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Chi-Squared Test of Fit and Sample Size-A Comparison between a Random Sample Approach and a Chi-Square Value Adjustment Method
Karlstad University, Faculty of Social and Life Sciences, Department of Health and Environmental Sciences. Karlstad University, Faculty of Arts and Social Sciences (starting 2013), Centre for Research on Child and Adolescent Mental Health.
2015 (English)In: Journal of Applied Measurement, ISSN 1529-7713, Vol. 16, no 2, 204-217 p.Article in journal (Refereed) Published
Abstract [en]

Chi-square statistics are commonly used for tests of fit of measurement models. Chi-square is also sensitive to sample size, which is why several approaches to handle large samples in test of fit analysis have been developed. One strategy to handle the sample size problem may be to adjust the sample size in the analysis of fit. An alternative is to adopt a random sample approach. The purpose of this study was to analyze and to compare these two strategies using simulated data. Given an original sample size of 21,000, for reductions of sample sizes down to the order of 5,000 the adjusted sample size function works as good as the random sample approach. In contrast, when applying adjustments to sample sizes of lower order the adjustment function is less effective at approximating the chi-square value for an actual random sample of the relevant size. Hence, the fit is exaggerated and misfit under-estimated using the adjusted sample size function. Although there are big differences in chi-square values between the two approaches at lower sample sizes, the inferences based on the p-values may be the same.

Place, publisher, year, edition, pages
2015. Vol. 16, no 2, 204-217 p.
National Category
Social Sciences Probability Theory and Statistics
URN: urn:nbn:se:kau:diva-36443PubMedID: 26075668OAI: diva2:822402
Available from: 2015-06-16 Created: 2015-06-16 Last updated: 2015-06-23Bibliographically approved

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Bergh, Daniel
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Department of Health and Environmental SciencesCentre for Research on Child and Adolescent Mental Health
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