New heterogeneous test statistics for the unbalanced fixed-effect nested design

Jiin Huarng Guo, L. Billard, Wei Ming Luh

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


When the underlying variances are unknown or/and unequal, using the conventional F test is problematic in the two-factor hierarchical data structure. Prompted by the approximate test statistics (Welch and Alexander-Govern methods), the authors develop four new heterogeneous test statistics to test factor A and factor B nested within A for the unbalanced fixed-effect two-stage nested design under variance heterogeneity. The actual significance levels and statistical power of the test statistics were compared in a simulation study. The results show that the proposed procedures maintain better Type I error rate control and have greater statistical power than those obtained by the conventional F test in various conditions. Therefore, the proposed test statistics are recommended in terms of robustness and easy implementation.

Original languageEnglish
Pages (from-to)259-276
Number of pages18
JournalBritish Journal of Mathematical and Statistical Psychology
Issue number2
Publication statusPublished - 2011 May 1

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Arts and Humanities (miscellaneous)
  • Psychology(all)


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