I conducted an experiment that investigated preferences for two-digit numbers. Each digit was randomly drawn from a list of digits between 1 and 9, with one digit presented at a leftish position and one at a rightish position on the screen. The resulting two-digit number was either congruent to a previously learned association or not. Each participants received 50 trials (i.e., 50 2-digit presentations) and should indicate how much they like the respective digit arrangement for each trial on scale from 0 to 10.
I found a main effect of congruency. However, I am wondering whether preferences could be alternatively explained by preferences for higher compared to lower numbers. Thus, I would like to consider the tenner of the two-digit number (i.e., the digit appearing at the leftish) position in my analyses. I guess that mixed models would be the analysis of choice; however, as I am completely new to this, I am struggling to find the right model.
Currently, my model looks like this:
preference ~ congruency*tenner + (1|subject)
Yet, I am almost convinced that this is not the most adequate solution and would hence be grateful for any suggestions.
*** EDIT - On the variables:
- congruency is nominal and binary (congruent vs. incongruent)
- tenner is interval-scaled (possible values: 1, 2, 3, 4, 5, 6, 7, 8, 9)
- preference is interval-scaled (possible values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)