relevance-package: Calculate Relevance and Significance Measures

In relevance: Calculate Relevance and Significance Measures

Calculate Relevance and Significance Measures

Description

Calculates relevance and significance values for simple models and for many types of regression models. These are introduced in 'Stahel, Werner A.' (2021) "Measuring Significance and Relevance instead of p-values." <https://stat.ethz.ch/~stahel/relevance/stahel-relevance2103.pdf>. These notions are also applied to replication studies, as described in the manuscript 'Stahel, Werner A.' (2022) "'Replicability': Terminology, Measuring Success, and Strategy" available in the documentation.

Details

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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.

Author(s)

Werner A. Stahel

Maintainer: Werner A. Stahel <[e-mail]>

References

Stahel, Werner A. (2021). New relevance and significance measures to replace p-values. To appear in PLoS ONE

See Also

Package regr, avaiable from https://regdevelop.r-forge.r-project.org

Examples

  data(swiss)
  rr <- lm(Fertility ~ . , data = swiss)
  termtable(rr)

relevance documentation built on Aug. 24, 2023, 3:03 p.m.