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11_t_Test_Dependent

11_t_Test_Dependent - t Test for Two Dependent Samples...

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1 t Test for Two Dependent Samples Dependent samples Difference scores Null and alternative hypotheses • Mean Standard Error – Effects of dependent samples on SE t ratio Repeated measures and counter-balancing • Assumptions So far, we’ve discussed . . . t test for one sample t test for two independent samples Now we turn to . . . t test for two dependent samples
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2 Two Dependent Samples Each observation in one sample is paired with another single observation in the other sample Two Dependent Samples Each observation in one sample is paired with another single observation in the other sample Generally known as – Dependent, related, or correlated samples Two Dependent Samples Each observation in one sample is paired with another single observation in the other sample Generally known as – Dependent, related, or correlated samples Special cases – Within subjects Repeated measures – Matched subjects Example What are the effects of caffeine on memory?
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3 Example Groups: A B caffeine placebo memory test memory test Example Groups: A B caffeine placebo memory test memory test Dependent Samples We want to make certain that groups A and B are matched on cognitive factors, such as memory span – e.g., We want to match on basic memory capacity before administering caffeine and placebo Dependent Samples We want to make certain that groups A and B are matched on cognitive factors, such as memory span – e.g., We want to match on basic memory capacity before administering caffeine and placebo How could we match the participants in the two groups?
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4 Dependent Samples We might test twins – Matched subjects design Dependent Samples Groups: A B caffeine twin #1 placebo twin #2 memory test twin #1 memory test twin #2 Dependent Samples Groups: A B caffeine twin #1 placebo twin #2 memory test twin #1 memory test twin #2 Dependent Samples Because we're testing twins, the two groups (A and B) should differ little on cognitive factors We have controlled for possible cognitive differences between A and B
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5 Pair 1 A 10 B 9 D 1 2 8 6 2 3 9 10 -1 4 8 5 3 5 5 4 1 Example: Scores on Memory Test after Caffeine (A) or Placebo (B) Pair 1 A 10 B 9 D 1 2 8 6 2 3 9 10 -1 4 8 5 3 5 5 4 1 Example: Scores on Memory Test after Caffeine (A) or Placebo (B) Example: Scores on Memory Test after Caffeine (A) or Placebo (B) Pair 1 A 10 B 9 D 1 2 8 6 2 3 9 10 -1 4 8 5 3 5 5 4 1 Example: Scores on Memory Test after Caffeine (A) or Placebo (B) Pair 1 A 10 B 9 D 1 2 8 6 2 3 9 10 -1 4 8 5 3 5 5 4 1
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6 Example: Scores on Memory Test after Caffeine (A) or Placebo (B) Pair 1 A 10 B 9 D 1 2 8 6 2 3 9 10 -1 4 8 5 3 5 5 4 1 Difference Scores D : difference score D = X 1 - X 2 Difference between each pair of scores in the two dependent samples
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