Statistics for Ecologists – Outline and Table of Contents

Welcome to the support pages for my book,Statistics for Ecologists. These pages provide information and support material for the book. You will find an outline and table of contents as well as support datafiles and additional material.

This is a book about the scientific process and how you apply it to data in ecology. You will learn how to plan for data collection, how to assemble data, how to analyze data and finally how to present the results. The book uses Microsoft Excel and the powerful Open Source R program to carry out data handling as well as producing graphs.Statistics help you make sense of data, which is generated in all branches of science. Ecology is a wide-ranging and important science, which helps our understanding of the natural world.

Students of ecology and environmental science will find this book aimed at them although many other scientists will find the text useful as the principles and data analysis are the same in many disciplines. No prior knowledge is assumed and the reader can develop their skills up to degree level.

This is a book about the scientific process and how you apply it to data in ecology. You will learn how to plan for data collection, how to assemble data, how to analyze data and finally how to present the results. The book uses Microsoft Excel and the powerful Open Source R program to carry out data handling as well as producing graphs. Specific topics include:How to plan ecological projects.How to record and assemble your data.How to use Excel for data analysis and graphs.How to use R for data analysis and graphs.How to carry out a wide range of statistical analyses including analysis of variance and regression.How to create professional looking graphs.How to present your results.

The changes from the first edition can be summarized like so:Completely revised chapter on graphics. The chapter is now a one-stop resource for all graphics related topics.New: graph types and their uses.New: Excel Chart Tools.New: R graphics commands.New: producing different chart types in Excel and in R.More support material online, including; example data, exercises and additional notes & explanations.New: chapter on basic community statistics, biodiversity and similarity.New: chapter summaries.New: end of chapter exercises.

The book is broadly laid out in four sections, roughly corresponding to the topics: planning, recording, analysing and reporting. The sections are rather unequal in length, with the focus on the analysis chapters and production of graphics.Throughout the book you will see example exercises that are intended for you to try out. In fact, they are expressly aimed at helping you on a practical level; reading how to do something is fine but you need to do it for yourself to learn it properly. The Have a Go exercises are hard to miss.

Use the following table/links to jump directly to a chapter and see the outline and a few notes.1.Planning2. Data recording3. Using software tools4. Looking at numbers5. Which analysis?6. Graphics7. Tests for differences8. Tests for correlation9. Association10. Differences with more than two samples11. Multiple regression12. Community analysis13. Presenting results14. SummaryGlossaryAppendix

This chapter is about the preparation stages required before starting to collect data or carry out any analyses. The chapter includes notes on planning for data collection and getting appropriate software (that is R and Excel).

This section outlines the scientific method and provides a framework for all projects and data analysis.

This section deals with the types of project that could be encountered and provides a framework that allows the reader to characterise a project, which leads to the most appropriate method of analysis.

This brief section highlights the importance of the spreadsheet and especially points out the usefulness of it in relation to pilot studies and as a tool for overview.

This section introduces the idea of the hypothesis, a subject that will be returned to in chapter 5.

This section introduces the different types of data that can be encountered (Interval, Ordinal and Categorical) and gives some examples of ordinal scales (Domin and Braun Blanquet) that can be used in data collection.

This section introduces methods of data collection and includes notes on the amount of data to collect as well as quadrat sizes for example. The ideas of random and systematic sampling are introduced. The main purpose of this section is to highlight the importance of your samples being representative.

This brief section highlights the importance of the software tools that will be used.

The R program is an important and powerful tool for data analysis. This section shows the reader how to obtain the program and install it on their computer.

A spreadsheet is a useful tool as it allows your data to be held in an formal manner that can be shared. The spreadsheet also allows us to carry out various analyses and produce graphs. In this section the main focus is on installation of the Analysis ToolPak in Excel. This tool allows a number of analyses to be carried out more efficiently that using the regular spreadsheet formulae.

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

This chapter is brief yet important! The arrangement of data is a fundamentally important aspect of data analysis. Get this part right and your subsequent analyses are greatly facilitated. Get this part wrong and you will have to spend a lot of time rearranging data before analysis can be done. The main thrust of this chapter is to introduce the idea of Biological Records and the Biological Recording format. This standard format is very flexible and allows your data to be used for multiple purposes very easily.

This section deals with the basics of Biological Records and what elements should be recorded.

The arrangement of data is of fundamental importance as a poor layout will make it hard to extract the information you require. This section shows how to arrange data in the Biological Recording format, which permits the data to be utilized more easily.

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

This chapter is aimed at getting the reader more familiar with the software that they will use for data analysis, specifically Excel and R.

This section introduces the R program and helps readers get started using this powerful program. The section includes notes on various topics including:Getting HelpBasic MathsInputting DataSummary StatisticsSaving WorkBy the end of this section the reader should be competent and confident with using R and be prepared for more detailed data analysis using the R interface.

This section introduces some important aspects of Excel, topics include:SortingData FilteringPaste SpecialFile FormatsLookup TablesPivot TablesThese skills are really important and when combined with Biological Recording format allow data to be utilized easily and flexibly.

This brief section shows how to transfer data from Excel into R. The spreadsheet is really useful as a data storage program and for initial overviews. Although many statistical and graphical analyses can be carried out in Excel the R program is a dedicated data analysis tool; the more complicated the data the more likely it is that you will be using R rather than Excel.

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

This chapter begins the actual process of data analysis. The exploratory methods introduced here are the basics that should be carried out on all data. Methods covered include:AveragesDispersionConfidence Intervals

This section deals with the idea of the average as a summary of a numerical sample:MeanMedianAfter some basic introduction the section deals with how to determine averages in Excel and R.

This section deals with the distribution of the data (that is normal or skewed). Specifically the reader is shown how to create Tally plots and Histograms to visualise the data distribution. The reader is shown how to create a histogram using Excel and R. There is also a brief section on producing density plots (using R), which can be used with a histogram to compare two different distributions.

This section looks at measures of dispersion, specifically:RangeQuartilesStandard DeviationThere are notes on how to determine these measures using Excel and using R. The idea of the box plot (box-whisker plot) is also introduced here as a useful visual aid. This section ends with some notes on why n-1 is used in calculations of standard deviation.

This brief section illustrates one method of testing the assumption that a sample is normally distributed. The Shapiro-Wilk test is shown (using the R program).

This section begins with a note of what summary statistics should be used with normal or skewed distribution. The rest of the section includes notes on some other statistics, namely:Standard ErrorConfidence IntervalsThese statistics are related to the normal distribution and link in with the idea of hypothesis testing.

Since the normal distribution is so important it is helpful to coerce data into normal form if is skewed. This section introduces the idea of data transformation and illustrates several common methods including:LogarithmicSquare RootArcsine (also called Angular)ReciprocalThere are some notes on how to do these transformations in Excel and using R.

This section introduces the idea of the running mean as a way to determine when the sample size is adequate.

This section illustrates a few of the more commonly encountered statistical symbols, summarized in a handy table.

Some self-assessment questions (answers in the appendix).

This brief chapter shows the reader how to select the most appropriate analytical test for their data. There is also a brief reminder of the idea of the hypothesis.

It can be helpful to think about the type of project you are undertaking, as this can help guide you towards the most appropriate method(s) of analysis. In this section you’ll see the different sorts of potential project and the kinds of analysis that might be suitable.

This section revisits the idea of the hypothesis as an analytical tool.

This section guides the reader towards the most appropriate test. The section includes a decision tree that points to the correct section of the book.

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

This chapter has been revised extensively from the original version. It is now a complete overview of graphical presentation and summary of data. You’ll see how to produce the best sort of graph for the job at hand, using examples in both Excel and R. Other chapters incorporate graphics as required but this chapter forms the general foundation, which you can use as a basic reference.

This section provides an overview of graph types, showing which sort is best for which task. There are also summaries about how to create graphs in Excel and in R, with the basics to get you started. There are notes about the Chart Tools in Excel and the basic R commands that help you produce and edit graphs.

This section shows the kind of graphical summary most useful in visualizing data, including:Stem Leaf plotHistogramDensity plotBox-Whisker plotThese graphs would generally be used to determine the distribution of the data sample(s).

This section shows the most useful graphs to illustrate differences:Box-Whisker plotBar chartThere are also notes about using legends, which are especially useful for multiple category bar charts.

This section focusses on the sorts of graph used for illustrating correlations, that is scatter plots. Line plots are also covered, they aren’t exactly used for correlation but show changes over fixed (time) periods, and so fit best in this section.

This section shows the kinds of graph used when looking at associations:Pie chartsMultiple category bar chartsPie charts are commonly used for displaying compositional data. A better alternative is a bar chart. There are notes about how to display the results if chi squared tests of association using R and Excel.

This section deals with the sorts of graph used to illustrate similarity between samples. These are dendrograms, and are used in community ecology (see Chapter 12).

The chapter ends with a brief summary, which includes…

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

This chapter examines the basic tests for differences between two samples, namely:Student’s t-testMann-Whitney U-test (a.k.a. Wilcoxon Signed Rank test)These underpin many of the more complicated tests and are important building blocks for further analysis.

The t-test is an important analytical tool that uses the properties of the normal distribution to make decisions about differences between two sample means. In this section the t-test is introduced with a little background/theory. A table of critical values for the t-test is provided (with a copy in the appendix).The way to use the t-test in both Excel and R is shown. There is also a section showing how to use the Analysis ToolPak in Excel to carry out the t-test.

The U-test is a non-parametric test, that is it is used when the sample data are skewed and do not form the normal distribution. The U-test compares two sample medians.The U-test is introduced with a little background/theory and its use in R is shown. Excel cannot carry out a U-test easily although some tips are shown. A table of critical values for the U-test is provided (with a copy in the appendix).

When data are in the form of matched pairs it is possible to use a special version of the t-test or U-test (according to the distribution of the data, see Chapter 4). Both tests are illustrated with examples.For normally distributed data the paired t-test is shown. For skewed data the Wilcoxon matched pairs test is shown. A table of critical values for the Wilcoxon test is provided (the t-test table is the same as for the regular t-test). Paired tests can be carried out in R and this is illustrated. Excel can carry out the t-test but not the Wilcoxon test.

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

When you have more than two samples to compare you will need a more complicated analytical approach. This chapter covers the two main methods of analysis:Analysis of Variance (ANOVA)Kruskal-Wallis testANOVA is used when you have normally distributed data (see Chapter 4). When the data are not normally distributed the Kruskal-Wallis test is used. Use of both Excel and R is illustrated in the text.

ANOVA allows you to compare more than two samples. When you have a single variable to compare the situation is called one-way ANOVA. However, you may have more than one variable and two-way ANOVA (or more) is possible. This section looks at a range of options when using ANOVA including:One-way ANOVAPost-Hoc testingTwo-way ANOVAANOVA is described in general and then the calculations are described for both R and Excel. Use of the Analysis ToolPak Excel add-in is also described for one or two-way ANOVA.There are critical values tables (with copies in the appendix) for the F-distribution and for Q, the Studentized range, which is used in post-hoc testing.There are also some notes about graphing the results of ANOVA for both R and Excel.

If your data are not normally distributed (see Chapter 4) then the Kruskal-Wallis test is suitable in lieu of 1-way ANOVA. This is described in the text as well as a method of post-hoc testing. Tables of critical values for the Kruskal-Wallis test are quite extensive and there are several versions, for use with different sample sizes. Table of critical values are presented in the support material rather than in the book itself (you can see the critical values tables here).

Excel is unable to carry out the test “automatically” but there are several functions that can help carry out the required calculations and these are described in the text (there is also an exercise that walks you through the necessary steps).

R can conduct Kruskal-Wallis easily and the processes are described in the text with some examples.

Conducting a post-hoc test for Kruskal-Wallis tests is slightly cumbersome. You can find custom R functions for K-W post-hoc testing on the support pages.

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

When you have several variables to correlate you need a more complicated analytical tool. Multiple regression is the one you require; this uses the properties of the normal distribution. In this chapter multiple regression is described in detail. Curved linear regression is also described (this was introduced in Chapter 8).

A special kind of regression is required when your response variable can only have two forms (e.g. present or absent); this is logistic regression (or binomial regression). Logistic regression is far from trivial to undertake in Excel, so it is described in detail using R.

Various aspects of multiple regression are described, including:

<ul>

<li style=”text-align: left;”>Multiple regression</li>

<li style=”text-align: left;”>Beta coefficients</li>

<li style=”text-align: left;”>Lines of best-fit</li>

<li style=”text-align: left;”>Model building and stepwise regression</li>

</ul>

Multiple regression is introduced and illustrated using both Excel and R. The use of R is extended by demonstrating how to carry out stepwise regression – this is a method of building the most appropriate regression for your data.

Curved linear regression is demonstrated using two examples:

<ul>

<li style=”text-align: left;”>Polynomial regression</li>

<li style=”text-align: left;”>Logarithmic regression</li>

</ul>

Curvilinear regression is described using both Excel and R. There are also notes about graphing the results and how to add curved lines of best fit to your graphs.

Logistic regression is another form of regression and is used when you have binary data (e.g. presence-absence). Excel cannot easily carry out logistic regression but R can do this fairly easily and this is illustrated using two different examples. Logistic regression is a form of Generalized Linear Modelling (GLM).

You’ll also see how to build a regression model and how to plot the results as a scatter plot with a line of “best-fit”. There is an online exercise in logistic regression model-building on the support pages.

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

This is a new chapter, especially written for the new second edition. In ecology you are often looking at several species at once, that is you are looking at communities. The analytical methods for exploring community data are generally rather more complicated than when dealing with single species. However, there are a couple of useful statistical approaches that can be easily carried out. These are diversity and similarity, which are described in this chapter.

In a general sense the term diversity (or biodiversity) relates to the number of species in a given area (or sample). However, this is only one way to measure biodiversity. In an ecological sense the term diversity covers several methods of analysis. It is therefore important that you state what sort of diversity you are referring to. The measures of diversity you’ll see in this section are:

<ul>

<li style=”text-align: left;”>Species Richness – the number of different species in a given area or sample.</li>

<li style=”text-align: left;”>Indices of diversity – take into account not only the number of species but also their relative abundance.</li>

</ul>

Two main indices of diversity covered in the text are:

<ul>

<li style=”text-align: left;”>Simpson’s index</li>

<li style=”text-align: left;”>Shannon entropy</li>
hello</ul>

You’ll see how to calculate diversity using Excel and R.

Comparing diversity indices can be tricky. The support website contains an exercise in comparing (Shannon) diversity using the Hutcheson t-test. You can download the Excel spreadsheet for use with your own data.

The analysis of similarity does essentially what the name suggests; it compares samples and allows you to see which are most similar to one another. This can be useful when comparing many samples.

This section covers several methods of calculating similarity, using both Excel and R.

Visualising similarity is done using a special sort of graph called a dendrogram. The text shows you how to draw a dendrogram in various ways:

<ul>

<li style=”text-align: left;”>By hand</li>

<li style=”text-align: left;”>Using Excel</li>

<li style=”text-align: left;”>Using R</li>

</ul>

The support material includes a walk-through exercise on building a dendrogram using Excel (there is an associated data file).

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

The presentation of your work is an important stage in the scientific process. It helps you to move forwards and to determine “what next?” as well as adding to the body of scientific knowledge and helping other researchers in the future.

This chapter is concerned with the reporting of results. There are sections covering some of the conventions for reporting of statistical tests as well as notes about writing reports in various formats.

This brief section gives some ideas about the kinds of presentation namely:

<ul>

<li style=”text-align: left;”>A written report</li>

<li style=”text-align: left;”>A talk</li>

<li style=”text-align: left;”>A poster</li>

</ul>

This brief section gives some ideas for places that your work might be published. There are many options ranging from a scientific journal to a press release.

It is important to present your findings in a manner that can be understood by your peers. If you are presenting results to the general public then you may have to alter the presentation to suit your audience, but you still keep to the conventions used by scientists in displaying results.

This section shows the main conventions used to display the results of statistical analyses.

This section has been heavily revised since the first edition. The “how to” parts have been removed to Chapter 6 and what remains is more of a guide to “good practice”. The section provides an overview/reminder of graph types and their uses and also of the main elements that you should aim to incorporate for best effect.

The aim of a paper is to disseminate your results as widely as possible. It is all about communication of your scientific endeavour! This section provides a summary of the main elements of a scientific paper. The various elements form a basic framework that applies to more or less all scientific presentations, regardless of the audience. You may place different emphasis on certain elements (or omit them entirely) but you always keep the basic framework in mind. The structure is important because readers need to know where to find certain pieces of information.

Plagiarism is a form of stealing. Essentially it involves you setting forth someone’s work and passing it off as if it were your own. Of course you need to use previous knowledge in your work but you need to acknowledge where your knowledge/information came from. This section gives a few pointers about how to avoid plagiarism. The key to avoiding plagiarism is to know how and when to cite references, the subject of the next section.

References come in two parts. There is a bit in the text that essentially says “look at this for information” and a list at the end that gives the original sources. References are important because they allow readers to see where your information came from and helps avoid plagiarism. References are also useful as pointers to information (e.g. to figures and tables in your report).

This section gives the key elements of references and shows some different methods for employing citations in your text.

A poster allows you to make a presentation, which is left on display for hours, sometimes days. It can potentially reach hundreds of people because it is hanging around for so long. At meetings there is usually a set session where you stand by your poster and present it to anyone who expresses an interest; otherwise it stands alone.

This section provides some notes about the use of posters as a means to disseminate your results.

PowerPoint (or equivalent software) is virtually ubiquitous and is familiar to most people. It can be a great tool for presenting information but it can also be used badly! This short section gives a few notes about “best practice” for use of PowerPoint presentations.

Some self-assessment questions (answers in the appendix).

A summary of the main topics covered in the chapter. Provides a quick summary/overview.

This is a very brief summary to remind you that there is more to data analysis than just doing statistics.

The glossary is a simple list of useful terms alongside a brief explanation.

The appendix contains two main sections:

<ul>

<li>Answers to self-assessment questions</li>

<li>Tables of critical values</li>

</ul>

The answers to the questions are set out in chapter order. The critical values tables are copies of those in the main text but presented en masse to form a more useful resource.