ch. 11&12_110409

ch. 11&12_110409 - Lab 227 Chapter 11...

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Lab 227 11/04/09 Chapter 11 - Repeated-Measures t-test Overview Repeated measures t-test is used when we want to measure the same people twice (e.g. over time). Advantage: minimize differences between conditions (time points) that are not due to the treatment – reduce error. Disadvantage: other confounding variables that are related to time can affect the outcome (e.g. fatigue, practice effects). Instead of looking at the difference between two means, we compute the mean difference (M D ) and the standard error of mean of difference scores ( SMD ). Hypotheses: The null hypothesis states that the mean of difference scores is zero H 0 : µ D = 0 The alternative hypothesis states that the mean of difference scores is different from zero H 1 : µ D ≠ 0 Overall t formula: = - t MD μDSMD Because µ D = 0 under the null hypothesis, we can eliminate it from the formula. = t MDSMD Standard error: Because we are essentially dealing with one sample mean, we can compute the standard error in the same way we did for the one-sample t-test. We compute the standard error from the difference scores and not from the raw scores. = SMD S2n Degrees of freedom: We use the difference scores to compute df but they remain the same: n-1. Example 1
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A researcher is testing the effects of a diet on weight loss in a sample of n=5 participants. She measures the participants when beginning the diet and then 6 months later. Is there a statistically significant difference in weight between the two time points? Test at the .05 level of significance. Participant Weight beginning Diet Weight at 6 months Difference (D) D 2 1 230 210 20 400 2 199 191 8 64 3 208 183 25 625 4 195 180 15 225 5 212 198 14 196 ∑D = 82 ∑D 2 = 1510 M D = = = . Dn 825 16 4 = -( ) = - = . SSD D2 D 2n 1510 67245 165 2 = = . = . S2 SSdf 165 24 41 3 Step 1 H 0 : µ
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ch. 11&12_110409 - Lab 227 Chapter 11...

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