synthetic {equate} | R Documentation |
This function returns the score distribution for a hypothetical synthetic examinee population, as required when equating under the nonequivalent groups design.
synthetic(x, y, w, method, internal = TRUE)
x, y |
bivariate score distributions of class “freqtab ” for forms X, with the anchor, and Y with the anchor. Columns 1 and 2 of each include all score combinations for the total and anchor test score scales, and column 3 contains the number of examinees obtaining each combination (see freqtab for details)
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w |
value between 0 and 1 specifying the weight applied to form X scores (and implicitly specifying the form Y weight as 1 - w )
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method |
string specifying the equating method, where the options are "tucker" , levine , and "frequency" (for frequency estimation). For the first two, equating type=linear is assumed, which can only be overridden via equate and equate.ln . Frequency estimation implies type=equipercentile
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internal |
logical indicating whether or not the anchor item scores are included in the total scores (default is TRUE ). This is only required for the Levine method
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The synthetic population score distribution is based on a weighted combination of the form X and Y distributions. The concept of a synthetic population was first described by Braun and Hollan (1982) and Kolen and Brennan (2004) summarize the assumptions made by each equating method.
For the Tucker and Levine methods, a list of length 1 ($synthstats
) including the mean and standard deviation for form X, form Y, form XV, form YV, and for the synthetic popultion taking forms X and Y.
For the frequency estimation method, a frequency table for the synthetic population taking forms X and Y ($synthtab
) is also returned.
Anthony Albano tony.d.albano@gmail.com
Braun, H. I., & Holland, P. W. (1982). Observed-score test equating: A mathematical analysis of some ETS equating procedures. In P. W. Holland and D. B. Rubin (Eds.), Test Equating (pp. 9-49). New York: Academic.
Kolen, M. J., & Brennan, R. L. (2004) Test Equating, Scaling, and Linking. (2nd ed.), New York: Springer.
x <- KBneat$x x <- freqtab(x[,1],0:36,x[,2],0:12) y <- KBneat$y y <- freqtab(y[,1],0:36,y[,2],0:12) synthetic(x,y,w=1,method="T") synthetic(x,y,w=1,method="L") synthetic(x,y,w=1,method="F")