freqadjust: Frequency Adjusting and Averaging

Description

These functions provide simple methods for smoothing score distributions, typically ones with unobserved score points, prior to performing equipercentile equating. freqbump smooths by adding a small relative frequency to each score while adjusting the probabilities to sum to one (see Kolen and Brennan, 2004, p. 48). freqavg replaces frequencies falling below a specified threshold with an average of adjacent values (see Moses and Holland, 2008).

Usage

freqbump(x, jmin = 10^-6, Kx = max(x[,1]))
freqavg(x, jmin = 1)

Arguments

two-column matrix of class freqtab, where column 1 specifies the score scale and column 2 the frequencies for each score point. For freqbump, x can also be a bivar

jmin

for freqbump, the frequency to be added to each score point (default is 10^-6) for freqavg, the minimum frequency, as an integer, below which frequencies will be replaced (default is 1)

integer indicating the number of items in the scale

Value

Returns a vector of adjusted frequencies. For freqavg, if no values fall below jmin these will simply be the original frequencies. For freqbump, frequencies are in the form of probabilities, summing to 1.

References

Kolen, M. J., and Brennan, R. L. (2004) Test Equating, Scaling, and Linking. (2nd ed.), New York: Springer. Moses, T., and Holland, P. W. (2008). Notes on a general framework for observed score equating (ETS Research Rep. No. RR-08-59). Princeton, NJ: ETS.

Examples

Run this code

set.seed(2005)
x <- round(rnorm(1000, 100, 10))
xscale <- 70:130
xtab <- freqtab(xscale, x)

xavg <- freqavg(xtab)
xbump <- freqbump(xtab)
cbind(xtab, avg = xavg,
  bump = round(xbump * sum(xtab[, 2]), 6))