by our analysis is there to support our observations and not to replace what we can see with our own eyes. So, the first stage in analysing your data is to just look at it – but look at it with a critical eye. In Figure 1.1, it is quite clear that saline‐pre‐treated animals subsequently treated with mCPP exhibit far lower levels of locomotor activity than any of the other three treatment combinations – this simple observation is an example of the eye‐ball test (sometimes also known as the B.O. test – Bloody Obvious!). Importantly, the data also suggest that subjects pre‐treated with mesulergine subsequently fail to respond as expected to acute treatment with mCPP (i.e. they fail to show mCPP‐induced hypolocomotion); the main conclusion here, therefore, is that mesulergine blocks the behavioural effect of mCPP supporting the notion that because mesulergine is a 5‐HT2C receptor antagonist, then the hypolocomotor activity induced by mCPP is most likely mediated via agonist activity at 5‐HT2C receptors. The subsequent Inferential Statistical analysis simply supports this observation; this is important since the results of our statistical analysis should always be consistent with what we can see with our own eyes. If your statistical analysis contradicts what you can see, then there is something wrong in the presentation of your data, the statistical analysis used, or in the interpretation of the statistical results.
Another example of where the B.O. test alone provides confidence in our observations is the classical concentration–effect curve obtained with receptor agonists in isolated tissue experiments in vitro. Figure 1.3 summarises the effect of increasing concentrations of the α1 adrenoceptor agonist, phenylephrine, on the rat anococcygeus muscle.
Figure 1.3 Phenylephrine‐induced contraction of the rat anococcygeus muscle. Values show Mean ± S.E.M (N = 70) of the percentage maximal response (Y‐axis) plotted according to Log10 of the phenylephrine concentration (X‐axis). The mean EC50 value for phenylephrine (solid square) = 3.6 (2.8, 4.7) × 10−7 M. Mauchly's test indicated that the assumption of sphericity had been violated, χ 2 (90) = 1903.64, p < 0.001. Subsequent Greenhouse–Geisser corrected (ε = 0.156) Repeated Measures ANOVA revealed significant variation between the responses according to dose [F(2.027, 139.862) = 1618.36, p < 0.001]. Post hoc analysis (repeated Paired t‐test with Bonferroni correction) revealed significant difference between successive concentrations (p < 0.01) in all cases except between the highest two concentrations examined (p > 0.05). Data on file.
Clearly phenylephrine induces contractions of this smooth muscle, the magnitude of which is obviously related to drug concentration until a maximal response is achieved. Do we really need high‐powered statistical analysis to tell us what our eyes can clearly see? Probably not, but for completeness, I have included a suitable analysis in the figure legend.
However, life, and the data we generate, is not always so clear‐cut. The problem occurs when we are presented with data that are somewhat equivocal such that the eye‐ball test starts to fail. In such cases we then rely heavily on the results of our statistical approach – that is perfectly acceptable, as long as we stick to a few basic rules that ensure we use the correct statistical approach to analyse and understand our data. If we fail to do so, then we severely run the risk of making erroneous, unsubstantiated conclusions. As scientists we need to have a robust, objective approach to data analysis, so we can arrive at our conclusions with confidence. It is important to acknowledge that nothing is ever proven with statistical analysis in the scientific world. Statistical analysis is all about probability, and the most we can hope for is to demonstrate the likelihood that two or more groups are either similar or different.
The structure of this book: Descriptive and Inferential Statistics
The process of statistical analysis is broadly divided into two principle divisions. The first, and smaller, division is entitled Descriptive Statistics and provides a range of values which allows the appropriate summary of experimental data. Such values include, for example, the Mean, Median, Mode, Variance, Standard Deviation, semi‐quartile range values, etc. and will be described in more detail in Chapters 5, 8 and 9. The second, and by far the larger division, concerns all the statistical tests that are employed to analyse data in order to draw appropriate conclusions about the relationship between different groups of values, and this division is entitled Inferential Statistics and will be the focus of the remainder of this book (from Chapter 10 onwards).
Before we continue this journey of discovery into the mystical world of experimental design and statistical analysis, I would just like to make a few comments about the approach and design taken throughout the book. To an experimental pharmacologist, statistical analysis simply provides a tool by which data obtained through robust experimentation may be understood. The purpose of this book is therefore to show the experimental pharmacologist how to use this tool: how to decide which statistical approach is appropriate for their data, how to prepare for and perform statistical analysis, and how to interpret the resulting output from the analysis. Consequently, this is very much a how‐to, hands‐on book; what it is clearly not is an academic text focused on the vagaries of statistical theory – I really have little interest in why such tests work, I just need to know which test to use and when!
You will notice that the book is organised into (I hope, at least that is the plan) logical sections. Each section will contain a description of the test being described with some examples of experimental data and their statistical analysis. There are a range of software packages available to analyse scientific data, and I dare say, you, your lecturers, Department, or Institution will each have their favourite. Each of the analysis chapters, therefore, conclude with a number of Screenshots showing the appropriate output from a limited number of statistical packages (notably GraphPad Prism, InVivo Stat, MiniTab, and IBM SPSS) of the example data. My aim (or, at least, hope!) is that you will be able to perform you own analysis of the data examples and recognise the similarity between what you see herein and from your own efforts.
Throughout this Introduction, there is one word that pops up repeatedly, and that is the term data. So, what are data? Considering that the aim of this book is to show you how to subject data to appropriate statistical analysis, it is probably most important before we go any further that you understand exactly what data are and appreciate that there are different types of data.
So, sit back and tighten your safety belt as we start our journey into the realm of data.
2 So, what are data?
As far as the experimental pharmacologist is concerned, data are simply numbers generated by our experimental observations. In some cases, the answer may be ‘Yes’ or ‘No’, ‘Present’ or ‘Absent’, where the observation has no discernible magnitude, but subsequently we assign value to these observations to allow statistical analysis. In other experiments, the data may simply be recorded as the number of times a particular event has occurred within a certain time period, for example, when a specific behaviour (e.g. head‐shake) is exhibited by rodents in behavioural experiments; such data are known as quantal data. In other cases, data may be described as a continuous variable, such as height or blood pressure. So, data may have different characteristics, and it is important to ascertain the type of data
