A university department head was interested in performance of students in four d

Question

A university department head was interested in performance of students in four different sections of introductory biology. Ten students were randomly selected from each of the four sections (morning A, morning B, Afternoon A, Afternoon B). The final scores for the students were collected. The resulting scores were used to conduct an ANOVA procedure which was found to be significant. Then a Tukey's HSD multiple comparison procedure was conducted and the following output produced.

The HSD is missing from this output (replaced with AAAA). Calculate the missing value.

a. Afternoon A

b. Morning B

c. Afternoon B

d. none of the groups are different from Morning A.

Based on this output what groups are different from MorningA? Select all that apply.

0.05 Alpha Error Degrees of Freedom Error Mean Square Critical Value of Studentized Range 3.800 36 9.923 Mean N section A 81.169 10 MorningA B 75.141 10 AfternnA 69.887 10 AfternnB

Explanation / Answer

HSD = q * sqrt (MSE/n)

        = 3.8 * sqrt (9.923/10)

        = 3.785

Minimum Significant Difference: 3.785

|Morning A – Morning B| = | 81.169 – 82.008| = 0.839     Þ insignificant

| Morning A – Afternoon A | = | 81.169 – 75.141| = 6.028 Þ significant

|Morning A – Afternoon B| = | 81.169 – 69.887 | = 11.282 Þ significant

If the difference value is more than the HSD value then the difference is significant.

Groups are different from Morning A:

Option a: Afternoon A

       Option c: Afternoon B

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