Table 11 Responses used to calculate bias estimates

Table 11 summarizes the response modeling in the bias analysis


Bias/Interaction: 1. Student, 2. Format


| Cat  Score  Exp.  Resd StRes|                    |


| 9.60  9.60  9.60   .01  .01 | Mean (Cnt: 296)    |

| 1.34  1.34  1.30   .31  .53 | S.D. (Population)  |

| 1.34  1.34  1.30   .31  .53 | S.D. (Sample)      |


Count of measurable responses = 296.00

Raw-score variance of observations      = 1.80 100.00%

Variance explained by Rasch measures    = 1.53  85.00%

Variance of residuals                   = 0.27  15.00%

Variance explained by bias/interactions = 0.18  10.00%

Variance remaining in residuals         = 0.09   5.00%





Observed value of the category in the data file


Value of category in this analysis. This is less than Cat. if there are structural zeroes.


Expected score based on current measures


Residual, the score difference between Score and Exp.


The residual divided by its standard error. The Rasch model is now over-parameterized, so the standardized residuals are expected to have an S.D. less than 1.0.


average of the observations


Count is the number of observations

S.D. (Population)

standard deviation treating this sample as the entire population

S.D. (Sample)

standard deviation treating this sample as a sample from the population. It is larger than S.D. (Population).


Count of measurable responses

the number of ratings used in estimating the bias terms. This may be only a small fraction of the entire data set.

Raw-score variance of observations

square of S.D. (Population) of Score in Table 11

Variance explained by Rasch measures

from Table 5

Variance of residuals

from Table 5

Variance explained by bias/interactions

Variance of Residuals - Variance remaining in residuals

Variance remaining in residuals

square of S.D. (Population) of Resd in Table 11

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Rasch Publications
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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