Writing contrasts. Return to the eye study described in given Example. Let μ₁, μ₂, μ₃, and μ₄ represent the mean scores for blue, brown, gaze down, and green eyes.

(a) Because a majority of the population sampled is Hispanic (eye color predominantly brown), we want to compare the average score of the brown eyes with the average of the other two eye colors. Write a contrast that expresses this comparison.

(b) Write a contrast to compare the average score when the model is looking at you versus the score when looking down.

Example

Sleep deprivation and reaction times. Sleep deprivation experienced by physicians during residency training and the possible negative consequences are of concern to many in health care. One study of 33 resident anesthesiologists compared their changes from baseline in reaction times on four tasks.⁸ Under baseline conditions, the physicians reported getting an average of 7.04 hours of sleep. While on duty, however, the average was 1.66 hours. For each of the tasks, the researchers reported a statistically significant increase in the reaction time when the residents were working in a state of sleep deprivation.

(a) If each task is analyzed separately as the researchers did in their report, what is the appropriate statistical method to use? Explain your answer.

(b) Is it appropriate to use a one-way ANOVA with I = 4 to analyze these data? Explain why or why not.