Question

Gender HeartRate
male 70
male 71
male 74
male 80
male 73
male 75
male 82
male 64
male 69
male 70
male 68
male 72
male 78
male 70
male 75
male 74
male 69
male 73
male 77
male 58
male 73
male 65
male 74
male 76
male 72
male 78
male 71
male 74
male 67
male 64
male 78
male 73
male 67
male 66
male 64
male 71
male 72
male 86
male 72
male 68
male 70
male 82
male 84
male 68
male 71
male 77
male 78
male 83
male 66
male 70
male 82
male 73
male 78
male 78
male 81
male 78
male 80
male 75
male 79
male 81
male 71
male 83
male 63
male 70
male 75
female 69
female 62
female 75
female 66
female 68
female 57
female 61
female 84
female 61
female 77
female 62
female 71
female 68
female 69
female 79
female 76
female 87
female 78
female 73
female 89
female 81
female 73
female 64
female 65
female 73
female 69
female 57
female 79
female 78
female 80
female 79
female 81
female 73
female 74
female 84
female 83
female 82
female 85
female 86
female 77
female 72
female 79
female 59
female 64
female 65
female 82
female 64
female 70
female 83
female 89
female 69
female 73
female 84
female 76
female 79
female 81
female 80
female 74
female 77
female 66
female 68
female 77
female 79
female 78
female 77

Let denote the mean heart rate of men and women respectively. To test:

Vs

The appropriate statistical test the above hypothesis, where we compare the means of continuous observations in two independent groups, would be an independent sample t-test. But before running the test, we must ensure that, along with the data being normal, the assumption of homogeneity of variance must be satisfied. We may test this assumption using F test for equality of variance:

Vs

Using excel:

We get the output:

We find that the test is significant (p-value = 0.006 < 0.05) at 5% level.We may reject the null and hence conclude that the homogeneity of variance assumption is violated.

Hence, instead of going for an independent sample t-test, we may go for Welch's t-test, which is robust to the violation.

Test statistic = 0.63

P-value = 0.53

Now, running an ANOVA on the same data, comparing the means of two groups:

F statistic = 0.40

P-value = 0.53

In Welch independent t-test, no assumption is made on the homogeneity of variance (or standard deviation) i.e. the test is robust to the assumption of homogeneity of variance. However, ANOVA requires this assumption to be satisfied.Hence, the correct option would be:

ANOVA requires the group standard deviations to be similar.

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