One Sample Standard Deviation

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.)

In the Sample Size and Power window, specify:

Alpha

is the significance level, usually 0.05. This implies a willingness to accept (if the true difference between standard deviation and the hypothesized standard deviation is zero) that a significant difference is incorrectly declared 5% of the time.

Hypothesized Standard Deviation

is the hypothesized or baseline standard deviation to which the sample standard deviation is compared.

Alternative Standard Deviation

can select Larger or Smaller from the menu to indicate the direction of the change you want to detect.

Difference to Detect

is the smallest detectable difference (how small a difference you want to be able to declare statistically significant). For single sample problems this is the difference between the hypothesized value and the true value.

Sample Size

is how many experimental units (runs, or samples) are involved in the experiment.

Power

is the probability of declaring a significant result. It is the probability of rejecting the null hypothesis when it is false.

In the lower part of the window you enter two of the items and the Sample Size and Power calculation determines the third.

Some examples in this chapter use engineering examples from the online manual of The National Institute of Standards and Technology (NIST). You can access the NIST manual examples at http://www.itl.nist.gov/div898/handbook.