But essentially all these tests do the same thing because they're seeing whether the parameters that we estimate over the entire sample are robust over all sub-samples, right, we can't, we wouldn't bother testing over all sub-samples though we can do, it's just if we have good reason to believe that behaviour in one sub-sample  different for behaviour in another E G use er Chow test or equivalently a dummy variable on the intercept to see whether there was any change.