A comparison of chi-squared statistics for testing homogeneity of survey data: High School and Beyond survey

Jeffrey Wilson, Patricia M. Wilson

Research output: Contribution to journalArticle


The performance of several test statistics for comparing vectors of proportions from certain survey data was compared. The statistics were used to analyze a subsample of data from the ‘High School and Beyond’ survey. These tests include the Wald test statistic and the modified Wald test statistic Fw, the chi-squared test statistic XRSB and its modification FRSB, a test X2DMB based on a probability model, and a method of moments approach, X2H. Data were also simulated based on two-stage cluster sampling design and the type I error level, and the power of these tests was obtained for selected combinations of parameter values. The statistics X2DMB, X2RSB, FRSB and X2H performed well both for a small number of clusters or a small number of units within clusters. The power performance of these tests is quite stable. Approximate intervals were constructed for design effect constants. Methods of estimating these constants based on a normality assumption worked best.

Original languageEnglish (US)
Pages (from-to)203-213
Number of pages11
JournalJournal of Applied Statistics
Issue number2
StatePublished - Jan 1 1991


ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this