The Means Differences data table is created after you select the Save Means Differences option in the Response Screening red triangle menu. The data table provides results for standard difference tests. If the practical differences and equivalences option has been specified, both tests of practical difference and tests of practical equivalence are also provided in the new data table. Each row compares a response across two levels of a categorical factor. Results of the pairwise comparisons are color-coded to facilitate interpretation. See Practical Difference for a description of how the practical difference is specified. See Example of Tests of Practical Significance and Equivalence for an example.
Y
The continuous response variables.
X
The categorical variables.
Level
The level of the categorical X variable.
-Level
The level of the categorical X variable being compared to the initial Level.
This Mean
The mean of the response variable for the level in the Level column. If the Robust option is selected, robust estimates of the means are used.
Base Mean
The mean of the response variable for the level in the -Level column. If the Robust option is selected, robust estimates of the means are used.
Difference
The estimated difference in means across the two levels, calculated as This Mean - Base Mean.
Std Err Diff
The standard error of the difference in means. This is a robust estimate if the Robust option is selected.
Difference L95
The lower limit of the 95% confidence interval for the difference between the means.
Difference U95
The upper limit of the 95% confidence interval for the difference between the means.
p-Value
The p-value for the usual Student's t test for a pairwise comparison. This is the robust version of the t test when the Robust option is selected. Tests that are significant at the 0.05 level are highlighted.
Logworth
The quantity -log10(p-value). This transformation adjusts p-values to provide an appropriate scale for graphing.
FDR p-Value
The FDR p-value for the Student’s t test for a pairwise comparison. See Statistical Details for the Response Screening Platform.
FDR Logworth
The quantity -log10(FDR p-Value).
Diff FDR L95
The lower limit of the 95% Benjamini-Yekutieli FDR adjusted confidence interval for the difference between the means.
Diff FDR U95
The upper limit of the 95% Benjamini-Yekutieli FDR adjusted confidence interval for the difference between the means.
Difference to Detect
The difference in means that is considered to be of practical interest. This is specified when you select the Practical Differences and Equivalences red triangle menu option. See Practical Differences and Equivalences.
Practical Dif PValue
The p-value for a test of whether the absolute value of the mean difference in Y between Level and -Level is less than or equal to the Difference to Detect. A small p-value indicates that the absolute difference exceeds the Difference to Detect. This indicates that Level and -Level account for a difference that is of practical consequence.
Practical Equiv PValue
Uses the Two One-Sided Tests (TOST) method to test for a practical difference between the means (Schuirmann 1987). The Difference to Detect specifies a threshold difference for which smaller differences are considered practically equivalent. One-sided t tests are constructed for two null hypotheses: the true difference exceeds the Difference to Detect; the true difference is less than the negative of the Difference to Detect. If both tests reject, this indicates that the absolute difference in the means falls within the Difference to Detect. Therefore, the groups are considered practically equivalent.
The Practical Equivalence PValue is the largest p-value obtained on the one-sided t tests. A small Practical Equiv PValue indicates that the mean response for Level is equivalent, in a practical sense, to the mean for -Level.
FDR Practical Dif PValue
The FDR p-value for the practical difference test for a pairwise comparison. See Statistical Details for the Response Screening Platform.
FDR Practical Equiv PValue
The FDR p-value for the TOST test for a pairwise comparison. See Statistical Details for the Response Screening Platform.
Practical Result
A description of the results of the tests for practical difference and equivalence. Values are color-coded to help identify significant results.
– Different (Pink): Indicates that the absolute difference is significantly greater than the practical difference.
– Equivalent (Green): Indicates that the absolute difference is significantly within the practical difference.
– Inconclusive (Gray): Indicates that neither the test for practical difference nor the test for practical equivalence is significant.