outlier detection using Median Absolute Deviation (MAD)

This function identifies outliers in a numeric vector using Median Absolute Deviation (MAD) method, with specialized handling for very small samples. Returns results in htest format for consistency with statistical tests.

Usage

mad.test(x, na.rm = TRUE)

Arguments

x: A numeric vector. Missing values (NA) are allowed and will be excluded from calculations.
na.rm: Logical. Should missing values be removed? Default is TRUE.

Value

An object of class "htest" containing:

statistic: The test statistic (MAD-based z-score of most extreme outlier)
parameter: Named vector with: n, median, mad, threshold
p.value: Approximate p-value based on outlier probability
method: Description of the method used
data.name: Name of the data vector
alternative: Character string describing the alternative hypothesis
outlier.indices: Indices of detected outliers (as additional element)

Details

For samples with n > 5, uses standard MAD method with threshold of 3. For very small samples (n <= 5), uses MAD with adjusted thresholds:

n = 3-4: threshold = 2.5
n = 5: threshold = 2.8

The test statistic is calculated as the maximum absolute deviation from median divided by adjusted MAD.

Examples

if (FALSE) { # \dontrun{
# Basic usage
x <- c(1, 2, 3, 100, 4, 5, 3)
mad.test(x)

# Small sample
x3 <- c(1, 2, 10)
mad.test(x3)
} # }