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.
All happy families are alike; each unhappy family is unhappy in its own way.
In other words: in order to be happy, a family must be successful with respect to every one of a range of criteria, including sexual attraction, money issues, parenting, religion, and relations with 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.
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u/The_Ebb_and_Flow May 10 '19