Question

3. Reaction time experiment (L. Cai, T. Li, Nishant, and A. van der Kouwe, 1996) The experiment was run to compare the effects of auditory and visual cues on speed of response of a human subject. A personal computer was used to present a "stimulus" to a subject, and the reaction time required for the subject to press a key was monitored. The subject was warned that the stimulus was forthcoming by means of an auditory or a visual cue. The experimenters were interested in the effects on the subjects' reaction time of the auditory and visual cues and also in different elapsed times between cue and stimulus. Thus, there were two different treatment factors: "cue stimulus" at two levels "auditory"or "visual," and "elapsed time between cue and stimulus" at three levels "five," "ten,"or "fifteen" seconds This gave a total of six treatment combinations, which can be coded as 1- auditory,5sec 2- auditory,10sec 3- auditory,15sec 4= visual,5sec 5= visual, 10sec 6- visual,15sec The results of a pilot experiment, involving only one subject, are given in file reaction.time.txt . The reaction times were measured by the computer and are shown in seconds. The order of observation is shown in parentheses. A=1 and 2 for auditory and visual. B-12, 3 for 5 sec, 10 sec and 15 sec respectively (a) Identify a set of contrasts that you would find particularly interesting in this experiment. (Hint: A comparison between the auditory treatments and the visual treatments might be of interest). These are your preplanned contrasts (b) Plot the data (response on Y, treatment on X axis). What does the plot suggest about the treatments? (c) Test the hypothesis that the treatments do not have different effects on the reaction time against the alternative hypothesis that they do have different effects. State the model used, assumptions, test statistic, decision rule, ANOVA table and decision clearly (d) Estimate all parameters of the model used in above part (e) Calculate a set of simultaneous 90% confidence intervals for your preplanned contrasts, using a method or methods of your choice. Try to choose a method that will produce shortest intervals State your conclusions (f) The pilot experiment employed a single subject. Of concern to the experimenters was the possibility that the subject may show signs of fatigue. Consequently, fixed rest periods were enforced between every pair of observations. Check whether or not all the assumptions (Your answer should include all types of residual plots discussed in lecture. ) on the one-way analysis of variance model are approximately satisfied for these data. Was the experimenter's concerns about fatigue valid? (g) Instead of checking if the 6 treatment combinations are different or not, fit a two way model to check (i) if the auditory and visual stimulus has any significant effect on response time, and (ii) if the elapsed time have any significant effect on response time (h) Estimate all model parameters of the above model (i) Estimate the error variance σ2 of this model. Find a 95% confidence interval for σ2 (ie, find an upper bound U so that P(o2 < U-0.95) (j) Based on the above two analysis can you drop one source of variation and suggest a the simplest model, that brings out the systematic variation just as well as the previous two models? Fit this model, show the ANOVA table and interpr

Answer 1