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Robust outlier rules

Source: R/outlier.R
outlier_flag_mad.Rd

  • outlier_flag_mad(): modified z-score of Iglewicz & Hoaglin (1993), |0.6745 (x - median) / MAD| > threshold with the raw MAD = median(|x - median|). When more than half of the values are identical (MAD = 0, e.g. values piled at a detection floor) no value is flagged by this rule.

  • outlier_flag_iqr(): Tukey's fences (Tukey 1977), x < Q1 - k IQR or x > Q3 + k IQR. method = "quantile" uses the type-7 quartiles of stats::quantile(); method = "hinges" uses Tukey's hinges of grDevices::boxplot.stats() (the boxplot whiskers).

Normal data: the IQR rule (about 2.7 SD) is stricter than the MAD rule (3.5 SD), so nearly every MAD outlier is also an IQR outlier. "MAD only" values appear with skewed or bimodal distributions; values flagged by both rules are the most robust signals.

Usage

outlier_flag_mad(x, threshold = 3.5)

outlier_flag_iqr(x, k = 1.5, method = c("quantile", "hinges"))

Arguments

x

Numeric vector (NA allowed).

threshold

Cut-off on the absolute modified z-score (3.5 recommended).

k

Fence multiplier (1.5 = outlier, 3 = far out).

method

"quantile" or "hinges", see Description.

Value

A logical vector of the same length as x (NA everywhere when fewer than 5 values are observed; FALSE for missing values otherwise).

References

Tukey JW (1977). Exploratory Data Analysis. Addison-Wesley.

Hoaglin DC, Iglewicz B, Tukey JW (1986). Performance of some resistant rules for outlier labeling. J Am Stat Assoc 81:991-999.

Iglewicz B, Hoaglin DC (1993). How to Detect and Handle Outliers. ASQC Quality Press.

Leys C, Ley C, Klein O, Bernard P, Licata L (2013). Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median. J Exp Soc Psychol 49:764-766.

Examples

x <- c(rnorm(50), 8)
which(outlier_flag_mad(x))
#> [1] 27 39 51
which(outlier_flag_iqr(x))
#> [1] 18 27 31 38 39 51