Many researchers, either directly or indirectly, rely on statistical ideas when carrying out animal experiments. While some statistical tools are well known and are applied routinely, other tools are less well understood and so are less well used. The overall aim of this book is to discuss statistical methodologies that can be applied throughout the many stages of the experimental process. Researchers should be able to carry out most of the techniques described, although the advice of a professional statistician is advisable for some of the more advanced topics. Making use of these techniques will ensure that experiments are conducted in a logical and efficient way, which should result in reliable and reproducible decisions.

The particular types of study addressed in this book, as the title suggests, are studies involving animals. We attempt to cover all of the statistical tools that the animal researcher should use to run successful studies. Of course many of the problems faced by the animal researcher are common to other disciplines, and hence the ideas contained within this book can be applied to other areas. It should be noted that certain topics described in the text have been simplified to allow non-statisticians to apply the ideas without professional statistical support. Such pragmatic descriptions, while simplifying the technical details, are not universal and will not be applicable in all scientific disciplines.

InVivoStat is a free-to-use statistical software package developed specifically for animal researchers. It consists of a series of modules, which produce graphical plots, summary statistics and statistical analyses. In this chapter we shall discuss how to use InVivoStat, describe the individual modules and consider some of the technical details of the analyses.

Getting started

InVivoStat can be downloaded from the website: www.invivostat.co.uk. Once installed it can be accessed via the Windows start menu.

Data import

Data can be imported into InVivoStat from Excel (using the xls or xlsx file formats) or from a text editor using the csv (comma delimited) format. It is recommended that the final dataset is first created in Excel, including all data manipulations, before importing into InVivoStat. If the Excel file contains multiple worksheets, then the user is prompted to select one of the worksheets to import into InVivoStat. Multiple datasets can be opened within InVivoStat but they must be imported individually.

Datasets cannot contain commas in either the variable names or within the body of the data. Variable names cannot also contain the symbols: ~ (tilde), + (plus) or * (asterisk), as these characters are used internally within InVivoStat. Users will not be able to import datasets that include these characters.

This book is aimed at practitioners who do not have a statistics degree and yet wish to apply statistics to help them arrive at valid and reliable conclusions while minimising the animal numbers required. Descriptions of the mathematical methods underpinning the topics covered in the book are purposefully kept to a minimum. If readers wish to gain a better understanding of the mathematics behind experimental design and statistical analysis then reading a more advanced textbook would help further their understanding.

The solutions to practical problems encountered when conducting animal experiments are explained using non-technical approaches. We believe that in many situations advanced statistical ideas can be employed successfully by researchers with no statistical qualification, using a combination of common sense and modern statistical analysis software packages. In our experience statistical ideas are often introduced to scientists using mathematical terminology. This can be off-putting to non-mathematicians and can leave researchers with, at best, only rudimentary statistical tools and at worst a fear of statistics.

To keep the descriptions of the statistical tools covered in this book as simple as possible, we shall occasionally give pragmatic explanations. While such explanations may not apply in all cases and in all scientific disciplines, this approach does allow us to introduce methods in a clear and concise way. By allowing ourselves the freedom to simplify the problems pragmatically, we aim to make statistical tools more accessible. The reader is invited, once they have familiarised themselves with (and hopefully found the benefit of using) the tools described in this book, to read more advanced texts on the subject.

Why design experiments?

It has long been recognised that the use of experimental design is crucial in animal research. By using more efficient experimental designs we can maximise the amount of information gained, while reducing the number of animals required. Even seemingly straightforward experiments employ designs that have features that may, in certain cases, help reduce the number of animals. It is also true that if the scientist spends time considering the experimental design, then practical problems can be solved systematically. Experimental design provides a logical framework that will allow the scientist to develop and understand the animal model in a more refined way.

Experimental design is also a useful tool for researchers who do not feel confident running statistical analyses. As observed by Montgomery (1997, p. 18), if you plan the design carefully and correctly, using a little common sense, then the analysis will almost certainly be relatively straightforward. The validity of the results of many statistical tests relies on the underlying experimental design and randomisation.

We shall begin by considering in more detail some of the real benefits to be gained when using experimental designs, from both practical and statistical perspectives. We will then define the fundamental concepts that define an experimental design and finally describe some commonly applied families of designs.

In this text we have aimed to show the reader how the use of experimental design and statistics can help the researcher gather the most information from each animal experiment while using as few animals as possible. Returning to the statement of Russell and Burch (1959, p. 111):

We hope that this text has convinced the reader that there is much merit in this statement.

The book has been aimed at any researcher performing animal experiments. Some of the subject matter can be applied by scientists without the help of a professional statistician. We have also used this platform to introduce the reader to some of the more complicated examples of experimental design and statistical analysis, examples of which are commonly found in real-life experiments. Hopefully we have given a flavour of these methods and encouraged the reader to either try them out for themselves or seek professional help to get started. Remember, as explained in Gaines Das (2004), sometimes it is the collaboration between the biologist and the statistician at all stages of the experimental process that leads to a successful experiment.

In the previous chapter we gave recommendations regarding the randomisation procedures that should be performed when employing factorial, block and crossover designs. We also considered randomisation when differentiating between the various ways that an animal can be measured repeatedly. In this chapter we shall discuss some of the more general issues associated with randomisation and highlight how randomisation can influence the statistical analysis.

As a general rule it should be remembered that:

• Where possible, the levels of each factor should be randomly assigned to the labels of the experimental design. So, for example, if a design is constructed (or obtained from a textbook) and the labels within the design are given as ‘1’, ‘2’ and ‘3’, then the actual treatments in the experiment (say drug X, drug Y and the control) should be randomly assigned to the labels ‘1’, ‘2’ and ‘3’.

• Randomisation should ensure that each animal has an equal chance of being allocated to any of the experimental groups.

• If a random factor is included in the statistical analysis, then we should always try to select the levels of the random factor randomly from a wider population of levels. For example, the study animals should be randomly selected from a larger population of animals. These study animals are then randomly assigned to the treatment groups. As we shall see, when we draw conclusions from the statistical analysis of an animal experiment, these conclusions can only be generalised to the wider population from which the animals were randomly taken. So, for example, the conclusions of an animal experiment conducted using males will not necessarily generalise to females.

• Design first and randomise second. Leaving to chance the exact relationship between the factors in the design may be the easier option, especially if there are many effects that could influence the experimental results. However, we believe it is best to take into account as many effects as possible, by including corresponding factors in the experimental design, as this usually leads to a simpler analysis, more reliable results and more informed decisions.

This chapter, devoted to randomisation, is purposefully placed between the experimental design and statistical analysis sections of the book. This is to emphasise that randomisation provides a justification (it should be stressed not the only justification) for the statistical analysis. Randomisation can be seen as a link between the experimental design and the statistical analysis.

Introduction

For the remainder of this text we shall consider the statistical analysis of (hopefully) well-designed animal experiments. If a suitable experimental design has been employed then the statistical analysis should be relatively straightforward. It should be as concise as possible while making best use of all available information. We argue that to achieve this, the experimental design should direct the statistical analysis.

By this stage of the experimental process the researcher should have:

• identified all effects that may increase the variability of the data and attempted to account for them in the experimental design;

• selected a suitable sample size;

• measured a response that contains as much information as possible;

• attempted to ensure that other nuisance effects have not biased the experimental results.

With these criteria satisfied the analysis should be straightforward and hopefully give reliable and meaningful conclusions.

Before we describe in more detail some of the analyses available when analysing data generated from animal experiments, there are a number of general issues worth considering.

Use the experimental design to direct the analysis

As stated above, in animal experiments we have the luxury of having almost complete control over the experimental design. We should make the most of this in the statistical analysis. As we have seen in the previous chapter, dii cult decisions regarding the analysis strategy can be solved, or at least a justifiable solution found, by recourse to the experimental design and randomization (for example, see Section 4.2.3 for decisions on repeated measures status and Section 4.2.2 for model selection).

Before we describe the experimental designs and statistical analyses that may be of use to the researcher, a few fundamental concepts are introduced. While many researchers are familiar with these concepts, they are the foundation for the arguments that follow and hence are considered first.

Decision-making: the signal-to- noise ratio

Arguably the primary role of the statistical analysis of an animal experiment is to allow the scientist to draw reliable conclusions from the results obtained. Statistics provides the decision-maker with a framework for achieving this. Importantly it also quantifies the confidence that should be placed in that decision.

Example 2.1: Plasma glucose level

Consider the following two experiments, designed to assess the effect of two treatments A and B, on reducing plasma glucose levels in diabetic mice. Treatment A was tested in experiment 1, treatment B in experiment 2. Both studies also included a control group to allow a test of the treatment effect. The plasma glucose level of the two control groups was around 280 mg/dL. Animals dosed with treatment A had an average plasma glucose level of 227 mg/dL whereas those dosed with treatment B had an average of 185 mg/dL. Without any further information it appears that treatment B was more effective at decreasing plasma glucose level. A scatterplot of the four averages is presented in Figure 2.1.

But was this conclusion valid? It is always difficult to compare results across experiments, even if the control groups appear to be similar. Other effects, unique to each experiment, may be influencing the results. We shall comment further on this later, where it will be shown that other experimental designs may be more appropriate.

Assume that different researchers carried out the two experiments; a plot of the individual results is presented in Figure 2.2.