To determine whether there is a relationship between the type of school attended

Question

To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school. [Raftery, A.E. and Hout, M. (1985). Does Irish education approach the meritocratic ideal? A logistic analysis. Economic and Social Review, 16, 115-140.]

Here are the three sample standard deviations for the verbal reasoning scores for the three groups (secondary school, vocational school, and primary school only):

Based on this information, do the data meet the condition of equal population standard deviations for the use of the ANOVA?

A. Yes, because 14.18 - 11.71 < 2.

B. Yes, because 14.18/11.71 < 2.

C. No, because the standard deviations are not equal.

D. Unable to determine from the information provided.

A. Yes, because 14.18 - 11.71 < 2.

B. Yes, because 14.18/11.71 < 2.

C. No, because the standard deviations are not equal.

D. Unable to determine from the information provided.

Explanation / Answer

Correct option:

B, Yes, because 14.18/11.71 < 2.

EXPLANATION:

Condition for ANOVA:

Equal population standrd deviations: This is checked by using as bootstap estimtes the sample standard deviatins. The largest sample SD must not be larger than twice the smallest.i.e., largest SD /smallest SD < 2. Here, 14.14/11.71 < 2.

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