Interquartile Range Method

This function identifies potential outliers in a numeric vector using the interquartile range (IQR) method.

Usage

iqrMethod(x, k = 1.5, skew = FALSE, drop.na = FALSE)

Arguments

x

A numeric vector.

k

A numeric value specifying the fence factor. k = 1.5 is the default as it strikes a balance between sensitivity to mild outliers and robustness against extreme outliers. k = 3 is more lenient and is sometimes used when a higher tolerance for outliers is desired.

skew

A logical value indicating whether to calculate the version of the fences that accounts for moderate skewness in the underlying data distribution. By default, skew = FALSE, which calculates the fences assuming a symmetric distribution. However, if skew = TRUE, the lower and upper fences incorporate the medcouple, to account for potential asymmetry in the underlying data distribution. These formulas are explicitly derived and optimized for the scenario where k = 1.5 (Hubert and Vandervieren, 2008). Consequently, if the user attempts to use a value of k other than 1.5, the code will issue a warning message indicating that the formula is only defined for k = 1.5. In such cases, the code will automatically reset k to 1.5 and proceed with the calculations using the appropriate formulas and constants.

drop.na

A logical value indicating whether to remove missing values (NA) from the calculations. If TRUE, missing values will be removed. If FALSE (the default), missing values will be included in the calculations.

Value

A tibble with two columns:

• data: The original numeric values.

• outlier: A logical vector indicating whether each value is a potential outlier or not.

Details

For symmetric distributions, observations that fall outside the range defined by the lower fence (Q1 - k × IQR) and upper fence (Q3 + k × IQR) are considered as potential outliers, where Q1 and Q3 are the 25th and 75th percentiles, respectively. The fence factor can be adjusted to make the method more or less robust (often 1.5 or 3). Optionally, the method can account for moderate skewness in data distributions by incorporating the medcouple. In such a case, the lower and upper fences are expressed in terms of the medcouple, adjusting the fences asymmetrically to better accommodate skewed distributions. Note that the implemented method does not explicitly account for tail heaviness. While the medcouple can provide some robustness against heavy tails, the method may still struggle to accurately identify potential outliers in distributions with extreme kurtosis or long-tailed behavior.

References

• Everitt, B. S., and Skrondal, A. (2010). The Cambridge Dictionary of Statistics. Cambridge University Press.

• Tukey, J. (1977). Exploratory Data Analysis. Addison-Wesley

• Hubert M., and Vandervieren E. (2008). An Adjusted Boxplot for Skewed Distributions. Computational Statistics & Data Analysis, 52(12):5186-5201

Author

Christian L. Goueguel

Examples

set.seed(3317)
x <- stats::rexp(7, rate = 0.5)
iqrMethod(x)
#> # A tibble: 7 × 2
#>     data outlier
#>    <dbl> <lgl>  
#> 1 7.50   FALSE  
#> 2 0.466  FALSE  
#> 3 0.315  FALSE  
#> 4 6.94   FALSE  
#> 5 0.0899 FALSE  
#> 6 0.328  FALSE  
#> 7 1.75   FALSE  

iqrMethod(x, skew = TRUE)
#> # A tibble: 7 × 2
#>     data outlier
#>    <dbl> <lgl>  
#> 1 0.0899 TRUE   
#> 2 7.50   FALSE  
#> 3 0.466  FALSE  
#> 4 0.315  FALSE  
#> 5 6.94   FALSE  
#> 6 0.328  FALSE  
#> 7 1.75   FALSE