Description Details Author(s) References See Also Examples
Calculates relevance and significance values for simple models and for many types of regression models. These are introduced in 'Stahel, Werner A.' (2021) "New relevance and significance measures to replace p-values." <https://stat.ethz.ch/~stahel/relevance/stahel-relevance2103.pdf>.
The DESCRIPTION file:
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Relevance is a measure that expresses the (scientific) relevance of an effect. The simplest case is a single sample of supposedly normally distributed observations, where interest lies in the expectation, estimated by the mean of the observations. There is a threshold for the expectation, below which an effect is judged too small to be of interest.
The estimated relevance ‘Rle’ is then simply the estimated effect divided by the threshold. If it is larger than 1, the effect is thus judged relevant. The two other values that characterize the relevance are the limits of the confidence interval for the true value of the relevance, called the secured relevance ‘Rls’ and the potential relevance ‘Rlp’.
If Rle > 1, then one might say that the effect is “significantly relevant”.
Another useful measure, meant to replace the p-value, is the “significance” ‘Sg0’. In the simple case, it divides the estimated effect by the critical value of the (t-) test statistic. Thus, the statistical test of the null hypothesis of zero expectation is significant if ‘Sg0’ is larger than one, Sg0 > 1.
These measures are also calculated for the comparison of two groups, for proportions, and most importantly for regression models. For models with linear predictors, relevances are obtained for standardized coefficients as well as for the effect of dropping terms and the effect on prediction.
The most important functions are
twosamples()
: calculate the measures for two paired or unpaired sampless or a simple mean. This function calls
inference()
: calculates the confidence interval and siginificance based on an estimate and a standard error, and adds relevance for a standardized effect.
termtable()
: deals with fits of regression models with a linear predictor.
It calculates confidence intervals and significances for
the coefficients of terms with a single degree of freedom.
It includes the effect of dropping each term
(based on the drop1
function)
and the respective significance and relevance measures.
termeffects()
: calculates the relevances for the coefficients
related to each term. These differ from the enties of termtable
only for terms with more than one degree of freedom.
Werner A. Stahel
Maintainer: Werner A. Stahel <stahel@stat.math.ethz.ch>
Stahel, Werner A. (2021). New relevance and significance measures to replace p-values. To appear in PLoS ONE
Package regr, avaiable from https://regdevelop.r-forge.r-project.org
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