Table 6.1 Examples of Options and Elements 

Platform Option	Object Added to Plot	Report Added to Report Window
Quantiles	Box plots	Quantiles report
Means/Anova	Mean diamonds	Oneway anova reports
Means and Std Dev	Mean lines, error bars, and standard deviation lines	Means and Std Deviations report
Compare Means	Comparison circles (except Nonparametric Multiple Comparisons option)	Means Comparison reports

Table 6.2 Descriptions of Oneway Analysis Platform Options 

Quantiles	Lists the following quantiles for each group: • 0% (Minimum) • 10% • 25% • 50% (Median) • 75% • 90% • 100% (Maximum) Activates Box Plots from the Display Options menu. See “Quantiles”.
Means/Anova or Means/Anova/Pooled t	Fits means for each group and performs a one-way analysis of variance to test if there are differences among the means. See “Means/Anova and Means/Anova/Pooled t”. The Means/Anova/Pooled t option appears only if the X factor has two levels.
Means and Std Dev	Gives summary statistics for each group. The standard errors for the means use individual group standard deviations rather than the pooled estimate of the standard deviation. The plot now contains mean lines, error bars, and standard deviation lines. For a brief description of these elements, see “Display Options”. For more details about these elements, see “Mean Lines, Error Bars, and Standard Deviation Lines”.
t test	Produces a t-test report assuming that the variances are not equal. See “The t-test Report”. This option appears only if the X factor has two levels.
Analysis of Means Methods	Provides four commands for performing Analysis of Means (ANOM) procedures. There are commands for comparing both means and variances. See “Analysis of Means Methods”.
Compare Means	Provides multiple-comparison methods for comparing sets of group means. See “Compare Means”.
Nonparametric	Provides nonparametric comparisons of group means. See “Nonparametric”.
Unequal Variances	Performs four tests for equality of group variances. Also gives the Welch test, which is an anova test for comparing means when the variances within groups are not equal. See “Unequal Variances”.
Equivalence Test	Tests that a difference is less than a threshold value. See “Equivalence Test”.
Power	Provides calculations of statistical power and other details about a given hypothesis test. See “Power”. The Power Details window and reports also appear within the Fit Model platform. For further discussion and examples of power calculations, see the Fitting Linear Models book.
Set a Level	You can select an option from the most common alpha levels or specify any level with the Other selection. Changing the alpha level results in the following actions: • recalculates confidence limits • adjusts the mean diamonds on the plot (if they are showing) • modifies the upper and lower confidence level values in reports • changes the critical number and comparison circles for all Compare Means reports • changes the critical number for all Nonparametric Multiple Comparison reports
Normal Quantile Plot	Provides the following options for plotting the quantiles of the data in each group: • Plot Actual by Quantile generates a quantile plot with the response variable on the y-axis and quantiles on the x-axis. The plot shows quantiles computed within each level of the categorical X factor. • Plot Quantile by Actual reverses the x- and y-axes. • Line of Fit draws straight diagonal reference lines on the plot for each level of the X variable. This option is available only once you have created a plot (Actual by Quantile or Quantile by Actual).
CDF Plot	Plots the cumulative distribution function for all of the groups in the Oneway report. See “CDF Plot”.
Densities	Compares densities across groups. See “Densities”.
Matching Column	Specify a matching variable to perform a matching model analysis. Use this option when the data in your Oneway analysis comes from matched (paired) data, such as when observations in different groups come from the same subject. The plot now contains matching lines that connect the matching points. See “Matching Column”.
Save	Saves the following quantities as new columns in the current data table: • Save Residuals saves values computed as the response variable minus the mean of the response variable within each level of the factor variable. • Save Standardized saves standardized values of the response variable computed within each level of the factor variable. This is the centered response divided by the standard deviation within each level. • Save Normal Quantiles saves normal quantile values computed within each level of the categorical factor variable. • Save Predicted saves the predicted mean of the response variable for each level of the factor variable.
Display Options	Adds or removes elements from the plot. See “Display Options”.
Script	This menu contains options that are available to all platforms. They enable you to redo the analysis or save the JSL commands for the analysis to a window or a file. For more information, see Using JMP.

Table 6.3 Descriptions of Display Options 

All Graphs	Shows or hides all graphs.
Points	Shows or hides data points on the plot.
Box Plots	Shows or hides outlier box plots for each group.
Mean Diamonds	Draws a horizontal line through the mean of each group proportional to its x-axis. The top and bottom points of the mean diamond show the upper and lower 95% confidence points for each group. See “Mean Diamonds and X-Axis Proportional”.
Mean Lines	Draws a line at the mean of each group. See “Mean Lines, Error Bars, and Standard Deviation Lines”.
Mean CI Lines	Draws lines at the upper and lower 95% confidence levels for each group.
Mean Error Bars	Identifies the mean of each group and shows error bars one standard error above and below the mean. See “Mean Lines, Error Bars, and Standard Deviation Lines”.
Grand Mean	Draws the overall mean of the Y variable on the plot.
Std Dev Lines	Shows lines one standard deviation above and below the mean of each group. See “Mean Lines, Error Bars, and Standard Deviation Lines”.
Comparison Circles	Shows or hides comparison circles. This option is available only when one of the Compare Means options is selected. See “Statistical Details for Comparison Circles”.
Connect Means	Connects the group means with a straight line.
Mean of Means	Draws a line at the mean of the group means.
X-Axis proportional	Makes the spacing on the x-axis proportional to the sample size of each level. See “Mean Diamonds and X-Axis Proportional”.
Points Spread	Spreads points over the width of the interval
Points Jittered	Adds small spaces between points that overlay on the same y value. The horizontal adjustment of points varies from 0.375 to 0.625 with a 4*(Uniform-0.5)5 distribution.
Matching Lines	(Only appears when the Matching Column option is selected.) Connects matching points.
Matching Dotted Lines	Only appears when the Matching Column option is selected.) Draws dotted lines to connect cell means from missing cells in the table. The values used as the endpoints of the lines are obtained using a two-way anova model.
Histograms	Draws side-by-side histograms to the right of the original plot.

Table 6.4 Description of Report Window Elements 

Element	Reference
Mean diamonds are added to the Oneway plot	See “Display Options” and “Mean Diamonds and X-Axis Proportional”.
Reports	See “The Summary of Fit Report”.
	See “The Analysis of Variance Report”.
	See “The Means for Oneway Anova Report”.
	See “The t-test Report”. Note: This report appears only if the Means/Anova/Pooled t option is selected.
	See “The Block Means Report”. Note: This report appears only if you have specified a Block variable in the launch window.

Table 6.5 Description of the Summary of Fit Report 

Rsquare	Measures the proportion of the variation accounted for by fitting means to each factor level. The remaining variation is attributed to random error. The R2 value is 1 if fitting the group means accounts for all the variation with no error. An R2 of 0 indicates that the fit serves no better as a prediction model than the overall response mean. For more information, see “Statistical Details for the Summary of Fit Report”. R2 is also called the coefficient of determination.
Adj Rsquare	Adjusts R2 to make it more comparable over models with different numbers of parameters by using the degrees of freedom in its computation. For more information, see “Statistical Details for the Summary of Fit Report”.
Root Mean Square Error	Estimates the standard deviation of the random error. It is the square root of the mean square for Error found in the Analysis of Variance report.
Mean of Response	Overall mean (arithmetic average) of the response variable.
Observations (or Sum Wgts)	Number of observations used in estimating the fit. If weights are used, this is the sum of the weights. See “Statistical Details for the Summary of Fit Report”.

Table 6.6 Description of the t-Test Report 

t Test plot	Shows the sampling distribution of the difference in the means, assuming the null hypothesis is true. The vertical red line is the actual difference in the means. The shaded areas correspond to the p-values.
Difference	Shows the estimated difference between the two X levels. In the plots, the Difference value appears as a red line that compares the two levels.
Std Err Dif	Shows the standard error of the difference.
Upper CL Dif	Shows the upper confidence limit for the difference.
Lower CL Dif	Shows the lower confidence limit for the difference.
Confidence	Shows the level of confidence (1-alpha). To change the level of confidence, select a new alpha level from the Set α Level command from the platform red triangle menu.
t Ratio	Value of the t-statistic.
DF	The degrees of freedom used in the t-test.
Prob > |t|	The p-value associated with a two-tailed test.
Prob > t	The p-value associated with a lower-tailed test.
Prob < t	The p-value associated with an upper-tailed test.

Table 6.7 Description of the Analysis of Variance Report 

Source	Lists the three sources of variation, which are the model source, Error, and C. Total (corrected total).
DF	Records an associated degrees of freedom (DF for short) for each source of variation: • The degrees of freedom for C. Total are N - 1, where N is the total number of observations used in the analysis. • If the X factor has k levels, then the model has k - 1 degrees of freedom. The Error degrees of freedom is the difference between the C. Total degrees of freedom and the Model degrees of freedom (in other words, N - k).
Sum of Squares	Records a sum of squares (SS for short) for each source of variation: • The total (C. Total) sum of squares of each response from the overall response mean. The C. Total sum of squares is the base model used for comparison with all other models. • The sum of squared distances from each point to its respective group mean. This is the remaining unexplained Error (residual) SS after fitting the analysis of variance model. The total SS minus the error SS gives the sum of squares attributed to the model. This tells you how much of the total variation is explained by the model.
Mean Square	Is a sum of squares divided by its associated degrees of freedom: • The Model mean square estimates the variance of the error, but only under the hypothesis that the group means are equal. • The Error mean square estimates the variance of the error term independently of the model mean square and is unconditioned by any model hypothesis.
F Ratio	Model mean square divided by the error mean square. If the hypothesis that the group means are equal (there is no real difference between them) is true, then both the mean square for error and the mean square for model estimate the error variance. Their ratio has an F distribution. If the analysis of variance model results in a significant reduction of variation from the total, the F ratio is higher than expected.
Prob>F	Probability of obtaining (by chance alone) an F value greater than the one calculated if, in reality, there is no difference in the population group means. Observed significance probabilities of 0.05 or less are often considered evidence that there are differences in the group means.

Table 6.8 Description of the Means for Oneway Anova Report 

Level	Lists the levels of the X variable.
Number	Lists the number of observations in each group.
Mean	Lists the mean of each group.
Std Error	Lists the estimates of the standard deviations for the group means. This standard error is estimated assuming that the variance of the response is the same in each level. It is the root mean square error found in the Summary of Fit report divided by the square root of the number of values used to compute the group mean.
Lower 95% and Upper 95%	Lists the lower and upper 95% confidence interval for the group means.

Table 6.9 Descriptions of Methods for Comparing Means 

ANOM	Compares group means to the overall mean. This method assumes that your data is approximately normally distributed. See “Example of an Analysis of Means Chart”.
ANOM with Transformed Ranks	This is the nonparametric version of the ANOM analysis. Use this method if your data is clearly non-normal and cannot be transformed to normality. Compares each group mean transformed rank to the overall mean transformed rank.

Table 6.10 Descriptions of Methods for Comparing Standard Deviations (or Variances) 

ANOM for Variances	Compares group standard deviations to the root mean square error. This method assumes that your data is approximately normally distributed. To use this method, each group must have at least four observations. See “Example of an Analysis of Means for Variances Chart”.
ANOM for Variances with Levene (ADM)	This is the nonparametric version of the ANOM for Variances analysis. Use this method if you suspect your data is non-normal and cannot be transformed to normality. Compares the group means of the absolute deviation from the median (ADM) to the overall mean ADM.

Table 6.11 Descriptions of the Analysis of Means Methods Options 

Set Alpha Level	Select an option from the most common alpha levels or specify any level with the Other selection. Changing the alpha level modifies the upper and lower decision limits.
Show Summary Report	For ANOM, creates a report showing group means and decision limits. • For ANOM with Transformed Ranks, creates a report showing group mean transformed ranks and decision limits. • For ANOM for Variances, creates a report showing group standard deviations (or variances) and decision limits. • For ANOM for Variances with Levene (ADM), creates a report showing group mean ADMs and decision limits.
Graph in Variance Scale	(Only for ANOM for Variances) Changes the scale of the y-axis from standard deviations to variances.
Display Options	Display options include the following: • Show Decision Limits shows or hides decision limit lines. • Show Decision Limit Shading shows or hides decision limit shading. • Show Center Line shows or hides the center line statistic. • Show Needles shows or hides the needles.

Option	Description	Reference	Nonparametric Menu Option
Each Pair, Student’s t	Computes individual pairwise comparisons using Student’s t-tests. If you make many pairwise tests, there is no protection across the inferences. Therefore, the alpha-size (Type I error rate) across the hypothesis tests is higher than that for individual tests.	See “Each Pair, Student’s t”.	Nonparametric > Nonparametric Multiple Comparisons > Wilcoxon Each Pair
All Pairs, Tukey HSD	Shows a test that is sized for all differences among the means. This is the Tukey or Tukey-Kramer HSD (honestly significant difference) test. (Tukey 1953, Kramer 1956). This test is an exact alpha-level test if the sample sizes are the same, and conservative if the sample sizes are different (Hayter 1984).	See “All Pairs, Tukey HSD”.	Nonparametric > Nonparametric Multiple Comparisons > Steel-Dwass All Pairs
With Best, Hsu MCB	Tests whether the means are less than the unknown maximum or greater than the unknown minimum. This is the Hsu MCB test (Hsu 1981).	See “With Best, Hsu MCB”.	none
With Control, Dunnett’s	Tests whether the means are different from the mean of a control group. This is Dunnett’s test (Dunnett 1955).	See “With Control, Dunnett’s”.	Nonparametric > Nonparametric Multiple Comparisons > Steel With Control

Table 6.12 Descriptions of Compare Means Options 

Difference Matrix	Shows a table of all differences of means.
Confidence Quantile	Shows the t-value or other corresponding quantiles used for confidence intervals.
LSD Threshold Matrix	Shows a matrix showing if a difference exceeds the least significant difference for all comparisons. Note: For Hsu’s MCB and Dunnett’s test, only Difference Matrix, Confidence Quantile, and LSD Threshold Matrix are applicable.
Connecting Letters Report	Shows the traditional letter-coded report where means that are not sharing a letter are significantly different.
Ordered Differences Report	Shows all the positive-side differences with their confidence interval in sorted order. For the Student’s t and Tukey-Kramer comparisons, an Ordered Difference report appears below the text reports. This report shows the ranked differences, from highest to lowest, with a confidence interval band overlaid on the plot. Confidence intervals that do not fully contain their corresponding bar are significantly different from each other.
Detailed Comparisons Report	Shows a detailed report for each comparison. Each section shows the difference between the levels, standard error and confidence intervals, t-ratios, p-values, and degrees of freedom. A plot illustrating the comparison appears on the right of each report. This option is not available for All Pairs, Tukey’s HSD, and Nonparametric Multiple Comparisons.

Table 6.13 Descriptions of Nonparametric Tests 

Wilcoxon Test1	Performs the test based on Wilcoxon rank scores. The Wilcoxon rank scores are the simple ranks of the data. The Wilcoxon test is the most powerful rank test for errors with logistic distributions. If the factor has two or more levels, the Kruskal-Wallis test is performed. The Wilcoxon test is also called the Mann-Whitney test.
Median Test	Performs the test based on Median rank scores. The Median rank scores are either 1 or 0, depending on whether a rank is above or below the median rank. The Median test is the most powerful rank test for errors with double-exponential distributions.
van der Waerden Test	Performs the test based on Van der Waerden rank scores. The Van der Waerden rank scores are the ranks of the data divided by one plus the number of observations transformed to a normal score by applying the inverse of the normal distribution function. The Van der Waerden test is the most powerful rank test for errors with normal distributions.
Kolmogorov-Smirnov Test	Performs the test based on the empirical distribution function, which tests whether the distribution of the response is the same across the groups. Both an approximate and an exact test are given. This test is available only when the X factor has two levels.
Exact Test	Provides options for performing exact versions of the Wilcoxon, Median, van der Waerden, and Kolmogorov-Smirnov tests. These options are available only when the X factor has two levels, and after the approximate test is requested.
Nonparametric Multiple Comparisons	Provides several options for performing nonparametric multiple comparisons. These tests are based on ranks, and control for the overall alpha level, except for the Wilcoxon Each Pair test. The following tests are available: Wilcoxon Each Pair performs the Wilcoxon test on each pair, and does not control for the overall alpha level. This is the nonparametric version of the Each Pair, Student’s t option found on the Compare Means menu. Steel-Dwass All Pairs performs the Steel-Dwass test on each pair. This is the nonparametric version of the All Pairs, Tukey HSD option found on the Compare Means menu. Steel With Control compares each level to a control level. This is the nonparametric version of the With Control, Dunnett’s option found on the Compare Means menu. Dunn With Control for Joint Ranks compares each level to a control level, similar to the Steel With Control option. The Dunn method is different in that it computes ranks on all the data, not just the pair being compared. Dunn All Pairs for Joint Ranks performs a comparison of each pair, similar to the Steel-Dwass All Pairs option. The Dunn method is different in that it computes ranks on all the data, not just the pair being compared. See Dunn (1964) and Hsu (1996).

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Table 6.14 Descriptions of the Wilcoxon, Median, and Van der Waerden Tests 

Level	Lists the factor levels occurring in the data.
Count	Records the frequencies of each level.
Score Sum	Records the sum of the rank score for each level.
Expected Score	Records the expected score under the null hypothesis that there is no difference among class levels.
Score Mean	Records the mean rank score for each level.
(Mean-Mean0)/Std0	Records the standardized score. Mean0 is the mean score expected under the null hypothesis. Std0 is the standard deviation of the score sum expected under the null hypothesis. The null hypothesis is that the group means or medians are in the same location across groups.
ChiSquare	Gives the values of the chi-square test statistic.
DF	Gives the degrees of freedom for the test.
Prob>ChiSq	Gives the p-value for the test.
S	Gives the sum of the rank scores. This is reported only when the X factor has two levels.
Z	Gives the test statistic for the normal approximation test. This is reported only when the X factor has two levels.
Prob>|Z|	Gives the p-value for the normal approximation test. This is reported only when the X factor has two levels.
Prob≥S	Gives a one-sided p-value for the test. This is reported only when the X factor has two levels, and the exact version of the test is requested. Exact tests are available only in JMP Pro.
Prob≥|S-Mean|	Gives a two-sided p-value for the test. This is reported only when the X factor has two levels, and the exact version of the test is requested. Exact tests are available only in JMP Pro.

Table 6.15 Description of the Kolmogorov-Smirnov Test 

Level	Lists the factor levels occurring in the data.
Count	Records the frequencies of each level.
EDF at Maximum	Lists the value at which the maximum deviation from the empirical distribution function (EDF) of each level and the overall EDF occurs.
Deviation from Mean at Maximum	Lists the value of the EDF of a sample at the maximum deviation from the mean of the EDF for the overall sample.
KS	A Kolmogorov-Smirnov statistic.
KSa	An asymptotic Kolmogorov-Smirnov statistic.
D=max|F1-F2|	Lists the maximum absolute deviation between the EDF of two class levels.
Prob > D	Lists the p-value for the test. In other words, the probability that D is greater than the observed value d, under the null hypothesis of no difference between class levels or samples.
D+=max(F1-F2)	Lists a one-sided test statistic that max deviation between the EDF of two class levels is positive.
Prob > D+	Lists the probability that D+ is greater than the observed value d+, under the null hypothesis of no difference between the two class levels.
D-=max(F2-F1)	Lists a one-sided test statistic that max deviation between the EDF of two class levels is negative.
Prob > D-	Lists the probability that D- is greater than the observed value for d-.

Table 6.16 Descriptions of the Nonparametric Multiple Comparisons Tests 

q*	Gives the quantile value used in the confidence intervals.
Alpha	Gives the alpha level used in the confidence intervals
Level	Gives the pair used in the current comparison
Score Mean Diff	Gives the difference of the score means.
Std Err Dif	Gives the standard error of the difference between the score means.
Z	Gives the standardized test statistic, which has an asymptotic standard normal deviation under the null hypothesis.
p-Value	Gives the asymptotic two-sided p-value for Z.
Hodges-Lehmann	Gives the Hodges-Lehmann estimator of location shift. It is the median of all paired differences between observations in the two samples.
Lower CL	Gives the lower confidence limit for the Hodges-Lehmann statistic.
Upper CL	Gives the upper confidence limit for the Hodges-Lehmann statistic.

Table 6.17 Descriptions of Tests for Equal Variances 

O’Brien	Constructs a dependent variable so that the group means of the new variable equal the group sample variances of the original response. An anova on the O’Brien variable is actually an anova on the group sample variances (O’Brien 1979, Olejnik, and Algina 1987).
Brown-Forsythe	Shows the F test from an anova where the response is the absolute value of the difference of each observation and the group median (Brown and Forsythe 1974a).
Levene	Shows the F test from an anova where the response is the absolute value of the difference of each observation and the group mean (Levene 1960). The spread is measured as (as opposed to the SAS default ).
Bartlett	Compares the weighted arithmetic average of the sample variances to the weighted geometric average of the sample variances. The geometric average is always less than or equal to the arithmetic average with equality holding only when all sample variances are equal. The more variation there is among the group variances, the more these two averages differ. A function of these two averages is created, which approximates a χ2-distribution (or, in fact, an F distribution under a certain formulation). Large values correspond to large values of the arithmetic or geometric ratio, and therefore to widely varying group variances. Dividing the Bartlett Chi-square test statistic by the degrees of freedom gives the F value shown in the table. Bartlett’s test is not very robust to violations of the normality assumption (Bartlett and Kendall 1946).

Table 6.18 Description of the Tests That the Variances Are Equal Report 

Level	Lists the factor levels occurring in the data.
Count	Records the frequencies of each level.
Std Dev	Records the standard deviations of the response for each factor level. The standard deviations are equal to the means of the O’Brien variable. If a level occurs only once in the data, no standard deviation is calculated.
MeanAbsDif to Mean	Records the mean absolute difference of the response and group mean. The mean absolute differences are equal to the group means of the Levene variable.
MeanAbsDif to Median	Records the absolute difference of the response and group median. The mean absolute differences are equal to the group means of the Brown-Forsythe variable.
Test	Lists the names of the tests performed.
F Ratio	Records a calculated F statistic for each test. See “Statistical Details for the Tests That the Variances Are Equal Report”.
DFNum	Records the degrees of freedom in the numerator for each test. If a factor has k levels, the numerator has k - 1 degrees of freedom. Levels occurring only once in the data are not used in calculating test statistics for O’Brien, Brown-Forsythe, or Levene. The numerator degrees of freedom in this situation is the number of levels used in calculations minus one.
DFDen	Records the degrees of freedom used in the denominator for each test. For O’Brien, Brown-Forsythe, and Levene, a degree of freedom is subtracted for each factor level used in calculating the test statistic. One more degree of freedom is subtracted for the overall mean. If a factor has k levels, the denominator degrees of freedom is n - k - 1.
p-Value	Probability of obtaining, by chance alone, an F value larger than the one calculated if in reality the variances are equal across all levels.

Table 6.19 Description of the Welch’s Test Report 

F Ratio	Shows the F test statistic for the equal variance test. See “Statistical Details for the Tests That the Variances Are Equal Report”.
DFNum	Records the degrees of freedom in the numerator of the test. If a factor has k levels, the numerator has k - 1 degrees of freedom. Levels occurring only once in the data are not used in calculating the Welch anova. The numerator degrees of freedom in this situation is the number of levels used in calculations minus one.
DFDen	Records the degrees of freedom in the denominator of the test. See “Statistical Details for the Tests That the Variances Are Equal Report”.
Prob>F	Probability of obtaining, by chance alone, an F value larger than the one calculated if in reality the means are equal across all levels. Observed significance probabilities of 0.05 or less are considered evidence of unequal means across the levels.
t Test	Shows the relationship between the F ratio and the t Test. Calculated as the square root of the F ratio. Appears only if the X factor has two levels.

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.