Question

3. Let us continue to study the keyboard experiment from the first lecture (last slide of Lecture 1). Let y be the amount of time used to type up a manuscript. Note that y depends on the keyboard, the manuscript, whether the manuscript has already been typed once and experimental error. Let ,1A and ,1B denote the effects of keyboard A and B respectively. T, denote the effect of manuscript i for i = 1, .. , 6 and denote the experimental error. Let ai denote the learning effect of typing the manuscript once. We are interested in estimating the difference between ,1A and μΒ Suppose Design 2 from the lecture notes is used in the experiment, which is An additive statistical model for the amount of time used in the run 1: A is and the model for the amount of time used in the run1: B is where γ is some constant. (a) Is ou positive or negative? Why is it not included in the first model? (b) Write down the statistical models for the other runs (e) Regardless of which design is used, what is the simplest estimate for μΑ yǐA ,M6B? using y1A,n, μΒ d) Explain why the third design is the best one. (Hit: Consider the bias of the estimator of HA-HB under the three different designs

Answer 1

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