ADA: Average Deviation Analog (ADA)
In qualvar: Implements Indices of Qualitative Variation Proposed by Wilcox (1973)

Description Usage Arguments Details Value References Examples

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

1	ADA(x, na.rm = TRUE)

`x`	a vector of frequencies
`na.rm`	if TRUE, missing values are removed. If FALSE, NA is returned if there is any NA value.

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{∑_{i=1}^k ≤ft| f_i - \frac{N}{K}\right|}{2 \frac{N}{K}(K-1)}

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

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.

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)