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.
Definitions of variance
1
n the quality of being subject to variation
 Synonyms:
 variability, variableness
 Antonyms:

invariability, invariableness, invariance
the quality of being resistant to variation
 Types:

variedness
characterized by variation

variegation
variability in coloration

personal equation
variability attributable to individual differences
 Type of:

changeability, changeableness
the quality of being changeable; having a marked tendency to change
n an activity that varies from a norm or standard
n an event that departs from expectations
 Synonyms:
 discrepancy, variant
 Type of:

departure, deviation, difference, divergence
a variation that deviates from the standard or norm
n a difference between conflicting facts or claims or opinions
 Synonyms:
 disagreement, discrepancy, divergence
 Types:

allowance, leeway, margin, tolerance
a permissible difference; allowing some freedom to move within limits
 Type of:

difference
the quality of being unlike or dissimilar
n discord that splits a group
 Synonyms:
 division
 Type of:

discord, dissension
disagreement among those expected to cooperate
n an official dispensation to act contrary to a rule or regulation (typically a building regulation)
“a zoning
variance”
 Type of:

dispensation
an exemption from some rule or obligation
n the second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value
 Types:

standard deviation
the square root of the variance

covariance
(statistics) the mean value of the product of the deviations of two variates from their respective means
 Type of:

moment
the nth moment of a distribution is the expected value of the nth power of the deviations from a fixed value