Pet preference was compared for four different types of animals (dogs, cats, birds, and fish), using a one-way within-groups ANOVA with nine participants.The standard error was calculated as 0.19.What are the critical cutoffs for the two-tailed Tukey HSD tests for these data, assuming a p level of 0.05, given the following groups' means: Dogs M = 4.43, Cats M = 4.18, Birds M = 2.73, Fish M = 4.07?
A) -4.0 and 4.0
B) -3.90 and 3.90
C) 3.90
D) 4.0

Question

Quizplus · Accepted Answer

To calculate the Tukey HSD test, we need to first find the mean square within (MSW) by dividing the sum of squares within (SSW) by the degrees of freedom within (dfW).

SSW = 6.13 ((4.43-4.10)^2 + (4.18-4.10)^2 + (2.73-4.10)^2 + (4.07-4.10)^2) 
dfW = 27 (9 participants - 4 groups) 
MSW = SSW/dfW = 6.13/27 = 0.227

Next, we need to calculate the Tukey HSD value using the formula:

q = (M1 - M2) / SE * sqrt(2 MSE / n)

where M1 and M2 are the means being compared, SE is the standard error (given as 0.19), MSE is the mean square error (equal to MSW), and n is the sample size (equal to 9).

Comparing Dogs to Cats: q = (4.43 - 4.18) / 0.19 * sqrt(2 * 0.227 / 9) = 1.35
Comparing Dogs to Birds: q = (4.43 - 2.73) / 0.19 * sqrt(2 * 0.227 / 9) = 8.88
Comparing Dogs to Fish: q = (4.43 - 4.07) / 0.19 * sqrt(2 * 0.227 / 9) = 1.04
Comparing Cats to Birds: q = (4.18 - 2.73) / 0.19 * sqrt(2 * 0.227 / 9) = 7.11
Comparing Cats to Fish: q = (4.18 - 4.07) / 0.19 * sqrt(2 * 0.227 / 9) = 0.50
Comparing Birds to Fish: q = (2.73 - 4.07) / 0.19 * sqrt(2 * 0.227 / 9) = 4.61

Using a p level of 0.05, the critical value for q with 4 and 27 degrees of freedom (the number of groups and the total number of participants minus one, respectively) is 3.90.

Therefore, the critical cutoffs for the Tukey HSD test are -3.90 and 3.90. The correct answer is B.

Pet Preference Was Compared for Four Different Types of Animals