The mathematics of statistical hypothesis testing is almost always defined in terms of a ‘null’ and an‘alternative’ hypothesis, where the ‘null’ necessarily inc

The mathematics of statistical hypothesis testing is almost always defined in terms of a ‘null’ and an‘alternative’ hypothesis, where the ‘null’ necessarily includes the equivalent of ‘no correlations/differences exist’ and the alternative hypothesis does not. This usually means that the alternative hypothesis is the ‘interesting’ one, which is probably what the researcher would like to occur. Which maybe isn’t entirely intuitive. But I f you don’t follow those restrictions, the math is meaningless. If you swap the terms in the math, you’ll confuse anyone who knows the stats, while not really benefitting anyone. And if you’re not using the math, why refer to a ‘null’ and ‘alternative’ hypothesis at all?