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Clinical Biostatistics: Head circumference exercise, 4

Question 4: Which of these would be suitable here?

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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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