Specialized Models • Response Screening • The PValues Data Table
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The PValues Data Table
The PValues data table contains a row for each pair of Y and X variables. If you specified a column for Group, the PValues data table contains a first column called Group. A row appears for each level of the Group column and for each pair of Y and X variables. The PValues data table also contains a table variable called Original Data that gives the name of the data table that was used for the analysis. If you specified a By variable, JMP creates a PValues table for each level of the By variable, and the Original Data variable gives the By variable and its level.
PValues Data Table, Partial View shows the PValues data table created using the Probe.jmp sample data table.
PValues Data Table, Partial View
PValues Data Table Columns
The PValues data table displays columns containing measures and statistics that are appropriate for the selected fit and combination of Y and X modeling types. The columns in the data table include:
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. See the Basic Analysis book for additional details about Fit Y by X statistics.
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 ).
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 details about the FDR correction, see Benjamini and Hochberg, 1995. For details about the false discovery rate, see The False Discovery Rate.
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.
Effect Size
Indicates the extent to which response values differ across the levels or values of X. Effect sizes are scale invariant.
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When Y is continuous, the effect size is the square root of the average sum of squares for the hypothesis divided by a robust estimate of the response standard deviation. If the interquartile range (IQR) is nonzero, the standard deviation estimate is . If the IQR is zero, the sample standard deviation is used.
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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.
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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. 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.
YMean
The mean of Y.
SSE
Appears when Y is continuous. The sum of squares for error.
DFE
Appears when Y is continuous. The degrees of freedom for error.
MSE
Appears when Y is continuous. The mean squared error.
F Ratio
Appears when Y is continuous. The F Ratio for the analysis of variance or regression test.
RSquare
Appears when Y is continuous. The coefficient of determination, which measures the proportion of total variation explained by the model.
DF
Appears when Y and X are both categorical. The degrees of freedom for the ChiSquare test.
LR Chisq
Appears when Y and X are both categorical. The value of the Likelihood Ratio ChiSquare statistic.
Columns Added for Robust Option
If you suspect that your data contains outliers, select the Robust option on the launch window to reduce the sensitivity of tests for continuous responses to outliers. With this option, Huber M-estimates (Huber and Ronchetti, 2009) are used in fitting regression and ANOVA models. Huber M-estimates are fairly close to least squares estimates when there are no outliers, but use outlier-downweighting when there are outliers.
The following columns are added to the PValues data table when the Robust option is selected in the launch window. The Robust option only applies when Y is continuous, so Robust column cells are empty when Y is categorical. See the Basic Analysis book for additional details about Huber M-estimation. For an example, see Example of Robust Fit.
Robust PValue
The p-value for the significance test corresponding to the pair of Y and X variables using a robust.
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.
Robust CpuTime
Time in seconds required to create the Robust report.
PValues Data Table Scripts
Relevant scripts are saved to the PValues data table. All but one of these reproduce plots provided in the report. When you select rows in the PValues table, the Fit Selected script produces the appropriate Fit Y by X analyses.