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Chapter 15

Chapter 15. t Test for Two Related Samples (Repeated Measures). Repeated measures?. Whenever the same subject is measured more than once. Two related samples occur whenever each observation in one sample is paired , on a one-to-one basis, with a single observation in the other sample.

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Chapter 15

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  1. Chapter 15 t Test for Two Related Samples (Repeated Measures)

  2. Repeated measures? • Whenever the same subject is measured more than once. • Two related samples occur whenever each observation in one sample is paired, on a one-to-one basis, with a single observation in the other sample.

  3. What is compared? • The mean difference scores between the two groups. • D = Σ D n • The sign of D is crucial.

  4. Problems with repeated measures: • Enough time must pass between measures to ensure no bias or lingering effects. • Counterbalancing – half of the subjects experience the conditions in the opposite order. A then B or B then A.

  5. Hypotheses • Null Hypothesis • H0: μD = 0 • Alternative Hypothesis • Directional • H1: μD > 0 • or • H1: μD < 0 • Non Directional • H1: μD ≠ 0

  6. t ratio for two population means(two related samples) t = sample mean difference – hypothesized population mean difference estimated standard error or D - µDhyp sD

  7. Calculations • Assign a value to n, the number of difference scores • Subtract X2 from X1 to obtain D • Sum all D scores • Calculate mean of D • Calculate SS for D • Find standard error SD • Solve for t

  8. Use the EPO data

  9. Use the EPO data (p 323)

  10. Calculations SSD = ΣD2 – SD = SD = (ΣD) 2 n SSD √ n - 1 SD √ n

  11. Calculations t = D– µDhyp SD

  12. Confidence interval (p 319) • D ± (tconf)(sD) • Find value of tconf in Table B

  13. Standardized Effect Size, Cohen’s d • d = D sD

  14. Progress Check 15.2

  15. t test for population correlation (p329) • t = • ρhyp = 0 r - ρhyp 1 – r2 √ n - 2

  16. Progress Check 15.6 (p 331) • A random sample of 27 California taxpayers reveals an r = .43 between years of education and annual income. Use t to test the null hypothesis at the .05 level of significance that there is no relationship between educational level and annual income for the population of California taxpayers. Answer on 511.

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