Factorial ANOVA with unbalanced data: A fresh look at the types of sums of squares
Carrie E. Smith, Robert A. Cribbie
Abstract
In this paper we endeavour to provide a largely non-technical description of the issues surrounding unbalanced factorial ANOVA and review the arguments made for and against the use of Type I, Type II and Type III sums of squares. Though the issue of which is the `best' approach has been debated in the literature for decades, to date confusion remains around how the procedures differ and which is most appropriate. We ultimately recommend use of the Type II sums of squares for analysis of main effects because when no interaction is present it tests meaningful hypotheses and is the most statistically powerful alternative.
Topics & Concepts
ConfusionFactorialFactorial analysisAnalysis of varianceStatisticsType (biology)EconometricsMathematicsFactorial experimentExplained sum of squaresLack-of-fit sum of squaresGeneralized least squaresComputer scienceArithmeticPsychologyNon-linear least squaresMathematical analysisEcologyBiologyEstimatorPsychoanalysisStatistical Methods in Clinical TrialsAdvanced Statistical Methods and ModelsOptimal Experimental Design Methods