ADA {qualvar}

Average Deviation Analog (ADA)

Description

Computes the average deviation analog (ADA) for a vector of frequencies of categories.

Usage

ADA(x, na.rm = TRUE)

Arguments

x

a vector of frequencies

na.rm

if TRUE, missing values are removed. If FALSE, NA is returned if there is any NA value.

Details

According to Wilcox (1973, p. 328), the ADA is 'an analog of the average or mean deviation'. The formula for the ADA is:

1 - \frac{\sum_{i=1}^k \left| f_i - \frac{N}{K}\right|}{2 \frac{N}{K}(K-1)}

Value

The value of the ADA statistics, which is normalised (varies between 0 and 1).

References

Wilcox, Allen R. 'Indices of Qualitative Variation and Political Measurement.' The Western Political Quarterly 26, no. 2 (1 June 1973): 325-43. doi:10.2307/446831.

Examples

x <- rmultinom(1, 100, rep_len(0.25, 4))
x <- as.vector(t(x))
ADA(x)

df <- rmultinom(10, 100, rep_len(0.25, 4))
df <- as.data.frame(t(df))
apply(df, 1, ADA)