title: The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ.
abstract: BACKGROUND
  This study examined the independent effect of skewness and kurtosis on the robustness of the linear mixed model (LMM), with the Kenward-Roger (KR) procedure, when group distributions are different, sample sizes are small, and sphericity cannot be assumed.
  
  
  METHODS
  A Monte Carlo simulation study considering a split-plot design involving three groups and four repeated measures was performed.
  
  
  RESULTS
  The results showed that when group distributions are different, the effect of skewness on KR robustness is greater than that of kurtosis for the corresponding values. Furthermore, the pairings of skewness and kurtosis with group size were found to be relevant variables when applying this procedure.
  
  
  CONCLUSIONS
  With sample sizes of 45 and 60, KR is a suitable option for analyzing data when the distributions are: (a) mesokurtic and not highly or extremely skewed, and (b) symmetric with different degrees of kurtosis. With total sample sizes of 30, it is adequate when group sizes are equal and the distributions are: (a) mesokurtic and slightly or moderately skewed, and sphericity is assumed; and (b) symmetric with a moderate or high/extreme violation of kurtosis. Alternative analyses should be considered when the distributions are highly or extremely skewed and samples sizes are small.
authors.affiliation: Universidad de Barcelona.
authors.forename: Jaime
authors.initials: J
authors.lastname: Arnau
authors.forename: Rebecca
authors.initials: R
authors.lastname: Bendayan
authors.forename: María J
authors.initials: MJ
authors.lastname: Blanca
authors.forename: Roser
authors.initials: R
authors.lastname: Bono
mesh_terms: D003710:Demography; D016014:Linear Models; D017145:Models, Educational; D008960:Models, Psychological; D018401:Sample Size