visual development

In this section we will analyze data from a fictitious experiment that measured visual contrast sensitivity in six male and six female children at 30, 36, 42, and 48 months of age. Each child was tested at each age in two conditions that differed in brightness. The between-subjects factor (gender) and the two within-subject factors (age and brightness) are fixed, whereas subjects is random. The data are in the file visDevelopment.rda, which contains the data frames visDevWide and visDev. The data frame visDev also contains a numeric variable, csf, which contains the dependent variable.

options(contrasts=c("contr.sum","contr.poly"))
load(url("http://pnb.mcmaster.ca/bennett/psy710/datasets/visDevelopment.rda") )
summary(visDev)
##       subj       gender    age     brightness      csf        
##  s1     : 8   female:48   a30:24   high:48    Min.   : 68.55  
##  s2     : 8   male  :48   a36:24   low :48    1st Qu.: 91.08  
##  s3     : 8               a42:24              Median :102.34  
##  s4     : 8               a48:24              Mean   :102.49  
##  s5     : 8                                   3rd Qu.:113.00  
##  s6     : 8                                   Max.   :133.00  
##  (Other):48
sapply(visDevWide,class)
##      subj    gender   high.30   high.36   high.40   high.48    low.30    low.36    low.42    low.48 
##  "factor"  "factor" "integer" "integer" "integer" "integer" "numeric" "numeric" "numeric" "numeric"

Questions

  1. Use ANOVA to evaluate the effects of gender, age and brightness on csf. Conduct two analyses: a split-plot analysis that includes the between-subjects variable and a within-subjects analysis that does not. Where necessary, correct the \(p\) values for deviations from sphericity. Do all of the \(p\) have to be adjusted? Why or why not?

  1. Use lmer in the lmerTest package to evaluate the effects of gender, age, and brightness (and interactions) with a mixed model. Treat subj as a random factor and all the other factors as fixed. Evaluate the fixed effects with \(F\) tests that assume sphericity and chi-square tests that do not assume spericity.

  2. Check the residuals of your split-plot model to see if they are distributed normally

  3. Estimate association strength and effect size for each fixed effect in the split-plot model.

  4. Evaluate the linear trend of csf across age. Is the overall linear trend (ignoring brightness and gender) significant? Does the linear trend differ between genders? Does it differ between brightness conditions?