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Unformatted text preview: STATISTICS 500 – Fall 2009 Homework 11, Handed out: 22 November 2009 on campus Friday, 4 Dec 2009, in lecture (11 am) or by e-mailto Chuanlong, [email protected], no later than noon. off campus Monday, 7 Dec 2009, by 4 pm to Nicole Rembert, email: [email protected] or FAX: 515-294-4040 (please include cover page with Stat 500 / Nicole Rembert). 1. power of ANOVA tests — This question reinforces a lecture point about the design of a factorial ANOVA experiment. Consider a 2 x 3 factorial, for example the data from the children’s memory experiment from HW 10. That study had 6 treatments, all combinations of 2 levels of reinforcement and 3 isolation times. Consider the following four estimates: 1. None - Verbal reinforcement, averaged over the three isolation times 2. None - Verbal, estimated only for 20 min isolation. i.e. the simple effect: none, 20min - verbal, 20min 3. 20min - 40min, averaged over the two reinforcement levels 4. Interaction between 20 and 40 min and reinforcement i.e. the difference in simple effects: (none, 20min - verbal, 20min) - (none, 40min - verbal, 40min) (a) Compute the s.e. for each contrast. Replace the contrast coefficients with the appropriate values, but you may leave the sample size as n and the error variance as σ 2 . Which contrast has the smallest standard error? Hint: Consider the design as a 1-way ANOVA and write out the appropriate coefficients for each of these contrasts. Then, remember the formula for the s.e. of a contrast in a 1-way ANOVA. Or: Work from the s.e.’s of the cell and marginal means....
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