Publication date: 11/10/2021

## Parameter Power

The power of a statistical test is the probability that the test will be significant, if a difference actually exists. The power of the test indicates how likely your study is to declare a true effect to be significant. The Parameter Power option addresses retrospective power analysis.

Note: To ensure that your study includes sufficiently many observations to detect the required differences, use information about power when you design your experiment. This type of analysis is called prospective power analysis. Consider using the DOE platform to design your study. Both DOE > Sample Size and Power and DOE > Evaluate Design are useful for prospective power analysis. For an example of a prospective power analysis using standard least squares, see Prospective Power Analysis.

The power of a test to detect a difference is affected by the following factors:

the sample size

the unknown residual error variance

the significance level of the test

the size of the effect to be detected

Suppose that you have already conducted your study, analyzed your data, and found that an effect of interest is not significant. You might be interested in the size of the difference that you might have been likely to detect or the power of the test that you conducted. Or you might want to know the number of observations that you would have needed to detect a difference of a given size with high probability.

The Parameter Power option inserts three columns of values relating to retrospective power analysis in the Parameter Estimates report. The least significant value (LSV0.05), the least significant number (LSN0.05), and a power calculation (AdjPower0.05) are provided.

The Parameter Power calculations apply to a new sample that has the same variability profile as the observed sample.

Caution: The results provided by the LSV0.05, LSN, and AdjPower0.05 should not be used in prospective power analysis. They do not reflect the uncertainty inherent in a future study.

LSV0.05 is the least significant value. This number is the smallest absolute value of the estimate that would make this test significant at significance level 0.05. To be more specific, suppose that the number of observations, the mean square error and that the sum of squares and cross-products matrix for the design remain unchanged. Then, if the absolute value of the estimate had been less than LSV0.05, the Prob>|t| value would have exceeded 0.05. See The Least Significant Value (LSV).

LSN is the least significant number. This number is the number of observations that would make this test significant at significance level 0.05. Specifically, suppose that the estimate of the parameter, the mean square error, and the sum of squares and cross-products matrix for the design remain unchanged. Then, if the number of observations had been less than the LSN, the Prob>|t| value would have exceeded 0.05. See The Least Significant Number (LSN).

AdjPower0.05 is the adjusted power value. This number is an estimate of the probability that this test will be significant. Sample values from the current study are substituted for the parameter values typically used in a power calculation. The adjusted power calculation adjusts for bias that results from direct substitution of sample estimates into the formula for the non-centrality parameter (Wright and O’Brien 1988). See The Adjusted Power and Confidence Intervals.

The LSV, LSN, and adjusted power are useful in assessing a test’s sensitivity. These retrospective calculations also provide an enlightening instructional tool. However, you must be cautious in interpreting these values (Hoenig and Heisey 2001).

For more information about LSV, LSN, and adjusted power, see Power Analysis. For an example of a retrospective analysis, see Example of Retrospective Power Analysis.