An equality hypothesis test formally tests if two or more population survival functions are different.
A common goal of survival analysis is to compare the survival function of two or more groups. A formal hypothesis test tests whether two or more survival functions are statistically equal in some overall sense. That is, there is no evidence to suggest that the true (population) survival functions are different. The most popular test is the Log-rank test, although various other tests differ in how much weight they give to the survival probabilities at the start or end of the distribution.
The null hypothesis states that there is no difference between the survival functions, against the alternative hypothesis that at least one of the survival functions is different. When the test p-value is small, you can reject the null hypothesis and conclude the population survival functions differ.
