![]() ![]() Reports of opinion polls, election returns, and survey results typically include mention of a margin of error of plus or minus some percentage. Bray, in Encyclopedia of Social Measurement, 2005 Introduction The only way to have more confidence without increasing the width (or vice versa) is to have a larger sample size. In this case we trade precision (narrower interval) for higher confidence. Thus there are trade-offs in interval estimation just as there are in hypothesis testing. This may seem a useless statement, but it turns out that proper experimental design ( Chapter 10) can often reduce the standard deviation. 3.ĭecreasing σ has the same effect as increasing the sample size. In other words, by increasing the sample size we can increase precision without loss of confidence, or vice versa. ![]() If the sample size is increased and the confidence coefficient remains constant, the maximum error of estimation will be decreased (the confidence interval will be narrower). In other words, the more confidence we require, the less precise a statement we can make, and vice versa. If the confidence coefficient is increased ( α decreased) and the sample size remains constant, the maximum error of estimation will increase (the confidence interval will be wider). The formula for E illustrates for us the following relationships among E, α, n, and σ: 1.
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