I Component of Effective Size (Tredoux, 1998)

Computes the Agresti-Agresti index of diversity I, the intermediate quantity used to construct effective size E' = 1/(1 - I) (Tredoux, 1998).

Usage

i_esize_T(lineup_tab)

Arguments

lineup_tab: A table of lineup choices.

Value

A scalar: the diversity index I.

Details

Tredoux (1998) used Agresti and Agresti's (1978) index of diversity: $$I = 1 - \frac{\sum_i o_i^2}{N^2},$$ where $o_i$ is the observed count for lineup member $i$ and $N$ is the total number of choices. This equals $1 - \sum_i p_i^2$, where $p_i = o_i/N$. The effective size is the reciprocal transform $E' = 1/(1-I)$, computed by esize_T.

References

Agresti, A., & Agresti, B. F. (1978). Statistical analysis of qualitative variation. Sociological Methodology, 9, 204-237.

Tredoux, C. G. (1998). Statistical inference on measures of lineup fairness. Law and Human Behavior, 22(2), 217-237.

Examples

lineup_vec <- round(runif(100, 1, 6))
lineup_tab <- table(lineup_vec)
i <- i_esize_T(lineup_tab)