Publication date: 05/24/2021

## Result Table

The Response Screening Result table contains a row for each pair of Y and X variables. The columns of the table contain measures and model fit statistics that are specific to the selected fit and Y and X modeling types.

Group

(Appears only if there is a grouping variable.) The level of the grouping column.

Y

The specified response columns.

X

The specified factor columns.

Count

The number of rows used for testing, or the corresponding sum of the Freq or Weight variable.

PValue

The p-value for the significance test corresponding to the pair of Y and X variables. For more information about Fit Y by X statistics, see Introduction to Fit Y by X in Basic Analysis.

LogWorth

The quantity -log10(p-value). This transformation adjusts p-values to provide an appropriate scale for graphing. A value that exceeds 2 is significant at the 0.01 level (-log10(0.01) = 2).

FDR PValue

The False Discovery Rate p-value calculated using the Benjamini-Hochberg technique. This technique adjusts the p-values to control the false discovery rate for multiple tests. If there is no Group variable, the set of multiple tests includes all tests displayed in the table. If there is a Group variable, the set of multiple tests consists of all tests conducted for each level of the Group variable. For more information about the FDR correction, see Benjamini and Hochberg (1995). For more information about the false discovery rate, see The False Discovery Rate.

FDR LogWorth

The quantity -log10(FDR PValue). This is the statistic to use for plotting and assessing significance. Note that small p-values result in high FDR LogWorth values. Cells corresponding to FDR LogWorth values greater than two (p-values less than 0.01) are colored with an intensity gradient.

Effect Size

Indicates the extent to which response values differ across the levels or values of X. Effect sizes are scale invariant.

When Y is continuous, the effect size is the square root of the average sum of squares from the hypothesis test divided by a robust estimate of the response standard deviation. If the interquartile range (IQR) is nonzero and IQR > range/20, the standard deviation estimate is IQR/1.3489795. Otherwise the sample standard deviation is used.

When Y is categorical and X is continuous, the effect size is the square root of the average ChiSquare value for the whole model test.

When Y and X are both categorical, the effect size is the square root of the average Pearson ChiSquare.

Rank Fraction

The rank of the FDR LogWorth expressed as a fraction of the number of tests. If the number of tests is m, the largest FDR LogWorth value has Rank Fraction 1/m, and the smallest has Rank Fraction 1. The Rank Fraction is used in plotting the PValues and FDR PValues in rank order of decreasing significance.

RSquare

(Appears only when Y is continuous.) The coefficient of determination, which measures the proportion of total variation explained by the model.

Kappa

(Appears only when Y and X are both categorical and have the same number of levels.) A measure of agreement between Y and X.

Corr

(Appears only when Y and X are both categorical.) The Pearson product-moment correlation in terms of the indices defined by the value ordering.

The following columns are added to the Result table when the Robust option is selected in the launch window. The Robust option applies only when Y is continuous, so Robust column cells are empty when Y is categorical.

Robust PValue

The p-value for the significance test corresponding to the pair of Y and X variables using a robust fit.

Robust LogWorth

The quantity -log10(Robust PValue).

Robust FDR PValue

The False Discovery Rate calculated for the Robust PValues using the Benjamini-Hochberg technique. If there is no Group variable, the multiple test adjustment applies to all tests displayed in the table. If there is a Group variable, the multiple test adjustment applies to all tests conducted for each level of the Group variable.

Robust FDR LogWorth

The quantity -log10(Robust FDR PValue).

Robust Rank Fraction

The rank of the Robust FDR LogWorth expressed as a fraction of the number of tests.

Robust Chisq

The chi-square value associated with the robust test.

Robust Sigma

The robust estimate of the error standard deviation.

Robust Outlier Portion

The portion of the values whose distance from the robust mean exceeds three times the Robust Sigma.

The following columns are added to the Result table when the Cauchy option is selected in the launch window. The Cauchy option applies only when Y is continuous, so Cauchy column cells are empty when Y is categorical.

Cauchy PValue

The p-value for the significance test corresponding to the pair of Y and X variables using a Cauchy fit.

Cauchy LogWorth

The quantity -log10(Cauchy PValue).

Cauchy FDR PValue

The False Discovery Rate calculated for the Cauchy PValues using the Benjamini-Hochberg technique. If there is no Group variable, the multiple test adjustment applies to all tests displayed in the table. If there is a Group variable, the multiple test adjustment applies to all tests conducted for each level of the Group variable.

Cauchy FDR LogWorth

The quantity -log10(Cauchy FDR PValue).

Cauchy Rank Fraction

The rank of the Cauchy FDR LogWorth expressed as a fraction of the number of tests.

Cauchy ChiSquare

The chi-square value associated with the test from the Cauchy fit.

Cauchy Sigma

The estimate of the error standard deviation from the Cauchy fit.

Cauchy Outlier Portion

The portion of the values whose distance from the mean of the Cauchy fit exceeds three times the Cauchy Sigma.