Sample size for confidence intervals for the difference between two means

The BIS.Net Team BIS.Net Team

To determine the sample size for a confidence interval for the difference of two means to have a specified margin-of-error we need to apply the following formula.

N = Z_Value(alpha / 2) ^ 2 * ((SD1 ^ 2 + Sd2 ^ 2) / margin-of-error ^ 2)

Where alpha is the specified level of significance. For a 95% confidence interval alpha =.05 as derived from (100-percent)/100

Sd1 is the known standard deviation for Sample 1, Sd2 the known standard deviation for Sample 2 and margin-of-error the specified value. The actual confidence interval will be equal to 2 times the margin-of-error.

Because the expression will return a non-integer number, whereas the computed sample size must be an integer, the actual margin-of-error will be slightly different to the specified value.

BIS.Net Analyst therefore recalculates the margin of error using the calculated integer sample size and following formula

AME = Sqrt((Z_Value(alpha / 2) ^ 2 * (SD1 ^ 2 + Sd2 ^ 2) / N)

Provided the resultant sample size is large, the above formula is robust to departures in normality.

For sake of simple practicality BIS.Net Analyst computes a single sample size applicable to both samples.

The formula does require known standard deviations. It is possible to fall into the trap of using t values instead of z values. T values are appropriate when calculating confidence intervals if the standard deviation is unknown. But to use a sample standard deviations and t value obtained prior to new sampling is dubious because the sample result is unlikely going to equal the prior sample standard deviation and hence is not a BIS.Net Analyst option.

Analysts need to obtain an estimate of the standard deviations from historical information. If these are not available then there is no choice but to take a large sample too obtain the standard deviations for future confidence intervals. The required sample size can be estimated by selecting Standard Deviation from the dropdown box.

Download the Inferences APP, comprised of mainstream and machine-powered analytics for statistical analysis

Analytics as a Service (AaaS) for Quality

Drive quality improvement through actionable insights using analytics you can trust! Use up to 200 analytics tools downloadable through a suite of Apps!

FREE usage of the analytics Apps for quality improvement
  • Augmented with machine-powered smarts
  • Always updated with the latest tools and features
  • No licencing or fixed subscriptions - Pay ONLY for the analysis you run from 20 USD cents per analysis, billed monthly! Set a budget so you don't exceed!