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How to Calculate Sample Size Needed for Standard Error

Statistical analysis of data produces a calculated standard deviation that is called a standard error when calculated using a sample. Standard errors from samples with similar methodologies can be compared. It is important that sufficient sample measurements of the standard error are taken to provide statistically valid results. The sample size of these standard errors depends on the statistical level of confidence needed. Use the guideline, the higher the level of confidence, the larger the sample size needed to guide your calculations. Calculating standard error requires gathering data which makes this procedure difficult and costly, and any sample size used likely will be small.

Calculator or software such as Excel with “square” and “square root” capabilities
Reference guide containing “z-values” and “t-values”

Instructions

- 1
  Calculate the standard deviation of the sample variable data; since this is for a sample, not the entire population, this is called the standard error. This is an estimate of standard deviation for the entire population of data.
- 2
  Determine the level of confidence needed for a statistically valid result. While any level of confidence can be used, 95% or greater is commonly chosen. This will be represented (1 – confidence level)/2 to reflect the appropriate column of the “Z table” and the fact that values greater and lesser than the standard error obtained in Step 1 are acceptable within the level of confidence. This is represented as “Zα.” For example, a confidence level of 96% results in a Z value of 2.054.
- 3
  Specify a margin of error required. This is specified in the same unit measure as the standard error. For example, the standard error calculated is 0.068, and the margin of error needs to be 0.005.
- 4
  Apply the formula n = (ZαSE/MOE) squared.

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