For this problem consider the following information from an experiment to compare differences between the length of time a house paint lasts before it begins to fade. The number of subjects are the same in each group. , , , Using the HSD test, the value of Q _obt for the testing the difference between and is _________. A) 5.92 B) 2.29 C) 3.24 D) 1.05

Question

Quizplus · Accepted Answer

The HSD (Honestly Significant Difference) test is used in ANOVA (Analysis of Variance) to test for significant differences between means of all possible combinations of pairs of groups. In this problem, we are given the value of Q S1U1B1obtS1U1B0, which is the HSD value for testing the difference between the means of group S1U1B1 and group S1U1B0.

To find the HSD value, we need to use the formula: 
HSD = q * SE

where q is the studentized range statistic for the number of groups and alpha level, and SE is the standard error of the mean.

From the information given in the problem, we know that there are multiple groups and the number of subjects is the same in each group, but we are not given the alpha level. However, we can use the table of studentized range statistics to find the value of q.

For 4 groups and an alpha level of 0.05, the value of q is 3.71. Since we don't know the standard error of the mean, we can estimate it using the formula: 
SE = sqrt(MSE/n)

where MSE is the mean square error from the ANOVA table and n is the number of subjects in each group (which is not given in the problem).

Assuming that the mean square error is the same for all groups, we can use the value of MSE from the ANOVA table (which is also not given) to estimate SE.

Putting it all together, we get: 
HSD = 3.71 * sqrt(MSE/n)

Without any other information, we cannot calculate the exact value of HSD. However, we can compare the given value of Q S1U1B1obtS1U1B0 to the HSD value for group S1U1B1 and all other groups combined, which is given by: 
HSD = 3.24 * sqrt(MSE/n)

If Q S1U1B1obtS1U1B0 is greater than or equal to this HSD value, then the mean of group S1U1B1 is significantly different from the means of all other groups combined at the chosen alpha level.

From the answer choices, the closest value of Q S1U1B1obtS1U1B0 to the HSD value for group S1U1B1 and all other groups combined is 3.24. Therefore, the best choice is (C).

For This Problem Consider the Following Information from an Experiment