The contrast sensitivity function (CSF) relates visual sensitivity
(i.e., the reciprocal of minimum contrast needed to detect a pattern) to
the spatial frequency of the visual target (i.e., a sine wave grating).
The CSF is an important clinical tool and also has been used to
characterize visual mechanisms that constrain vision in a variety of
contexts. An experiment was conducted to assess the change in the CSF in
1-3 month old human infants. Contrast sensitivity was measured for sine
wave gratins with spatial frequencies of 1, 2, 3, and 4 cycles per
degree.Twenty infants in three age groups (4, 8, and 12 weeks)
participated in the study and each infant was tested with all four
spatial frequencies. The data are stored in the long- and wide-format
data frames csf.long and csf.wide, and in the
matrix csf.mat.
options(contrasts=c("contr.sum","contr.poly"))
load(url("http://pnb.mcmaster.ca/bennett/psy710/datasets/csf2022.rda") )
summary(csf.long)
## subjID age sf sensitivity
## s1 : 4 w12:80 sf1:60 Min. : 0.2558
## s2 : 4 w4 :80 sf2:60 1st Qu.: 2.9995
## s3 : 4 w8 :80 sf3:60 Median : 6.7183
## s4 : 4 sf4:60 Mean : 11.7792
## s5 : 4 3rd Qu.: 14.5027
## s6 : 4 Max. :112.1023
## (Other):216
sapply(csf.wide,class)
## subjID age sf1 sf2 sf3 sf4
## "factor" "factor" "numeric" "numeric" "numeric" "numeric"Use ANOVA to evaluate the effects of age and
sf on sensitivity. Where necessary, correct
the \(p\) values for deviations from
sphericity. Do all of the \(p\) have to
be adjusted? Why or why not?
Use lmer in the lmerTest package to
evaluate the effects of age, and sf (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
sphericity.
Use lme in the nlme package to evaluate
the effects of age, and sf (and interactions)
with a mixed model. Treat subj as a random factor and all
the other factors as fixed. For this model, assume that the
variance-covariance matrix of the residuals is not compound
symmetric. In other words, allow the correlations between levels of the
within-subject factor to vary (i.e., not be a constant value). List the
ANOVA table for the fixed effects.
Use Tukey tests to evaluate the pairwise differences among age groups (while ignoring spatial frequency).
Use a linear contrast to determine if the quadratic trend of sensitivity across spatial frequency differed across ages. Use Tukey tests to do pairwise comparisons of the quadratic trends in each age group.