Question

2. This data comes from the paper by Cai et al, 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. Thurs, there were a total of six treatment combinations, which were coded as, 1 auditory, 5 seconds 2 = auditory, 10 seconds 3 auditory, 15 seconds 4 = visual, 5 seconds 5 = visual, 10 seconds 6 = visual, 15 seconds Suppose we were interested in the four contrasts T1 - T4, T2 – T5, T3 – T6, and (T1 + T2 +T3)/3 – (T4+75 +T6)/3 a. Interpret the contrasts of interest in the context of the problem. b. Based on the problem statement, formulate a hypothesis involving each contrast and conduct each hy- pothesis test at individual level a = 0.05. Carefully justify your hypotheses, explain your results, and clearly state your conclusion. c. What is the overall significance of these four tests? (i.e. what is the probability that at least one of the tests results in a false positive if all the null hypotheses are actually true?)

Answer 1

The contrasts of interest in this problem are comparing the effects of auditory and visual cues and different elapsed times on reaction time. Hypothesis tests can be conducted to determine if there are significant differences. The overall significance can be evaluated using the familywise error rate.

Step-by-step explanation:

The contrasts of interest in this problem are comparing the effects of auditory and visual cues, as well as different elapsed times between cue and stimulus, on the reaction time of the human subject. The four contrasts T1 - T4, T2 – T5, T3 – T6, and (T1 + T2 + T3)/3 – (T4 + T5 + T6)/3 represent specific comparisons between these treatment combinations.

To formulate hypotheses for each contrast, we can assume that there is no difference in reaction time between the treatments being compared. We can then conduct hypothesis tests at an individual level with a significance level of 0.05 to determine if there is enough evidence to reject these null hypotheses.

The overall significance of these four tests can be determined by considering the probabilities of all null hypotheses being true and not obtaining any false positives. This probability is known as the familywise error rate and is typically controlled using methods such as the Bonferroni correction.