In general, when doing hypothesis testing, we want to claim that the concerned statistic is different between the two population. Hence we assume as our null hypothesis that there is no difference in the two population and the alternative hypothesis that there is a difference between the two populations which we want to claim. According to me, this is similar to "proof by contradiction" in mathematics.
But what if my aim is to claim that the two populations are similar. Let us say that I want to show that my model is correct, and to show this I am claiming that the my model data and experimental data are similar. In this case, if I want to do hypothesis testing, I cannot (or should not) assume that my null hypothesis is that there is no difference in populations. Because it will be akin to "proof by assumption" which is not permitted in mathematics. And if I do not assume that my null hypothesis is "no difference in populations", then my null distribution won't come out to be the conventional distributions like normal, t distribution, chi-square etc. and I won't be able to perform the standardized tests.
And even if I assume my null hypothesis to be no difference in the populations. Then by choosing a lesser alpha value like 0.05, I am making very easy for my claim to pass the test. The probability of my claim will pass the test will be 95%. So should my methodology be to assume the "conventional" null hypothesis of no difference but then choose a high alpha value like 0.95 for testing my claim. Is this a correct way to think about this or are there other standard ways when the aim is to claim that there is no difference in the populations.
There should be some standard way to tackle this but I think I lack the terminology to search for the relevant information.