Interquartile Range Method — iqr

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

Usage

iqr_outliers(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 are kept in the output (with a missing flag) and ignored when computing the fences.

Value

A tibble with two columns:

data: The original numeric values.
flag: 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

data(forageLIBS)
# iron contents (mg/kg): a few samples are far above the others
fe <- forageLIBS$Fe[!is.na(forageLIBS$Fe)]
iqr_outliers(fe)
#> # A tibble: 365 × 2
#>     data flag 
#>    <int> <lgl>
#>  1  1190 TRUE 
#>  2   391 TRUE 
#>  3   595 TRUE 
#>  4   591 TRUE 
#>  5  1030 TRUE 
#>  6   454 TRUE 
#>  7   424 TRUE 
#>  8  1080 TRUE 
#>  9  2060 TRUE 
#> 10   630 TRUE 
#> # ℹ 355 more rows
iqr_outliers(fe, skew = TRUE)   # adjusted for the skewness of the contents
#> # A tibble: 365 × 2
#>     data flag 
#>    <int> <lgl>
#>  1    64 TRUE 
#>  2  1190 TRUE 
#>  3  1030 TRUE 
#>  4    62 TRUE 
#>  5    63 TRUE 
#>  6  1080 TRUE 
#>  7  2060 TRUE 
#>  8    59 TRUE 
#>  9    50 TRUE 
#> 10    54 TRUE 
#> # ℹ 355 more rows