The Power option calculates statistical power and other details about a given hypothesis test.
• LSV (the Least Significant Value) is the value of some parameter or function of parameters that would produce a certain p-value alpha. Said another way, you want to know how small an effect would be declared significant at some p-value alpha. The LSV provides a measuring stick for significance on the scale of the parameter, rather than on a probability scale. It shows how sensitive the design and data are.
• LSN (the Least Significant Number) is the total number of observations that would produce a specified p-value alpha given that the data has the same form. The LSN is defined as the number of observations needed to reduce the variance of the estimates enough to achieve a significant result with the given values of alpha, sigma, and delta (the significance level, the standard deviation of the error, and the effect size). If you need more data to achieve significance, the LSN helps tell you how many more. The LSN is the total number of observations that yields approximately 50% power.
• Power is the probability of getting significance (p-value < alpha) when a real difference exists between groups. It is a function of the sample size, the effect size, the standard deviation of the error, and the significance level. The power tells you how likely your experiment is to detect a difference (effect size), at a given alpha level.
Note: When there are only two groups in a one-way layout, the LSV computed by the power facility is the same as the least significant difference (LSD) shown in the multiple-comparison tables.
Power Details Window and Reports
The Power Details window and reports are the same as those in the general fitting platform launched by the Fit Model platform. For more details about power calculation, see the Fitting Linear Models book.
For each of four columns Alpha, Sigma, Delta, and Number, fill in a single value, two values, or the start, stop, and increment for a sequence of values. See Figure 6.27. Power calculations are performed on all possible combinations of the values that you specify.
Related Information
• “Example of the Power Option” on page 192
• “Statistical Details for Power” on page 200 Table 6.20 Description of the Power Details Report
Alpha (α) Significance level, between 0 and 1 (usually 0.05, 0.01, or 0.10).
Initially, a value of 0.05 shows.
Sigma (σ) Standard error of the residual error in the model. Initially, RMSE, the estimate from the square root of the mean square error is supplied here.
Delta (δ) Raw effect size. For details about effect size computations, see the Fitting Linear Models book. The first position is initially set to the square root of the sums of squares for the hypothesis divided by n;
that is, .
Number (n) Total sample size across all groups. Initially, the actual sample size is put in the first position.
Solve for Power Solves for the power (the probability of a significant result) as a function of all four values: α, σ, δ, and n.
Solve for Least Significant Number
Solves for the number of observations needed to achieve approximately 50% power given α, σ, and δ.
Solve for Least Significant Value
Solves for the value of the parameter or linear test that produces a p-value of α. This is a function of α, σ, n, and the standard error of the estimate. This feature is available only when the X factor has two levels and is usually used for individual parameters.
Adjusted Power and Confidence Interval
When you look at power retrospectively, you use estimates of the standard error and the test parameters.
• Adjusted power is the power calculated from a more unbiased estimate of the non-centrality parameter.
• The confidence interval for the adjusted power is based on the confidence interval for the non-centrality estimate.
Adjusted power and confidence limits are computed only for the original Delta, because that is where the random variation is.
δ = SS n⁄
Normal Quantile Plot
You can create two types of normal quantile plots:
• Plot Actual by Quantile creates a plot of the response values versus the normal quantile values. The quantiles are computed and plotted separately for each level of the X variable.
• Plot Quantile by Actual creates a plot of the normal quantile values versus the response values. The quantiles are computed and plotted separately for each level of the X variable.
The Line of Fit option shows or hides the lines of fit on the quantile plots.
Related Information
• “Example of a Normal Quantile Plot” on page 194
CDF Plot
A CDF plot shows the cumulative distribution function for all of the groups in the Oneway report. CDF plots are useful if you want to compare the distributions of the response across levels of the X factor.
Related Information
• “Example of a CDF Plot” on page 195
Densities
The Densities options provide several ways to compare the distribution and composition of the response across the levels of the X factor. There are three density options:
• Compare Densities shows a smooth curve estimating the density of each group. The smooth curve is the kernel density estimate for each group.
• Composition of Densitiesshows the summed densities, weighted by each group’s counts.
At each X value, the Composition of Densities plot shows how each group contributes to the total.
• Proportion of Densitiesshows the contribution of the group as a proportion of the total at each X level.
Related Information
• “Example of the Densities Options” on page 196