qualvar (version 0.2.0)

B: B (modified geometric mean)

Description

Computes the B index for a vector of frequencies of categories.

Usage

B(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 B statistics, which is normalised (varies between 0 and 1).

Details

According to Wilcox (1973, p. 330), and following Kaiser (1968), the B index relies on the geometric mean, but corrects it for undesirable properties. The formula for the B index is: $$1 - \sqrt{1 - \left(\sqrt[K]{\prod_{i=1}^k \frac{f_i K}{N}}\right)^2}$$

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. Kaiser, Henry F. 'A Measure of the Population Quality of Legislative Apportionment.' The American Political Science Review 62, no. 1 (March 1968): 208. doi:10.2307/1953335.

Examples

# NOT RUN {
x <- rmultinom(1, 100, rep_len(0.25, 4))
x <- as.vector(t(x))
B(x)

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