Table 31.2, 31.3 DPF list = Person measures for item classes

Table 31.2 sorts by class then item. Table 31.3 sorts by item then class. The person measures by item class are plotted in the DPF Plot.


Table 31 supports the investigation of item bias, Differential Person Functioning (DPF), i.e., interactions between individual persons types of items. Specify DPF= for item classifying indicators in item labels. Person bias and DPF are the same thing.


Example output:

You want to examine person bias (DPF) between starting-blocks in Exam1.txt. You need a column in your Winsteps item label that has two (or more) item type codes.


Table 31.1 is best for pairwise comparisons, e.g., Positive vs. Negative items. Use Table 31.1 if you have two classes.


Table 31.2 or Table 31.3 are best for multiple comparisons, e.g., regions against the national average.


Table 31.2 sorts by class then item.


DPF class specification is: DPF=$S1W2


| TAP       OBSERVATIONS    BASELINE       DPF     DPF     DPF   DPF  DPF        KID             |



| 1-          11     .18    .23   -2.94    -.05   -3.52   -.58  1.05  -.55 .5937      1 Adam    M|

| 2-           2     .50    .46   -2.94     .04   -2.80    .14  1.65   .09 .0000      1 Adam    M|

| 3-           1    1.00    .61   -2.94     .39   -2.78>   .16  2.07   .08 .0000      1 Adam    M|

| 4-           1     .00    .00   -2.94     .00   -2.94    .00   .00   .00 1.000      1 Adam    M|

| 1-          11     .36    .39    -.26    -.03    -.67   -.41  1.35  -.30 .7686      2 Anne    F|


Table 31.3 sorts by item then class.


DPF class specification is: DPF=$S1W2


| TAP       OBSERVATIONS    BASELINE       DPF     DPF     DPF   DPF  DPF        KID             |



| 1-          11     .18    .23   -2.94    -.05   -3.52   -.58  1.05  -.55 .5937      1 Adam    M|

| 1-          11     .36    .39    -.26    -.03    -.67   -.41  1.35  -.30 .7686      2 Anne    F|


This displays a list of the local difficulty/ability estimates underlying the paired DPF analysis. These can be plotted directly from the Plots menu.


DPF class specification identifies the columns containing DPF classifications, with DPF= set to $S1W2 using the selection rules.


The DPF effects are shown ordered by CLASS within person (row of the data matrix).


TAP CLASS identifies the CLASS of items. KID is specified with ITEM=, e.g., the first CLASS is "1-"

OBSERVATIONS are what are seen in the data

COUNT is the number of observations of the classification used for DPF estimation, e.g., 11 responses were made by person 1 to non-extreme items in item class "1-".

AVERAGE is the average observation on the classification, e.g., 0.18 is the average score class "1-" items by person 1.

COUNT * AVERAGE = total score of person on the item class.

BASELINE is the prediction without DPF

EXPECT is the expected value of the average observation when there is no DPF, e.g., 0.92 is the expected average for person 1 on item class "1-" without DPF.

MEASURE is the what the overall ABILITY measure would be without DPF, e.g., -2.94 is the overall person ability of person 1 as reported in Table 18.

DPF: Differential Person Functioning

DPF SCORE is the difference between the observed and the expected average observations, e.g., 0.92 - 0.89= -0.03

DPF MEASURE is the person ability for this item class, e.g., person 1 has a local ability of -3.52 for item CLASS "1-".

The average of DPF measures across CLASS for an item is not the BASELINE MEASURE because score-to-measure conversion is non-linear. ">" (maximum score), "<" (minimum score) indicate measures corresponding to extreme scores.

DPF SIZE is the difference between the DPF MEASURE for this class and the BASELINE measure ability, i.e., -3.93 - -4.40 = .48. Item 4 is .48 logits more difficult for class F than expected.

DPF S.E. is the approximate standard error of the difference, e.g., 0.89 logits

DPF t is an approximate Student's t-statistic test, estimated as DPF SIZE divided by the DPF S.E. with a little less than (COUNT-1) degrees of freedom.

Prob. is the two-sided probability of Student's t. See t-statistics.



Person performance profiles by subtest


1. Put a subtest code in each item label
@subtest=1W1  ; position of subtest code in item label

2. Run Table 31 Differential Person Functioning for @subtest.

3. Table 31.2 shows the subtest (ITEM CLASS) measure (DPF MEASURE) for each item subtest for each person. Also the person's overall measure (BASELINE MEASURE)

4. Copy Table 31.2 into Excel

5. Excel "Data" "Text-to-columns", and then delete unwanted columns

5. Excel now has Person code, Subtest code, Person measure on Subtest, Overall measure

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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
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez
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