# outlierTest: Bonferroni Outlier Test In car: Companion to Applied Regression

## Description

Reports the Bonferroni p-values for testing each observation in turn to be a mean-shift outliner, based Studentized residuals in linear (t-tests) and generalized linear models (normal tests).

## Usage

 ```1 2 3 4 5 6 7 8``` ```outlierTest(model, ...) ## S3 method for class 'lm' outlierTest(model, cutoff=0.05, n.max=10, order=TRUE, labels=names(rstudent), ...) ## S3 method for class 'outlierTest' print(x, digits=5, ...) ```

## Arguments

 `model` an `lm` or `glm` model object. `cutoff` observations with Bonferonni p-values exceeding `cutoff` are not reported, unless no observations are nominated, in which case the one with the largest Studentized residual is reported. `n.max` maximum number of observations to report (default, `10`). `order` report Studenized residuals in descending order of magnitude? (default, `TRUE`). `labels` an optional vector of observation names. `...` arguments passed down to methods functions. `x` `outlierTest` object. `digits` number of digits for reported p-values.

## Details

For a linear model, p-values reported use the t distribution with degrees of freedom one less than the residual df for the model. For a generalized linear model, p-values are based on the standard-normal distribution. The Bonferroni adjustment multiplies the usual two-sided p-value by the number of observations. The `lm` method works for `glm` objects. To show all of the observations set `cutoff=Inf` and `n.max=Inf`.

## Value

an object of class `outlierTest`, which is normally just printed.

## Author(s)

John Fox [email protected] and Sanford Weisberg

## References

Cook, R. D. and Weisberg, S. (1982) Residuals and Influence in Regression. Chapman and Hall, https://conservancy.umn.edu/handle/11299/37076.

Fox, J. (2016) Applied Regression Analysis and Generalized Linear Models, Third Edition. Sage.

Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition, Sage.

Weisberg, S. (2014) Applied Linear Regression, Fourth Edition, Wiley.

Williams, D. A. (1987) Generalized linear model diagnostics using the deviance and single case deletions. Applied Statistics 36, 181–191.

## Examples

 `1` ```outlierTest(lm(prestige ~ income + education, data=Duncan)) ```

### Example output

```No Studentized residuals with Bonferonni p < 0.05
Largest |rstudent|: