﻿ 4 facet Arithmetic Test: Measuring, Anchoring and Describing

# 4 facet Arithmetic Test: Measuring, Anchoring and Describing

Many measurement problems are best tackled with two Facets runs:

1. Measurement of student ability, judge severity, item difficulty, etc.

The actual participant elements that interacted to provide the observations are measured, and then the elements anchored at those measures. This provides a stable frame of reference for further analyses.

2. Descriptive summaries of various effects identified by demographics, judge training, sub-test content, etc.

Participating elements are replaced by their hypothesized components, and further analyses are performed, with care to provide connected, i.e, unambiguous, measurement conditions.

Using R. Mislevy's data set (extracted from the Armed Services Vocational Aptitude Battery - ASVAB), it is hypothesized that 776 students (black females, black males, white females, and white males) each have an arithmetic ability (a fixed effect). The analyst wants to decompose these abilities into gender (sex) and race (ethnicity) effects. First the item difficulties are calibrated and the 776 examinees measured:

Facets specifications and data (in file Measure.txt):

title = Arithmetic Competency - R. Mislevy

anchorfile = measanc.txt ; an anchored file is written out

facets = 4 ; demographics included in the facets

pt-biserial = y ; point-biserial as a rough fit statistics

vertical = 1N,2A,3A,4* ; for communication

yard = 0, 4 ;

models =

?, , ,?,D ; use this model for measuring items and students

; ?,?,?, ,D ; use this model for demographic summaries - commented out here

*

positive = 2,3,4 ; all facets except item difficulties are abilities

noncenter = 2,  4 ; noncenter students and one demographic

labels =

1,Arithmetic

1-4 ; 4 arithmetic items

*

2,Race

1=Black

2=White

*

3,Sex

1=Female

2=Male

*

4,Students

1-776 ; no more information about the students

*

Data =

1-4,2,2,1,0,0,0,0  ; on the 4 items, white male student 1, failed

|

1-4,1,1,776,1,1,1,1 ; on the 4 items, black female student 776, succeeded

or

Dvalues = 1, 1-4  ; place 1-4 in first data facet location of all data records

Data=

2,2,1,0,0,0,0 ; on the 4 items, white male student 1, failed

|

1,1,776,1,1,1,1 ; on the 4 items, black female student 776, succeeded

Then the descriptive phase is performed to estimate the demographic effects. This is set up by editing the anchor file produced in the measurement phase, and changing the model statement:

Facets specifications and data (in file Measanc.txt, also in file Meas2anc.txt):

title = Arithmetic Competency - R. Mislevy

; anchorfile = measanc.txt

facets = 4

pt-biserial = y

vertical = 1N,2A,3A,4*

yard = 0, 4

positive =   2,3,4 ; facets 1, 2, 3 this time

noncenter=   2,4 ; facet , Race, 2 floats

Models=

;?,,,?,RS1,1, (D) ; comment out the measurement model

?,?,?,,RS1,1, (D) ; use the summarizing model

*

Rating (or partial credit) scale=RS1,D ; use the measurement run rating scale

0=,0,A, ; Rasch-Andrich thresholds in the description run

*

Labels=

1,Arithmetic,A ; these are anchored at their Rasch-Andrich thresholds

1,1,-.6079245

2,2,-.1628681

3,3,.4518689

4,4,.9676156

*

2,Race,A ; the A is inoperative, because there are no logit values

1,Black,

2,White,

*

3,Sex,A

1,Female,

2,Male,

*

4,Students,A ; this facet is ignored this run

1,1,-2.537946 ; these anchored measures are ignored this run

|

1-4,1,1,776,1,1,1,1

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