Dear mixed models community,


I'm encountering some difficulties with analysis of recent psychophysical
data. I would appreciate some help.

I would like to examine the relationship between the mean and standard
deviation (std) of each of my 12 experimental conditions (this is a 6(color
saturation levels) * 2(spatial compatibility between stimulus and response)
within-subjects design; 13 subjects participated in the experiment). The
Wagenmaker's law holds that the relationship between mean and std across
experimental conditions should be perfectly linear.

I find a perfect linear relationship across color saturation levels, but
for each stimulus-response mapping separatly. In line with this
observation, I would like to demonstrate that the parameters of the linear
relationship between mean and std are influenced by random variability
across subjects as well as compatibility between stimulus and response.

I played with lme4 and found that the model with the lower BIC index was
std ~ mean + compatibility + (1|subject)]. MCMC p-values showed that both
mean and compatibility were significant (p < .0001). Note that the
interaction term mean*compatibility was not significant and its parameter
was closed to zero.


I concluded the following:

 ""There is a robust linear relationship between mean and SD, but the
 compatibility factor modulates its intercept. The best-fitting parameter
 for the effect of compatibility indicated that the intercept was lowered
 by 15 SD units in the incompatible condition. "" Is imy conclusion correct?



Best,

Mat

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