Here, we want to obtain the sample size required to estimate a population parameter to a given margin of error. We will not use specific values but will find the number of samples required to estimate a mean with a confidence interval ±0.5 and ±1 standard deviation wide.
The following steps will identify the number of samples required to find an estimate of the population mean to a confidence interval of +/- 0.5 and +/-1 standard deviations wide:
- Go to the Stat menu, go to Power and Sample Size, and select Sample Size for Estimation….
- In the Parameter section, select Mean (Normal) from the dropdown.
- Under Planning Value, enter Standard deviation: as
1. - In Margins of error for confidence intervals:, enter
0.5and1(separated by a space). - Click on OK.
We are trying to find the sample size required to estimate the population mean as +/- 0.5 or 1 standard deviations. Eighteen samples would give us a confidence interval that is 1 standard deviation wide; seven samples would give us a confidence interval of 2 standard deviations wide. This tool does not tell us the number of samples required to prove a difference, only the number of samples required for a given confidence interval.
We have entered the standard deviation in the dialog box as 1 and then entered the margin of error as a ratio of the standard deviation. We could have used actual standard deviations and margins of error. If we use the example of the GDP figures in the UK from 2009 to 2013, we will find a standard deviation of 0.43 from the Comparing the population mean to a target with a 1-Sample t-test recipe. By entering the standard deviation as 0.43, we could check how many samples are needed to estimate the mean percentage growth to a margin of error of 0.1 percent.