Statistics without tears by Derek Rowntree

Author:Derek Rowntree
Language: eng
Format: epub
Tags: Statistics
Publisher: Allyn and Bacon
Published: 1981-12-07T16:00:00+00:00

106 Comparing samples

After all, the area under each sample-curve is supposed to rejTre-sent only 50 observations, while the sampling distributions of the means are supposed to represent populations of infinite size. However, although they're not tall enough on this scale, the lower parts of those two curves are correctly shown; and it is the overlap at the base that we are chiefly interested in here.)

The area where female-mean may be

greater than male-mean Blood-pressures (mm)

While there is a considerable overlap between the two samples, there is scarcely any overlap between the two distributions of possible sample-means.

We can calculate the probability of picking out a pair of samples (one female, one male) in which the female mean equalled or exceeded the male. In one in 100 cases, we might expect the men's mean to be outside the range 116 to 124. And in one in 100 cases, the women's mean might be outside the range 106 to 114. In only one out of 100 x 100 pairs of samples of fifty would both means be outside the limits. So even that possibility is extremely unlikely - one in 10,000 chances. But, even then, the female mean might be low while the male is high; or both may be low; or both may be high; only when the female mean is high and the male mean low is there a chance that the female mean would exceed the male. We would therefore have to take 4 x 10,000 samples to cover all these four equally possible eventualities. So the probability of picking out a pair of samples of 50 in which the female mean exceeds the male mean is

less than ^ 1.^^ . It is so small as to be negligible.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.