Comparison of SPRT and Sequential Bayes Procedures for Classifying Examinees into Two
Categories Using a Computerized Test
Author(s): Judith A. Spray and Mark D. Reckase
Source: Journal of Educational and Behavioral Statistics, Vol. 21, No. 4 (Winter, 1996), pp.
405-414
Published by: American Educational Research Association and American Statistical Association
Stable URL: http://www.jstor.org/stable/1165342 .
Accessed: 29/11/2014 15:41
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of scholarship. For more information about JSTOR, please contact .
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JSTOR to digitize, preserve and extend access to Journal of Educational and Behavioral Statistics.
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, Journal of Educational and Behavioral Statistics
Winter 1996, Vol. 21, No. 4, pp. 405-414
Comparison of SPRT and Sequential Bayes
Procedures for Classifying Examinees Into Two
Categories Using a ComputerizedTest
Judith A. Spray and Mark D. Reckase
American College Testing
Keywords:classification,computerized
testing,sequentialBayes,sequentialprobabil-
ity ratio test
Many testingapplicationsfocus on classifyingexamineesinto one of two
categories(e.g., pass/fail) ratherthan on obtainingan accurate estimate
of level of ability. Examplesof such applicationsinclude licensureand
certification,college selection,and placementinto entry-levelor develop-
mentalcollege courses.Withthe increasedavailabilityof computersfor the
administrationand scoring of tests, computerizedtestingprocedureshave
been developedfor efficientlymakingthese classificationdecisions. The
purposeof the researchreportedin this article was to comparetwo such
procedures,one basedon the sequentialprobabilityratio test and the other
on sequentialBayesmethodology,to determinewhichrequiredfewer items
for classificationwhentheprocedureswerematchedon classificationerror
rates. The results showed that under the conditionsstudied, the SPRT
procedurerequired fewer test itemsthanthe sequentialBayesprocedureto
achieve the same level of classificationaccuracy.
Two methods that have been proposedto classify examinees into two
categories(e.g., passversusfail) usingcomputerized testingarethe sequential
probability ratio test, or SPRT (Ferguson,1969a, 1969b; Reckase, 1983;
Wald, 1947), and a procedurebased on sequentialBayes estimatesof an
examinee'slatenttraitor ability(Kingsbury& Weiss, 1983). The latterwill
be referredto in this articleas the sequentialBayes procedure,or SB. Both
methodsfocus on the administration of single test items ratherthanblocks
of test items, sometimesreferredto as testlets (Lewis & Sheehan, 1990;
Sheehan& Lewis, 1992). The testlet-basedtechniquewill not be discussed
in the presentarticle.
It is difficultto comparethe two procedureshead-to-headprimarilydue
to the difficultyin matchingor equatingthe two proceduresso thatcompari-
sons are meaningful.Both the SPRTand SB proceduresrequirecertain,but
different,test characteristics or parametersto be establishedpriorto testing.
However,bothproceduresyield similaroutcomemeasuresthatarecompara-
ble. For example, both proceduresclassify an examinee with some latent
ability into one of two mutuallyexclusive categorieswith a certaindegree
of accuracyfollowingtheadministration of anexpectednumberof testitems.'
This content downloaded from 35.8.11.3 on Sat, 29 Nov 2014 15:41:47 PM
All use subject to JSTOR Terms and Conditions
Categories Using a Computerized Test
Author(s): Judith A. Spray and Mark D. Reckase
Source: Journal of Educational and Behavioral Statistics, Vol. 21, No. 4 (Winter, 1996), pp.
405-414
Published by: American Educational Research Association and American Statistical Association
Stable URL: http://www.jstor.org/stable/1165342 .
Accessed: 29/11/2014 15:41
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .
http://www.jstor.org/page/info/about/policies/terms.jsp
.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact .
.
American Educational Research Association and American Statistical Association are collaborating with
JSTOR to digitize, preserve and extend access to Journal of Educational and Behavioral Statistics.
http://www.jstor.org
, Journal of Educational and Behavioral Statistics
Winter 1996, Vol. 21, No. 4, pp. 405-414
Comparison of SPRT and Sequential Bayes
Procedures for Classifying Examinees Into Two
Categories Using a ComputerizedTest
Judith A. Spray and Mark D. Reckase
American College Testing
Keywords:classification,computerized
testing,sequentialBayes,sequentialprobabil-
ity ratio test
Many testingapplicationsfocus on classifyingexamineesinto one of two
categories(e.g., pass/fail) ratherthan on obtainingan accurate estimate
of level of ability. Examplesof such applicationsinclude licensureand
certification,college selection,and placementinto entry-levelor develop-
mentalcollege courses.Withthe increasedavailabilityof computersfor the
administrationand scoring of tests, computerizedtestingprocedureshave
been developedfor efficientlymakingthese classificationdecisions. The
purposeof the researchreportedin this article was to comparetwo such
procedures,one basedon the sequentialprobabilityratio test and the other
on sequentialBayesmethodology,to determinewhichrequiredfewer items
for classificationwhentheprocedureswerematchedon classificationerror
rates. The results showed that under the conditionsstudied, the SPRT
procedurerequired fewer test itemsthanthe sequentialBayesprocedureto
achieve the same level of classificationaccuracy.
Two methods that have been proposedto classify examinees into two
categories(e.g., passversusfail) usingcomputerized testingarethe sequential
probability ratio test, or SPRT (Ferguson,1969a, 1969b; Reckase, 1983;
Wald, 1947), and a procedurebased on sequentialBayes estimatesof an
examinee'slatenttraitor ability(Kingsbury& Weiss, 1983). The latterwill
be referredto in this articleas the sequentialBayes procedure,or SB. Both
methodsfocus on the administration of single test items ratherthanblocks
of test items, sometimesreferredto as testlets (Lewis & Sheehan, 1990;
Sheehan& Lewis, 1992). The testlet-basedtechniquewill not be discussed
in the presentarticle.
It is difficultto comparethe two procedureshead-to-headprimarilydue
to the difficultyin matchingor equatingthe two proceduresso thatcompari-
sons are meaningful.Both the SPRTand SB proceduresrequirecertain,but
different,test characteristics or parametersto be establishedpriorto testing.
However,bothproceduresyield similaroutcomemeasuresthatarecompara-
ble. For example, both proceduresclassify an examinee with some latent
ability into one of two mutuallyexclusive categorieswith a certaindegree
of accuracyfollowingtheadministration of anexpectednumberof testitems.'
This content downloaded from 35.8.11.3 on Sat, 29 Nov 2014 15:41:47 PM
All use subject to JSTOR Terms and Conditions
