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# Statistics

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### The null hypothesis and the p-value

When looking for an effect or difference between groups, we do so in the context of the null hypothesis, which states that there is no difference between the groups you are testing. For example, if you were investigating the effect that short bursts of exercise have on heart rate, your null hypothesis would state ‘Short bursts of exercise will have no effect on heart rate’.

When interpreting results, you work to either accept or reject the null hypothesis. Accepting the null hypothesis means that there is no significant difference between the samples (there is no difference between heart rate before and after exercise) while rejecting the null hypothesis means that there is a significant difference (there is a difference in heart rate before exercise compared to after exercise).

But how do we know when to reject a null hypothesis, and when to accept it? All statistical tests that are discussed here incorporate the probability value (p-value). In technical terms, the p-value is the probability of finding the observed (or more extreme) results when the null hypothesis is true, i.e. if there really is no difference between our two samples in reality, what is the chance of us receiving the results we have observed (or results that are even more extreme)?

In simpler terms, a p-value is used as a ‘cut-off point’ in terms of accepting or rejecting the null hypothesis. In biology, the convention is that a p-value of less than or equal to 0.05 is ‘significant’, and if our p-value is 0.05 or below (p ≤ 0.05), we reject the null hypothesis, and accept that there is a significant difference between our samples. Likewise, if our p-value is above 0.05 (p > 0.05), we accept the null hypothesis, and conclude that there is no significant difference between our samples. The p-values are equivalent to percentages, e.g. a p-value of 0.05 is the same as 5%, while a p-value of 0.01 is equivalent to 1%.

The p-value is a fundamental concept to science, and if you pick up a research publication in the biological sciences at random, there is a good chance that you will find a p-value mentioned at some point. Each statistical test on the following pages works on different data and in different ways, but all will utilise a p-value, which will guide our accepting or rejecting of the null hypothesis.

#### Stretch and challenge note

In statistical terminology, the null hypothesis is often denoted as H0. You may also come across the alternative hypothesis, denoted as H1. This hypothesis is essential the opposite of the null hypothesis, and is accepted when the null hypothesis is rejected, and vice versa.

For example, if your null hypothesis read ‘There is no difference between the mean weights of two different species of birds’, the alternative hypothesis may read ‘One species of bird has a different mean weight than another species of bird’.