# DM: Deviation from the mode (DM) In qualvar: Implements Indices of Qualitative Variation Proposed by Wilcox (1973)

## Description

Computes the deviation from the mode for a vector of frequencies of categories.

## Usage

 1 DM(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. 327), 'the measure can be thought of as an index of deviation from the modal frequency, analogous to the variance as a measure of deviation from the mean'. The formula for the DM is:

1 - \frac{∑_{i = 1}^k (f_m - f_i)}{N(K-1)}

## Value

The value of the DM 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

 1 2 3 4 5 6 7 8 9 x <- rmultinom(1, 100, rep_len(0.25, 4)) x <- as.vector(t(x)) names(x) <- c("a", "b", "c", "d") DM(x) df <- rmultinom(10, 100, rep_len(0.25, 4)) df <- as.data.frame(t(df)) names(df) <- c("a", "b", "c", "d") apply(df, 1, DM) 

### Example output

[1] 0.92
[1] 0.9200000 0.9333333 0.9466667 0.8800000 0.9466667 0.9066667 0.9066667
[8] 0.9466667 0.8933333 0.8933333


qualvar documentation built on May 2, 2019, 1:14 a.m.