28.7 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 exclusive⁵⁵ 5 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 hypothesis⁶⁶ 6 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..