﻿ Bias (direction: difficulty/ability/omit) = Ability

# Bias (direction: difficulty/ability/omit) = Ability

The size of the estimated bias in Table 12 and Table 13 is reported in logits(or Umean= units), and its significance is reported as a t-statistic. The direction, i.e., sign, of the bias depends on how it is to be interpreted. In Table 14 and on the Excel plots, the bias direction accords with the reported facet direction, Positive=.

In the specific observations being analyzed for local bias:

Bias Direction = Plus or + or Positive or Ability or Leniency or Easiness (higher score = higher measure)

Bias Direction = Minus or - or Negative or Difficulty or Severity (higher score = lower measure)

Observed score > Expected score

Person is more able here than overall. Element is less difficult here than overall

Observed score < Expected score

Person is less able here than overall. Element is more difficult here than overall

Mathematically:

local measure = global measure + bias measure

local measure = global measure - bias measure

To suppress bias analysis: Bias direction = Omit

Example: Table 13:

# ----------------------------------

| 9791 10506.0 6771 -.11 | -.10 <= observed-expected is negative (lower person performance than expected), so person ability bias is negative.

Bias = Minus

# ----------------------------------

| 9791 10506.0 6771  -.11 |  .10 <= observed-expected is negative (higher difficulty than expected), so item difficulty bias is positive.

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Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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