DOCOMNT RIESUBE ED 171 786 TH 009 257

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DOCOMNT RIESUBE ED 171 786 TH 009 257 AUTHOR Hill, Richard K TITLE Use of the Rasch Model tc Sc lve Data Problems Encountered by the California Assessment Program

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DOCOMNT RIESUBE

ED 171 786

TH 009 257

AUTHOR

Hill, Richard K.

TITLEUse of the Rasch Model tc Sc lve. Data Problems

Encountered by the California Assessment Program.

PUB DATE

Apr 79

NOTE

11p. ;Paper presented at the Annual Meeting of the

National Council on Measurement in Education (San

Francisco, California, April, 1979)

EDES PRICE

MF01/PC01 Plus Postage.

DESCRIPTORSBlack Students; Caucasian Students; *ComplexityLevel; Cultural Differences; *Data Analysis; Item

Analysis; *Mathematical Models; Primary Education;

Racial Differences; Reading Achievement; *Reading

Tests; Spanish Americans; State Programs; *Test Bias; *Testing Problems; Testing Programs; Test Items

IDENTIFIERS

California; California Acc=ccraont Program; Rasch

Model; *Basch Scaled Scores

ABSTRACT

Pour problems faced by the staff of the California Assessment Program (CAP) were solved by applying Rasch scaling techniques: (1) item cultural bias in the Entry Level Test (ELT) given to all first grade pupils; (2)nonlinear regression analysis of the third grade Reading Test scores; (3) comparison et school growth from grades two to three, using the Reading Test; Sand (4)analysis of growth from grades two to three, based on the Reading Test,in the areas of word identification, vocabulary, comprehension, and study

locational skills. Solution of the prcblems demonstrated thatexisting Pasch Models have practical significance and should be more

widely used by educators. (MH) Reproductions supplied by EDRS are the best that can be made from the original dccument. fA Z o Dm 33 o
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03I This paper presents four problems that the staff of the California Assessment Program (CAP), the statewide testing program for the state of

California, found difficult to solve.

Each of these problems proved to

be readily solvable when techniques being developed by advocates of the ti Rasch model were applied.The purpose of this paper is not to present new approaches for using the Rasch model, but to demonstrate that the approaches that have been developed already have great practical significance and should be disseminated and used more widely by practitioners.

CZ)UJItem Cultural Bias in the Entry Level Test

In order to collect baseline data, the California Assessment Program annually administers the Entry Level Test (ELT) to every first grader in

California each September.

At the time of the first administration of the

ELT in September, 1973, it consisted of 36 items covering five subtests. Along with item data, the ethnic group of each child was reported. A one percent systematic sample of the state resulted in a file of 3,010 pupils available for analysis.

The problem was to determine which, if any, of

the test items contained cultural bias. The approach taken by the staff at that time was to run a factor analysis, considering responses to each of the items and membership in each of the ethnic groups to be a variable.

The factor structure of the

test itself was quite clean; most of the 36 items loaded into only one factor, and loaded jointly only with all the other items in their own subtest. The loadings of the ethnic groups were much less definitive, and it was not known if the problem was one of statistics, such as the restric- tion of range of interitem correlations when items are extremely easy (several items in the test had p-values greater than .9), or if the items in the tests were truly unbiased.

The results of this analysis were reported

by Lorrie Shepard at the 1975 NCME Annual Meeting in a paper entitled

Developing the California Entry Level Test:

Construct Validity of the

Subtests.

The opinion of the staff was that the amount of culturalbias in the test was unclear, although there was belief that it was relatively unbiased. Le.) (i?The data were reanalyzed last spring using the Rasch model. Rasch item difficulties were computed separately for whites, blacks, and Spanish- surnamed children.' Plots of Rasch item difficulties for whites versus cin blacks and whites versus SpaniE --surnamed wereconstructed.These two plots are shown as figures 1 an

2.Each plot demonstrated two distinct

patterns of straight lines - orline consisting of the first six items on the test, and one very difficu item from the end of the test, and a second:: line drawn from theremainingtems. MEE *paper presented at the 1979 Air,' 4*, Meeting of the National Council on

Measurement in Education, Sat

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kasch item difficulties for whites vs. Spanish-surnamed children on the Entry Level Test.

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Rash Item Difficulty

Whites

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Rasch item difficulties for

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Entry Level Test,

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Rasch Item Dif-F,rulty

Cites65

The first six items should have been the most

culture-fair items on the test. They all were classified as Immediate Recall, andconsisted of the teacher showing the children pairs of objects, putting the pictures away, and then having the children choose the picture that matched the stimulus picture.

If it is indeed true that these were culture-fair

items, then it can be shown from the graphs that some cultural bias is contained in the vast majority of items in the ELT. To compute the amount of bias, the correlations and associated regression lines were computed for whites vs. blacks and whites vs.

[PDF] DOCOMNT RIESUBE ED 171 786 TH 009 257