Design of Experiments Guide  • Prospective Sample Size and Power • One-Sample and Two-Sample Means
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One-Sample and Two-Sample Means
After you click either One Sample Mean, or Two Sample Means in the initial Sample Size selection list (Sample Size and Power Choices), a Sample Size and Power window appears. (See Initial Sample Size and Power Windows for Single Mean (left) and Two Means (right).)
Initial Sample Size and Power Windows for Single Mean (left) and Two Means (right)
The windows are the same except that the One Mean window has a button at the bottom that accesses an animation script.
The initial Sample Size and Power window requires values for Alpha, Std Dev (the error standard deviation), and one or two of the other three values: Difference to detect, Sample Size, and Power. The Sample Size and Power platform calculates the missing item. If there are two unspecified fields, a plot is constructed, showing the relationship between these two values:
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power as a function of sample size, given specific effect size
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power as a function of effect size, given a sample size
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effect size as a function of sample size, for a given power.
The Sample Size and Power window asks for these values:
Alpha
is the probability of a type I error, which is the probability of rejecting the null hypothesis when it is true. It is commonly referred to as the significance level of the test. The default alpha level is 0.05. This implies a willingness to accept (if the true difference between groups is zero) that, 5% (alpha) of the time, a significant difference is incorrectly declared.
Std Dev
is the error standard deviation. It is a measure of the unexplained random variation around the mean. Even though the true error is not known, the power calculations are an exercise in probability that calculates what might happen if the true value is the one you specify. An estimate of the error standard deviation could be the root mean square error (RMSE) from a previous model fit.
Extra Parameters
is only for multi-factor designs. Leave this field zero in simple cases. In a multi-factor balanced design, in addition to fitting the means described in the situation, there are other factors with extra parameters that can be specified here. For example, in a three-factor two-level design with all three two-factor interactions, the number of extra parameters is five. (This includes two parameters for the extra main effects, and three parameters for the interactions.) In practice, the particular values entered are not that important, unless the experimental range has very few degrees of freedom for error.
Difference to Detect
is the smallest detectable difference (how small a difference you want to be able to declare statistically significant) to test against. For single sample problems this is the difference between the hypothesized value and the true value.
Sample Size
is the total number of observations (runs, experimental units, or samples) in your experiment. Sample size is not the number per group, but the total over all groups.
Power
is the probability of rejecting the null hypothesis when it is false. A large power value is better, but the cost is a higher sample size.
Continue
evaluates at the entered values.
Back
returns to the previous Sample Size and Power window so that you can either redo an analysis or start a new analysis.
Animation Script
runs a JSL script that displays an interactive plot showing power or sample size. See the section, Sample Size and Power Animation for One Mean, for an illustration of the animation script.

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Help created on 9/19/2017