Introduction

Statisticians and life scientists who teach statistics are often visited in their offices by a researcher or student they may have never met before, who is clutching a dauntingly thick pile of paper and perhaps a couple of CDs with labels like ‘Experiment 1’ or ‘Trial 2’. The visitor sits down, drops everything heavily on the desk, and says, ‘Here are my results. What stats do I need?’

This is not a good thing to do. First, the person whose advice you are seeking may not have the time to work out exactly how you have done the experiment, so they may give you bad advice. Second, the answer can be a very nasty surprise like, ‘There are problems with your experimental design’.

The decision about the appropriate statistical analysis needs to be made by considering the hypothesis being tested, the experimental design, and the type of data. It can save a lot of time, trouble, and disappointment if you think about possible ways of analysing the data at the time the experiment is designed, rather than only after the data have been collected.

The following tables are a guide to choosing an appropriate test. You need to start at Table 19.1, which initially gives three columns that are mutually exclusive choices. Once you have decided among these, work downwards within the column you have chosen. There may be more choices and here you also need to select the appropriate column and continue downwards.

Introduction

Every time you make a decision based on the probability of a particular result, there is a risk that your decision is wrong. There are two sorts of mistakes you can make and these are called Type 1 error and Type 2 error.

Type 1 error

A Type 1 error or false positive occurs when you decide the null hypothesis is false when in reality it is not. Imagine you took a sample of size n from a population with known statistics of μ and σ and subjected this sample to a particular experimental treatment. Since the population statistics are known, you could test whether this sample mean was significantly different to the population mean by doing a Z test (Section 7.3).

If the treatment had no effect, the null hypothesis would apply and your sample would simply be equivalent to one drawn at random from the population. Nevertheless, 5% of the sample means of size n will lie outside the 95% confidence interval of μ ± 1.96. Therefore, 5% of the time you would incorrectly reject the null hypothesis of no difference between your sample mean and the population mean (Figure 8.1) and accept the alternate hypothesis. This is a Type 1 error.

Introduction

Before starting on experimental design and statistics, it is important to be familiar with how science is done. This is a summary of a very conventional view of scientific method.

Basic scientific method

The essential features of the ‘hypothetico-deductive’ view of scientific method (see Popper, 1968) are that a person observes or samples the natural world and uses all the information available to make an intuitive, logical guess, called an hypothesis, about how the system functions. The person has no way of knowing if their hypothesis is correct – it may or may not apply. Predictions made from the hypothesis are tested, either by further sampling or by doing experiments. If the results are consistent with the predictions then the hypothesis is retained. If they are not, it is rejected, and a new hypothesis formulated (Figure 2.1).

The initial hypothesis may come about as a result of observations, sampling, and/or reading the scientific literature. Here is an example from ecological entomology.

The Portuguese millipede Ommatioulus moreleti was accidentally introduced into southern Australia from Portugal in the 1950s. This millipede lives in leaf litter and grows to about four centimetres long. In the absence of natural enemies from its country of origin (especially European hedgehogs, which eat a lot of millipedes), its numbers rapidly increased to plague proportions in South Australia. Although it causes very little damage to agricultural crops, O. moreleti is a serious ‘nuisance’ pest because it invades houses.