qualvar (version 0.1.0)

ADA: 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.

Value

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

Details

According to Wilcox (1973, p. 328), the ADA is 'an analog of the average or mean deviation'. The formula for the ADA is: $$1 - \frac{\sum_{i=1}^k \left| f_i - \frac{N}{K}\right|}{2 \frac{N}{K}(K-1)}$$

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)