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What is the Null Hypothesis?

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University Course Reader · STEM

The trial failed to reject the null hypothesis, so the drug's effect on recovery time remains unproven.

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Overview

The null hypothesis is the default claim a study tests against: the thing being studied has no effect, and any pattern in the data is chance. A drug trial starts by assuming the drug does nothing and the two groups differ by luck. Researchers then ask how often luck alone would produce a gap that big. If rarely, they reject the null and take the effect seriously. If often, the null stands, which is different from proving there is nothing to find.
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Overview

The null hypothesis is the claim that the thing being tested does nothing, and every study starts by assuming it. It is the boring answer, treated as true until the data makes it hard to believe. The researcher works out how often plain luck would produce their result if the drug, the diet or the app did nothing. If luck manages it all the time, boring wins, and most of science is people trying to knock the boring answer over and failing. That is the point. 😎

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Detail

The null hypothesis is the starting assumption of a statistical test: the thing being studied does nothing, and any pattern in the data is chance. Researchers test the opposite of what they hope to find for a plain reason. At the start of a study nobody knows what the effect is, how big it is or which way it points, so there is nothing definite to test for. "The drug does something" could mean any size of effect and gives nothing to measure. "The drug does nothing" says exactly what the data should look like, so that is what the data is measured against. The test asks how often chance alone would produce a result at least as large as the one observed. That probability is the p-value, and below a threshold fixed in advance, usually 5%, the null is rejected. Rejecting it tells the study that chance is unlikely to explain the result, so something real is probably at work. It does not say the drug is that something: a difference between the two groups or a flaw in the setup would reject the null just as well. Keeping the null does not prove there is no effect, because a small study can miss a real one. Two mistakes follow: rejecting a null that was true, a false positive (a Type I error), and keeping one that was false, a false negative (a Type II error). And rejecting the null says nothing about size. A real effect too small to matter still rejects it.
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Detail

The null hypothesis is the claim that nothing is going on, and every statistical test begins there because it is the only claim you can pin down before you know anything. "My new fertiliser works" is a hope with no number attached: works how much, on what, in which direction? "My new fertiliser does nothing and these taller plants are chance" is a claim you can put a number on: how often does chance grow plants this much taller? Rarely, and the null is rejected. Often, and it survives, and your fertiliser story stays a story. What trips people is what the two outcomes mean. Knocking the null over is not a win for your idea. It means luck alone probably did not do this, so something real happened, and that something could be your fertiliser, better soil in that corner, or a watering can that leaked. Failing to knock it over is not a loss either, since a handful of plants can hide a real effect. Two ways to be wrong come free with the method: reject a null that was true, or keep one that was false. And there is one thing the null never tells you: whether the effect is big enough to care about. Rejecting it clears the bar for real. Clearing the bar for useful is a separate jump. 😎

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Analogy

A criminal court starts from a presumption of innocence. The accused is treated as innocent, and the prosecution has to bring evidence that innocence cannot explain. The jury never asks whether the accused seems guilty. It asks whether the evidence would be this strong if the accused were innocent, and only when that becomes hard to believe does the presumption fall. The null hypothesis is the presumption of innocence: nothing happened, until the data makes that hard to believe. A not-guilty verdict works the same way as keeping the null. It means the evidence did not clear the bar, and it says nothing about what actually happened.
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Analogy

A spam filter starts from one assumption about every email: this message is genuine. That is the null hypothesis, and each email is a fresh test of it. The filter reads the message and asks how likely it would look this way if it were genuine. Fake invoice, unknown sender, a link to click now: too unlikely, the assumption falls, and the email goes to junk. Nothing suspicious: the assumption stands and the email stays in your inbox. It never proves an email is genuine; it just has not seen enough to say otherwise. Sometimes it bins a message from your boss, which is the null rejected when it was true. Sometimes a scam lands in your inbox, which is the null kept when it was false. 😎
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Formal definition — The same term, explained the usual way

The null hypothesis (H₀) is the default statement in a hypothesis test, typically asserting no effect, no difference between groups, or no association between variables. A test statistic is computed from the sample under the assumption that H₀ is true, and the resulting p-value gives the probability of data at least as extreme as that observed. If the p-value falls below a pre-specified significance level, H₀ is rejected in favour of the alternative hypothesis (H₁); otherwise it is retained. Failure to reject H₀ does not establish its truth, and rejection does not establish the alternative or indicate the magnitude of any effect. Rejecting a true H₀ is a Type I error; retaining a false H₀ is a Type II error.

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