When you launch Response Screening through the Fit Model platform, the Fit Response Screening report contains an Effect Tests table and two plots. The plots shown are the FDR PValue Plot for Effects and the FDR Logworth by Effect Size plot. Both plots are interpreted in the same way as for the platform itself. See Response Screening Plots.
The Effect Tests table contains a row for each pair consisting of a Y variable and a model Effect. If you select the Robust Fit option on the launch window, the models are fit using Huber M-estimation. If you specified a By variable, an Effect Tests table is created for each level of the By variable. The table includes the following columns:
Y
The specified response columns.
Switch
(Available when Switch columns are specified in the launch.) Specifies the column that is included in the model. This identifies which model the row is describing. When the Effect column contains “Switch”, the Switch column specifies the effect.
Tip: Click on the Switch column header to sort the Effect Tests table by Switch. This enables you to more clearly see the effects within each model tested. For multiple Ys, sort on Switch and then on Y to arrange the effects within models for each response.
Effect
The specified model effects.
FRatio
The test statistic for a test of the Effect. This is the value found in the Effect Tests report in Least Squares Fit.
Chi Square
(Available only when a robust fit is specified in the launch.) The test statistic for a test of the Effect.
PValue
The p-value for the significance test corresponding to the FRatio. See “Effect Tests” in Fitting Linear Models for more information about Effect Tests.
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 (because -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. For more information about the FDR correction, see Benjamini and Hochberg (1995). For more information about the false discovery rate, see Statistical Details for the Response Screening Platform or Westfall et al. (2011).
FDR Logworth
The quantity -log10(FDR PValue). This is the best statistic for plotting and assessing significance. Note that small p-values result in high FDR logworth values.
Rank Fraction
(Not shown by default.) 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. Equivalently, the Rank Fraction ranks the p-values in increasing order, as a fraction of the number of tests. The Rank Fraction is used in plotting the PValues and FDR PValues in rank order of decreasing significance.
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 chi-Square 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.
– When a robust fit is specified in the launch, the effect size is calculated as the square root of (chi-square test statistic/n), where n is the number of observations.
Test DF
The degrees of freedom for the effect test.