The Anna Karenina principle states that a deficiency in any one of a number of factors dooms an endeavor to failure. Consequently, a successful endeavor (subject to this principle) is one where every possible deficiency has been avoided.

The name of the principle derives from Leo Tolstoy’s book Anna Karenina, which begins:

“Happy families are all alike; every unhappy family is unhappy in its own way.”

In other words: in order to be happy, a family must be successful on each and every one of a range of criteria e.g: sexual attraction, money issues, parenting, religion, in-laws. Failure on only one of these counts leads to unhappiness. Thus there are more ways for a family to be unhappy than happy.

In statistics, the term Anna Karenina principle is used to describe significance tests: there are any number of ways in which a dataset may violate the null hypothesis and only one in which all the assumptions are satisfied.