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A Primer on Statistical Hypotheses

A Primer on Statistical Hypotheses

Hypothesis testing is the foundation around which we prove our science is worth funding, publishing and sitting through a conference presentation for. I can’t overstate the  importance of understanding hypothesis testing, such is the integral part it plays in biological analyses.

The Null Hypothesis

Fundamental to statistics is the concept of a null hypothesis, and one many undergraduates struggle to conceptualise. A null hypothesis states the status quo; nothing interesting is happening. We start with this hypothesis then attempt to prove it wrong.

The null hypothesis must be testable and able to be disproved. Otherwise what’s the point? We could just make up some wild statement, be unable to disprove it, and then conclude that it’s the truth. This is unscientific to the core, and would never be allowed by an examiner, an editor, or a peer reviewer.

Allow me to co-opt a textbook example for illustrative purposes. Let’s say I want to find out whether there are dolphins living in my local river. We have two potential basic hypotheses: there are no dolphins in the river, or there are dolphins in the river. If we take the latter hypothesis, and I go out every week for a year looking for dolphins and never see a single one – what does that mean? Does that mean there are no dolphins in the river? Or did I just fail to see them? Perhaps I’m looking at the wrong time of day, or they are especially shy. I have failed to disprove our hypothesis.

But if we take the other angle, there are NO dolphins in the river, the first time I see a dolphin we can reject our hypothesis. There is at least one dolphin in the river, so it cannot be true that there are none. We have disproved our hypothesis, because it was structured in a falsifiable manner.

The Alternate Hypothesis

The Laurel, to the null hypothesis’s Hardy, is the alternate hypothesis. This expresses the opposite scenario, i.e. there are dolphins in the river; there is an effect of adding fertiliser; males and females differ in height. By disproving the null hypothesis, we accept the alternative hypothesis. If we cannot disprove the null, then we cannot prove anything is occurring beyond the null hypothesis status quo.

If I stopped here, I expect the comments section would explode with statements rubbishing null hypothesis testing. Here’s the secret most biologists don’t know: null hypothesis testing is not universally supported by scientists. Yet we indoctrinate our undergraduates to it and scientific papers are littered with examples.

The Limitations of the Null Hypothesis

I am one of the culprits; in a statistics course I tutored for many years we drilled undergraduates on null and alternate hypotheses, breaking them of any inquisitiveness that allowed them to muse “but the null hypothesis is nonsense”. Now is the time to question the usefulness of a hypothesis that states “there is no effect”. What it more important, whether there is an effect, or whether that effect is meaningful?

A statistical significance is just that; it does not indicate biological significance. Think of hatching rates of bird eggs. If one population has a “statistically significant” hatching rate 2% higher than a neighbouring population, is this biologically relevant? Probability says a difference of is 2% is significant; common sense ought to question whether a 2% increase has any impact on population dynamics. Hypothesis testing ought to be one step of many in analysing biological data; however, we have raised a generation of biologists to fetishize the null hypothesis and ignore both biological significance and effect size.

All this is priming you for future conversations about the meaning and use of hypothesis testing. But before then, we still need to establish some basic statistical knowledge. Feel free to comment if you have particularly strong feelings about null hypothesis tests, but rest assure we will return.

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