Confidence intervals for diversity indices

Computes estimates, standard errors, and approximate confidence intervals for the Berger-Parker, Simpson, and Shannon diversity indices. For the Shannon index, the value 1/r is added to each frequency count where r is the number of categories. These indices have a range of 0 to 1 where 0 indicates no diversity and 1 indicates maximum diversity.

For more details, see Section 1.13 of Bonett (2021, Volume 3)

Usage

ci.diversity(alpha, f)

Arguments

alpha

alpha level for 1 - alpha confidence

f

vector of multinomial frequency counts

Value

Returns a 3-row matrix. The columns are:

• Estimate - estimate of diversity index

• SE - standard error of estimate

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

f = c(847, 320, 57, 274, 36)
ci.diversity(.05, f)
#>         Estimate      SE     LL     UL
#> Berger    0.5598 0.01587 0.5287 0.5909
#> Simpson   0.7722 0.01229 0.7481 0.7963
#> Shannon   0.7292 0.01224 0.7052 0.7532

# Should return:
#         Estimate      SE     LL     UL
# Berger    0.5598 0.01587 0.5287 0.5909
# Simpson   0.7722 0.01229 0.7481 0.7963
# Shannon   0.7292 0.01224 0.7052 0.7532