# Doing Science: Design, Analysis, and Communication of Scientific Research

By Ivan Valiela | Go to book overview

3
Statistical Analyses

Some studies produce unambiguous results, in which case we do not need statistics. In most cases, however, we need some objective way to evaluate differences in our results. To provide a way to evaluate results with some degree of objectivity, we can use diverse statistical techniques, the subject of this chapter.

[W]here measurement is noisy, uncertain, and difficult, it is only natural that statistics should flourish.

S. S. Stevens

As mentioned in Chapter 2, the core statistical notion (provided by Sir Ronald A. Fisher) was that of seeing whether the effects of some variable of interest are likely to be larger than the effects of chance variation.1 Statisticians have devised many procedures to do such comparisons and to establish relationships among variables.

Most statistical texts start, reasonably enough, by introducing the reader to the simpler ways by which to see how well we know the mean of a sample, and how sure we might be that it differs from the mean of a hypothetical population. Then they go on to tests that compare two sample means, and so on. I did not follow that pattern in this book, because this is not a book on statistics, but rather an introduction to principles (not to techniques) of doing science. I would have preferred to go right away to principles of design of scientific work, but that turned out to be difficult without some previous discussion of statistical concepts. Therefore, in this chapter I review a few statistical tests before going on to principles of experimental design in chapter 4, to provide readers with terms and strategies of data analysis. Some readers might want to read chapter 4 first and return to this chapter as needed. For the sake of reference, I do review the array from simpler to more complex tests in section 3.5.

Throughout, I refrain from entering into arithmetical details for each test, because these can be found in the many excellent statistics textbooks. Motulsky (1995) provides a lucid intuitive introduction to statistical analyses. Sokal and Rohlf (1995) give a thorough and authoritative review of the methods. Here we will emphasize concepts, but we will have to do a bit of algebra to sort out the concepts.

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1
Chance or random variation is another way we refer to variation caused by additive contributions from many and unidentified variables. This is the “leftover” variation against which we want to compare the variation caused by the treatment we are studying.

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Doing Science: Design, Analysis, and Communication of Scientific Research

• Title Page *
• Preface v
• Contents vii
• Doing Science 1
• 1 - Obtaining Scientific Information 3
• Sources and Further Reading *
• 2 - Elements of Scientific Data and Tests of Questions 29
• Sources and Further Reading *
• 3 - Statistical Analyses 49
• Sources and Further Reading *
• 4 - Principles of Research Design 79
• Sources and Further Reading 97
• 5 - Communication of Scientific Information: Writing 99
• Sources and Further Reading *
• 6 - Communicating Scientific Information: the Scientific Paper 127
• Sources and Further Reading *
• 7 - Other Means of Scientific Communication 147
• Sources and Further Reading *
• 8 - Presenting Data in Tables 171
• Sources and Further Reading *
• 9 - Presenting Data in Figures 183
• Sources and Further Reading *
• 10 - Case Studies of Graphical Data Presentation 219
• 11 - Perceptions and Criticisms of Science 255
• Sources and Further Reading *
• Index 285
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