Using four methods to teach ANOVA, do these four samples differ enough from each

Question

Using four methods to teach ANOVA, do these four samples differ enough from each other to reject the null hypothesis that type of instruction has no effect on mean test performance?

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Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that test score is related to teaching method.

One of the conditions that allows us to use ANOVA safely is that of equal (population) standard deviations. Can we assume that this condition is met in this case?

Yes, since 0.793 0.360 < 2.

No, since 0.793/0.360 > 2

No, since the four sample standard deviations are not all equal.

No, since the population standard deviations are not given, so we cannot check this condition.

Method to teach ANOVA Mean SD N method 1 (single teacher) 4.85 0.360 34 method 2 (co-teachers) 4.61 0.715 31 method 3 (computer) 4.61 0.688 36 method 4 (lab) 4.38 0.793

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Explanation / Answer

The assumption, that the populations' standard deviations are equal, is important in principle, and it can only be approximately checked by using as bootstrap estimates the sample standard deviations. In practice, statisticians feel safe in using ANOVA if the largest sample SD is not larger than twice the smallest.

Largest Sample SD = 0.793

Smallest Sample SD = 0.360

so Largest sample SD/ Smallest samle SD = 0.793/0.360 = 2.20> 2

so the answer is option b => No, since 0.793/0.360 > 2

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