A change to the norm is called a variance. It suggests a difference or shifting away from the expected or usual, an example being snow in July, which is a variance in the weather of the United States, even in Minnesota.
When the word variance is used in a comparison, it is usually preceded by the word "at," as in "Her values were at variance with her actions," meaning the two differed. This makes sense, as the word, first seen in Middle English, comes from the Latin verb variāre, which means "to change." If a contractor needs to go outside the standing building code, he needs to obtain a variance, which is legal permission to make a change from the norm.