TECHNOLOGY OVERVIEW

# Sample size for confidence intervals for the difference between two means 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. ## Analytics as a Service (AaaS) for Quality

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