11_t_Test_Dependent

11_t_Test_Dependent - t Test for Two Dependent Samples Dependent samples Difference scores Null and alternative hypotheses Mean Standard Error

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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 • Computations are simplified by working
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This note was uploaded on 08/22/2011 for the course PSY 207 taught by Professor Pfordesher during the Fall '07 term at SUNY Buffalo.

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11_t_Test_Dependent - t Test for Two Dependent Samples Dependent samples Difference scores Null and alternative hypotheses Mean Standard Error

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