A calculus of the absurd

27.7 Hypothesis testing

Here’s one vision for how science should work: I theorise that A has some effect on B. Of course, A might not have any effect on B. To do this, we can construct two hypotheses: the "null hypothesis" which is the possibility that there is no effect and the "alternate hypothesis" which is mutually exclusive147147 i.e. it is not possible for both the null and alternate hypothesis to be true to the null hypothesis. [?]

For example, let’s suppose that we have a jar filled with objects of type "A" and "B". Last time I checked, 37% of the objects were of type A. I suspect, however, that since last time I checked the proportion of objects that of type "A" has decreased.

From this, we can come up with some hypotheses

Null hypothesis: there is no change (i.e. the proportion is still 37%).

Alternate hypothesis: the proportion of items which are of type "A" has decreased (i.e. the proportion is \(<\) 37%).

If we have some data, we can try to work out how likely or unlikely the data is under the null hypothesis - if getting that data is really unlikely under the null hypothesis then we can reject the null hypothesis in favour of the alternate hypothesis148148 You mustn’t ever disprove the null hypothesis, you can only uphold/reject it. We’re not saying that we’ve disproved the hypothesis, we’re saying that it’s either likely or unlikely to be true..