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|—Things your math teacher never taught you|
The null hypothesis (H0) is a statistical and scientific tool to test a hypothesis. It usually refers to a default state, e.g., that two quantities are unrelated. Paired with each null hypothesis is an alternative hypothesis (called H1 or HA). The two hypotheses divide the relevant world into two subsets: the desperately-hoped for result, HA, and everything else, H0. Think of the null hypothesis as the "killjoy hypothesis."
- Blood pressure lowering drug X: the null hypothesis is that drug X has no effect on blood pressure.
Although such simple hypotheses are most common, a null hypothesis can be that two drugs have differing effectiveness (in a bioequivalence trial) or that the sun will rise 2-4 times in the morning (in alcohol-soaked nightmares).
No matter the actual hypothesis, the observed evidence is evaluated for how probable such a result, and all other more extreme results, is if the null hypothesis were true. In a hypothesis test, the null hypothesis can be rejected or can fail to be rejected; it cannot be proven or validated.
This can be applied more broadly, particularly when dealing with pseudoscience:
- Homeopathy: that water prepared by dilution and succussion is indistinguishable in its medical effects from water that has not.
- Nanobots: that matter at nanoscale does not behave as hypothesised by Drexler.
- Cryonics: that information in the brain is not sufficiently preserved by the freezing process.
- Lunar anomalies: that all those things that look like alien moonbases, ziggurats and robot heads are, in fact, just rocks.
The burden of proof is on the person advocating the idea to present convincing evidence which would cause one to reject the null hypothesis. Were that to happen the burden of proof would fall to the person against the idea who would have to refute or explain the evidence.
The following cases are examples where sufficient evidence has been presented and the null hypothesis can be rejected.
- Climate change: that human influence has not changed Earth's climate.
- Evolution: that species are not changed by natural selection to fit an ecological niche.
Given that the null hypothesis has been rejected it now falls to those who would wish to deny the evidence for global warming or evolution to present their counterarguments. The burden of proof is on them. The prior alternative hypothesis becomes the next default null hypothesis.