Question

Suppose we have a Between-Subjects, One Factor, Two-Level experiment. What would be wrong with using two dummy variables (two columns of 0’s and 1’s) to represent that independent variable with two levels?

Answer 1

It factor variable contains n levels then we create the dummy variables for n-1 levels.
Because if we create the n dummy variables then it will be meaningless and some times linear models fails.
Because if the factor variable has two levels then it measures the effect for one level and affect of other level is not necessary to additionally added. Creating two dummy's means we are adding the same variable twice . therefore we only use one variable for two levels.