Use the One-Sample Standard Deviation option on the Sample Size and Power window (Sample Size and Power Choices) to determine the sample size needed for detecting a change in the standard deviation of your data. The usual purpose of this option is to compute a large enough sample size to guarantee that the risk of a type II error, β, is small. (This is the probability of failing to reject the null hypothesis when it is false.)
can select Larger or Smaller from the menu to indicate the direction of the change you want to detect.
H0: σ = σ0, where σ0 is the hypothesized standard deviation. The true standard deviation is σ0 plus the difference to detect.
In this example the hypothesized standard deviation, σ0, is 10 (the square root of 100) and σ is 12.4499 (the square root of 100 + 55 = 155). The difference to detect is 12.4499 – 10 = 2.4499.
Select DOE > Sample Size and Power.
Click the One Sample Standard Deviation button in the Sample Size and Power Window.
Leave Alpha as 0.05.
Enter 10 for Hypothesized Standard Deviation.
Select Larger for Alternate Standard Deviation.
Enter 2.4499 as Difference to Detect.
Click Continue.
The Sample Size is calculated as 171. (See the right of Window To Compare Single-Direction One-Sample Standard Deviation.) This result is the sample size rounded up to the next whole number.
Note: Sometimes you want to detect a change to a smaller standard deviation. If you select Smaller from the Alternative Standard Deviation menu, enter a negative amount in the Difference to Detect field.
Window To Compare Single-Direction One-Sample Standard Deviation