# outlier

##### R function for univariate outliers detection

The function allows to perform univariate outliers detection using three different methods. These methods are those described in: Wilcox R R, "Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy", Springer 2010 (2nd edition), pages 31-35.

- Keywords
- outlier

##### Usage

`outlier(x, method = "mean", addthres = TRUE)`

##### Arguments

- x
Vector storing the data.

- method
Outliers identification method, either "mean" (default), "median", or "boxplot".

- addthres
Takes FALSE or TRUE (default) if user does not want or does want some threshold lines be added to the returned chart.

##### Details

Two of the three methods are robust, and are therefore less prone to the masking effect. (1) With the mean-based method, an observation is considered outlier if the absolute difference between that observation and the sample mean is more than 2 Standard Deviations away (in either direction) from the mean. In the plot returned by the function, the central reference line is indicating the mean value, while the other two are set at \(mean-2*SD and mean+2*SD\).

(2) The median-based method considers an observation as being outlier if the absolute difference between the observation and the sample median is larger than the Median Absolute Deviation divided by 0.6745. In this case, the central reference line is set at the median, while the other two are set at \(median-2*MAD/0.6745\) and \(median+2*MAD/0.6745\).

(3) The boxplot-based method considers an observation as being an outlier if it is either smaller than the 1st Quartile minus 1.5 times the InterQuartile Range, or larger than the 3rd Quartile minus 1.5 times the InterQuartile Range. In the plot, the central reference line is set at the median, while the other two are set at \(1Q-1.5*IQR\) and \(3Q+1.5*IQR\).

##### Value

The function also returns a list containing information about the chosen method, the mid-point, lower and upper boundaries where non-outlying observations are expected to fall, total number of outlying observations, and a dataframe listing the observations and indicating which is considered outlier. In the charts, the outlying observations are flagged with their ID number.

##### Examples

```
# NOT RUN {
# create a toy dataset
mydata <- c(2,3,4,5,6,7,8,9,50,50)
# locate outlier(s) using the median-based method
outlier(mydata, method="median", addthres=TRUE)
# }
```

*Documentation reproduced from package GmAMisc, version 1.0.0, License: GPL (>= 2)*