﻿ WHEXACT= Wilson-Hilferty exact normalization

# WHEXACT= Wilson-Hilferty exact normalization = Yes

Some versions of Winsteps have the standard WHEXACT=NO.

ZSTD INFIT is the "t standardized Weighted Mean Square" shown at the bottom of RSA p. 100. ZSTD (standardized as a z-score) is used of a t-test result when either the t-test value has effectively infinite degrees of freedom (i.e., approximates a unit normal value) or the Student's t-statistic distribution value has been adjusted to a unit normal value.

ZSTD OUTFIT is the "t standardized Unweighted Mean Square" based on the terms on RSA p. 100.

The Wilson-Hilferty transformation converts mean-square values to their equivalent "t standardized" normal deviates. See RSA p. 101

The degrees of freedom are 2/(qi*qi). The Wilson-Hilferty transformation is accurate for d.f.>25. With very small d.f., it becomes misleading, consequently the d.f. are not allowed to fall below 1, so that qi ≤ 1.4142.

Under certain circumstances, it can report the paradoxical finding that the mean-square apparently reports an overfit condition, but the normal deviate an underfit.

To allow this possibility, specify WHEXACT=Y

To suppress it, specify WHEXACT=N

The final q/3 term is omitted from the transformation.

Example: A person takes a test of 20 dichotomous items and obtains an unweighted chi-square value of 19.5.

WHEXACT=Y

The OUTFIT mean-square is 0.975, i.e., apparently slightly overfitting. The exact normal deviate is .03, i.e., very slightly underfitting.

WHEXACT=N

The OUTFIT mean-square is 0.975, i.e., apparently slightly overfitting. The reported normal deviate is -.08, i.e., slightly overfitting.

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