title: Valid statistical approaches for analyzing sholl data: Mixed effects versus simple linear models.
abstract: The Sholl technique is widely used to quantify dendritic morphology. Data from such studies, which typically sample multiple neurons per animal, are often analyzed using simple linear models. However, simple linear models fail to account for intra-class correlation that occurs with clustered data, which can lead to faulty inferences.
  
  
  
  Mixed effects models account for intra-class correlation that occurs with clustered data; thus, these models more accurately estimate the standard deviation of the parameter estimate, which produces more accurate p-values. While mixed models are not new, their use in neuroscience has lagged behind their use in other disciplines.
  
  
  
  A review of the published literature illustrates common mistakes in analyses of Sholl data. Analysis of Sholl data collected from Golgi-stained pyramidal neurons in the hippocampus of male and female mice using both simple linear and mixed effects models demonstrates that the p-values and standard deviations obtained using the simple linear models are biased downwards and lead to erroneous rejection of the null hypothesis in some analyses.
  
  
  
  The mixed effects approach more accurately models the true variability in the data set, which leads to correct inference.
  
  
  
  Mixed effects models avoid faulty inference in Sholl analysis of data sampled from multiple neurons per animal by accounting for intra-class correlation. Given the widespread practice in neuroscience of obtaining multiple measurements per subject, there is a critical need to apply mixed effects models more widely.
authors.affiliation: Clinical and Translational Science Center, Department of Public Health Sciences, Division of Biostatistics, University of California, Davis, CA, United States.
authors.forename: Machelle D
authors.initials: MD
authors.lastname: Wilson
authors.affiliation: Department of Molecular Biosciences, University of California, Davis, CA, United States.
authors.forename: Sunjay
authors.initials: S
authors.lastname: Sethi
authors.affiliation: Department of Molecular Biosciences, University of California, Davis, CA, United States.
authors.forename: Pamela J
authors.initials: PJ
authors.lastname: Lein
authors.affiliation: Department of Molecular Biosciences, University of California, Davis, CA, United States. Electronic address: kpkeil@ucdavis.edu.
authors.forename: Kimberly P
authors.initials: KP
authors.lastname: Keil
mesh_terms: D000818:Animals; D003627:Data Interpretation, Statistical; D003712:Dendrites; D005260:Female; D006624:Hippocampus / Q000166:cytology; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008297:Male; D008810:Mice, Inbred C57BL; D008853:Microscopy / Q000379:methods*; D015233:Models, Statistical
keywords: Dendritic morphology; False discovery rate; Golgi staining; Mixed model; Sholl analysis