uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Performing the Kernel Method of Test Equating with the Package kequate
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.ORCID iD: 0000-0002-9007-2440
Department of Statistics, USBE, Umeå University.
Department of Statistics, USBE, Umeå University.
2013 (English)In: Journal of Statistical Software, ISSN 1548-7660, E-ISSN 1548-7660, Vol. 55, no 6, 1-25 p.Article in journal (Refereed) Published
Abstract [en]

In standardized testing it is important to equate tests in order to ensure that the test takers, regardless of the test version given, obtain a fair test. Recently, the kernel method of test equating, which is a conjoint framework of test equating, has gained popularity. The kernel method of test equating includes five steps: (1) pre-smoothing, (2) estimation of the score probabilities, (3) continuization, (4) equating, and (5) computing the standard error of equating and the standard error of equating difference. Here, an implementation has been made for six different equating designs: equivalent groups, single group, counterbalanced, non-equivalent groups with anchor test using either chain equating or post-stratification equating, and non-equivalent groups using covariates. An R package for the kernel method of test equating called kequate is presented. Included in the package are also diagnostic tools aiding in the search for a proper log-linear model in the pre-smoothing step for use in conjunction with the R function glm.

Place, publisher, year, edition, pages
American Statistical Association , 2013. Vol. 55, no 6, 1-25 p.
Keyword [en]
observed-score test equating, R package, kernel equating, item-response theory
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:uu:diva-208912ISI: 000325948000001OAI: oai:DiVA.org:uu-208912DiVA: diva2:658862
Available from: 2013-10-23 Created: 2013-10-10 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Contributions to Kernel Equating
Open this publication in new window or tab >>Contributions to Kernel Equating
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The statistical practice of equating is needed when scores on different versions of the same standardized test are to be compared. This thesis constitutes four contributions to the observed-score equating framework kernel equating.

Paper I introduces the open source R package kequate which enables the equating of observed scores using the kernel method of test equating in all common equating designs. The package is designed for ease of use and integrates well with other packages. The equating methods non-equivalent groups with covariates and item response theory observed-score kernel equating are currently not available in any other software package.

In paper II an alternative bandwidth selection method for the kernel method of test equating is proposed. The new method is designed for usage with non-smooth data such as when using the observed data directly, without pre-smoothing. In previously used bandwidth selection methods, the variability from the bandwidth selection was disregarded when calculating the asymptotic standard errors. Here, the bandwidth selection is accounted for and updated asymptotic standard error derivations are provided.

Item response theory observed-score kernel equating for the non-equivalent groups with anchor test design is introduced in paper III. Multivariate observed-score kernel equating functions are defined and their asymptotic covariance matrices are derived. An empirical example in the form of a standardized achievement test is used and the item response theory methods are compared to previously used log-linear methods.

In paper IV, Wald tests for equating differences in item response theory observed-score kernel equating are conducted using the results from paper III. Simulations are performed to evaluate the empirical significance level and power under different settings, showing that the Wald test is more powerful than the Hommel multiple hypothesis testing method. Data from a psychometric licensure test and a standardized achievement test are used to exemplify the hypothesis testing procedure. The results show that using the Wald test can provide different conclusions to using the Hommel procedure.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. 24 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 106
Keyword
observed-score test equating, item response theory, R, equipercentile equating, asymptotic standard errors, non-equivalent groups with anchor test design
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-234618 (URN)978-91-554-9089-8 (ISBN)
Public defence
2014-12-12, Sal IV, Universitetshuset, Biskopsgatan 3, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2014-11-20 Created: 2014-10-21 Last updated: 2015-02-03

Open Access in DiVA

No full text

Other links

http://www.jstatsoft.org/v55/i06/

Authority records BETA

Andersson, Björn

Search in DiVA

By author/editor
Andersson, Björn
By organisation
Department of Statistics
In the same journal
Journal of Statistical Software
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 1086 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf