. Calculating the statistic tobt using, D

Recall for single sample:

















Testing a headache drug: Two groups who have been matched on sex, age and SES are asked to participate. Group one gets a placebo and group 2 gets our new drug. We want to know if your drug reduces headache intensity. We measure headache intensity on a scale (lower scores=lower intensity). Test at alpha = .01 1 tailed.

Group 1 Group 2

98 82

96 72

140 90

120 108

130 72

125 80

110 98

D. Evaluating the statistic



















3. Student's t for independent samples

A. Independent groups defined









B. Hypothesis generation for independent group designs









C. Calculating the statistic,



i. sampling distribution

















Ii. tobt for independent samples

e.g.,

Group 1-given joke Group 2-no joke

18 9

16 13

21 8

14 15

17 17

19 21

22 11

24

25

18



D. Evaluating the statistic, df= n1 + n2 -2























E. tobt when sample sizes are equal





4. Assumptions in using the t test

A. correlated samples

B. independent samples





i. sampling distribution of x1- x2 is normally distributed





ii. Homogeneity of variance = the variances in the populations from which the samples means were sampled are equal

C. t is robust, especially when n > 30.



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