Resampling-Based Inference Methods for Comparing Two Coefficients Alpha

Resampling-Based Inference Methods for Comparing Two Coefficients Alpha The two-sample problem for Cronbach’s coefficient $$\alpha _C$$ α C , as an estimate of test or composite score reliability, has attracted little attention compared to the extensive treatment of the one-sample case. It is necessary to compare the reliability of a test for different subgroups, for different tests or the short and long forms of a test. In this paper, we study statistical procedures of comparing two coefficients $$\alpha _{C,1}$$ α C , 1 and $$\alpha _{C,2}$$ α C , 2 . The null hypothesis of interest is $$H_0 : \alpha _{C,1} = \alpha _{C,2}$$ H 0 : α C , 1 = α C , 2 , which we test against one-or two-sided alternatives. For this purpose, resampling-based permutation and bootstrap tests are proposed for two-group multivariate non-normal models under the general asymptotically distribution-free (ADF) setting. These statistical tests ensure a better control of the type-I error, in finite or very small sample sizes, when the state-of-affairs ADF large-sample test may fail to properly attain the nominal significance level. By proper choice of a studentized test statistic, the resampling tests are modified in order to be valid asymptotically even in non-exchangeable data frameworks. Moreover, extensions of this approach to other designs and reliability measures are discussed as well. Finally, the usefulness of the proposed resampling-based testing strategies is demonstrated in an extensive simulation study and illustrated by real data applications. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Psychometrika Springer Journals

Resampling-Based Inference Methods for Comparing Two Coefficients Alpha

Loading next page...
 
/lp/springer_journal/resampling-based-inference-methods-for-comparing-two-coefficients-fl2QcHnzcC
Publisher
Springer US
Copyright
Copyright © 2017 by The Psychometric Society
Subject
Psychology; Psychometrics; Assessment, Testing and Evaluation; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law; Statistical Theory and Methods
ISSN
0033-3123
eISSN
1860-0980
D.O.I.
10.1007/s11336-017-9601-x
Publisher site
See Article on Publisher Site

Abstract

The two-sample problem for Cronbach’s coefficient $$\alpha _C$$ α C , as an estimate of test or composite score reliability, has attracted little attention compared to the extensive treatment of the one-sample case. It is necessary to compare the reliability of a test for different subgroups, for different tests or the short and long forms of a test. In this paper, we study statistical procedures of comparing two coefficients $$\alpha _{C,1}$$ α C , 1 and $$\alpha _{C,2}$$ α C , 2 . The null hypothesis of interest is $$H_0 : \alpha _{C,1} = \alpha _{C,2}$$ H 0 : α C , 1 = α C , 2 , which we test against one-or two-sided alternatives. For this purpose, resampling-based permutation and bootstrap tests are proposed for two-group multivariate non-normal models under the general asymptotically distribution-free (ADF) setting. These statistical tests ensure a better control of the type-I error, in finite or very small sample sizes, when the state-of-affairs ADF large-sample test may fail to properly attain the nominal significance level. By proper choice of a studentized test statistic, the resampling tests are modified in order to be valid asymptotically even in non-exchangeable data frameworks. Moreover, extensions of this approach to other designs and reliability measures are discussed as well. Finally, the usefulness of the proposed resampling-based testing strategies is demonstrated in an extensive simulation study and illustrated by real data applications.

Journal

PsychometrikaSpringer Journals

Published: Jan 2, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off