





Determining sample size: an exampleSuppose you are investigating mean personal income. You want to determine the sample size needed so that your sample estimate is within $500 of the true population value. Furthermore, you want to be 95% confident that the sample mean falls within $500 of the actual, unknown population mean. Now you need an estimate of the variance in the population. Some a priori knowledge of the subject matter is often sufficient to guide this judgment. Based on past studies you have read and your own experience, you make a judgment about the size of the population standard deviation: $1,000. Confidence level: 95% Desired precision: +/ $500 Estimated standard deviation: +/$1,000 Required sample size: 15.37 or 16 Wow! You only need a sample size of 16 to estimate mean personal income when the population standard deviation is $1000 and allowed precision is $500. But suppose you want to be more precise, say twice as precise? $500 is not a very precise interval to use, relative to your estimated standard deviation of $1,000. You accomplish this by halving the width of the desired precision interval. Then, Confidence level: 95% Desired precision: +/ $250 Estimated standard deviation: +/$1,000 Required sample size: 61.47 or 62 Notice the tradeoff; doubling your precision increased your sample size by nearly a factor of four. Whenever precision is increased by a factor of x, sample size is increased by a factor of x^{2}. Some practical hints include assuming the worstcase scenario in order to be conservative with your estimates of sample size. One way to accomplish thisthe example is particularly simple using proportional datais to assume maximum variability or disagreement (i.e. a 50/50 split).


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