Exercise: Head circumference, 4

Question 4: Which of these would be suitable here?

Suggested answer

The samples are fairly large, both greater than 50, so we could use the large sample z method. The distributions are slightly skew, with two rather extreme values for the males, and the spread of the distribution looks slightly wider for the males. The two sample t test is very robust to small departures from assumptions, so it would make very little difference which method we used.

As many programs do not provide a separate large sample test, we may have to use the command for the two sample t method with unequal variances is any case. This give the mean difference, males minus females, = 18.6 mm, standard error = 3.4 mm, 95% confidence interval = 11.9 to 25.4 mm, t = 5.45, P<0.0001. The t method with equal variances gives mean difference, males minus females, = 18.6 mm, standard error = 3.3 mm, 95% confidence interval = 12.2 to 25.1 mm, t = 5.73, P<0.0001.

There does not seem much point in giving the confidence interval to three significant figures and we can round both confidence intervals to 12 to 25 mm.

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