This activity gives you practice assessing whether the assumptions of a statisti

Question

This activity gives you practice assessing whether the assumptions of a statistical test have been met.

A researcher interested in the effect of temperature on athletic ability timed how long it took two groups of people to sprint 50 yards. One group sprinted after spending 15 minutes in an extremely hot room (105 degrees F), and the other group sprinted after spending 15 minutes in a comfortable (71 degrees F) room. Sixty people were recruited and, to avoid exposing a large number of people to extreme heat, 20 were assigned to the hot room and 40 to the comfortable room. The distribution of times for the hot group was slightly positively skewed with a mean of 7.8 seconds and a variance of 4.2 seconds. The distribution of times for the comfortable group was normal with a mean of 6.7 and a variance of 0.9 seconds. An independent means t test was performed.

Why shouldn’t you use a t test to analyze these data?
The assumption of homogeneity of variances is violated to a degree that the test is unlikely to be robust

Temperature and athletic ability study
Explain/Justify your answer to the previous question.

Explanation / Answer

One of the core assumptions of a t-test is homoscedasticity or homogeneity of variance and in this case, the variance of the two groups are highly unequal. If this assumption it not met, researchers cannot draw accurate and specific inferences about the rejection of the null hypothesis.

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