Statistical Inference and Probability by MacInnes John;

Author:MacInnes, John; [MacInnes, John]
Language: eng
Format: epub
Publisher: SAGE Publications
Published: 2021-05-03T08:30:47.410345+00:00

For a 95% CI that would give us a range for the 0.053 = - 0.032 up to 0.021 + 0.053 = +0.074.

It would not be safe to conclude that the small difference we see in our sample is one we would have seen in the population had we been able to measure it. Note that this failure to reject the null hypothesis does not allow us to conclude that there was no difference between how men and women voted, only that if such a difference existed, its size was not substantial enough for us to be confident about such a result from the evidence we gathered.

What happens to null hypotheses that are not rejected? Rather than being accepted, they settle into a kind of epistemological limbo. This might seem obtuse, and Jerzey Neyman, the original proponent of confidence intervals, made the case for switching the focus onto the costs and benefits of any errors arising from deciding to reject or accept a hypothesis. The most important factor to think about is the power of our test, which describes the kind of effect size our methods are capable of discovering. In the example we are looking at here, our sample is not large enough to give solid evidence of a two percentage point difference in voting behaviour, if that is what actually existed in the target population. Had the difference been greater – around 5% – we would have found it easier to detect. Imagine we have found that 235 women (0.358) and 265 men (0.413) had voted Conservative. Now our calculations would be as follows:

SE = = 0.027, 1.96 * 0.027 = 0.053

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