Differential Item Functioning DIF Sample Size Nomogram

Differential Item Functioning (DIF) compares the difficulty of an item for a person sample of interest, the Focal Group (F), with the difficulty of the item for another group, the Reference Group (R). As we plan to investigate DIF, several questions arise:

The nomogram is based on a Student's t-statistic with two independent groups of different sizes, NF and NR, but equal standard deviations, S. The t-statistic of the DIF size, D, is

t-statistics for two independent groups

Group size values are chosen such that the two-sided probability of observing t or greater is p = .05 for the specified DIF size, D. The standard deviation, S, is chosen at a reasonable value, 1.88 logits, based on inspection of empirical data.

Example: if our Focal group size is 100, and our Reference group size is 1000, then the DIF size will need to be 0.4 logits or more to be statistically significant.

John Michael Linacre

Fisher R.A. (1926). The arrangement of field experiments. Journal of the Ministry of Agriculture, 33: 504.

Tristan, A. (2006). An adjustment for sample size in DIF analysis. Rasch Measurement Transactions, 20:3, p. 1070-71.

Differential Item Functioning DIF Sample Size Nomogram
Revised 11 November 2015, with acknowledgement to Siddhi Pittayachawan.

Linacre J.M. (2013) Differential Item Functioning DIF Sample Size Nomogram, Rasch Measurement Transactions, 26:4 p. 1391

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