Why a statistical test?

From the earlier account of the logic of experimentation, it is not clear why we might need statistical tests. There could well be null hypotheses that require very straightforward, invariant observations to cause their rejection. For example, the null hypothesis ‘There are no squirrels in this forest’ can be rejected if someone sees a squirrel. The observations, model and hypothesis leading to this being the relevant null hypothesis are, however, hard to imagine. Most teachers of biology have long since learned not to make such categorically definitive statements. In my experience, stating that there are no crabs in a rock-pool leads almost immediately and universally to the unmistakable scuttling of (at least) one crab across the pool!

Our observations are, far more commonly, not ones that lead us to null hypotheses of such absolutes as ‘no entities present’. Usually, we are concerned with quantitative measurements. As explained above, these are rarely taken on such small, manageable populations that we can measure every unit in the population about which we are hypothesizing. We must therefore deal with samples. These can provide only statistical estimates of the required parameters of the population. They are subject to sampling error and are variable and inexact.

Consequently, any statement about them or conclusions drawn from them are themselves under the influence of the uncertainty inherent in the measurements. Dealing with this uncertainty involves trying to calculate how uncertain our conclusions are.