Zoo Research Guidelines Statistics for typical zoo datasets © British and Irish Association of Zoos and Aquariums 2006 All rights reserved. No part of this publication my be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system, without permission in writing from the publisher. Plowman, A.B. (ed)(2006) Zoo Research Guidelines: Statistics for typical zoo datasets. BIAZA, London. First published 2006 Published and printed by: BIAZA Zoological Gardens, Regent’s Park, London NW1 4RY, United Kingdom ISSN 1479-5647 2 Zoo Research Guidelines: Statistics for typical zoo datasets Edited by Dr Amy Plowman Paignton Zoo Environmental Park, Totnes Road, Paignton, Devon TQ4 7EU, U.K. Contributing authors: Prof Graeme Ruxton Institute of Biomedical and Life Sciences, Graham Kerr Building, University of Glasgow, Glasgow G12 8QQ Dr Nick Colegrave Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, King's Buildings, West Mains Road, Edinburgh EH9 3JT Dr Juergen Engel Zoolution, Olchinger Str. 60, 82178 Puchheim, Germany. Dr Nicola Marples Department of Zoology, Trinity College, Dublin 2, Ireland. Dr Vicky Melfi Paignton Zoo Environmental Park, Totnes Road, Paignton, Devon TQ4 7EU, U.K. Dr Stephanie Wehnelt, Zoo Schmiding, Schmidingerstr. 5, A-4631 Krenglbach, Austria. Dr Sue Dow Bristol Zoo Gardens, Clifton, Bristol BS8 3HA, U.K. Dr Christine Caldwell Department of Psychology, University of Stirling, Stirling FK9 4LA, Scotland Dr Sheila Pankhurst Department of Life Sciences, Anglia Ruskin University, Cambridge CB1 1PT, U.K. Dr Hannah Buchanan-Smith Department of Psychology, University of Stirling, Stirling FK9 4LA, Scotland. Heidi Mitchell Marwell Zoological Park, Colden Common, Winchester, Hampshire SO21 1JH, U.K. Acknowledgements These guidelines are a result of a workshop organized by the BIAZA Research Group and hosted at Edinburgh Zoo in July 2004. All the authors were participants at the workshop, additional participants were Rob Thomas, Charlie Nevison and Colleen Schaffner and we acknowledge their valuable contributions to these guidelines. Particular thanks also go to Rob Thomas for organizing the workshop logistics and to Minitab for sponsorship of the day. 3 Contents 1. Introduction (A.B. Plowman) 1.1 What are these guidelines for? 1.2 Why are these guidelines needed? 1.3 How to use these guidelines and flowchart guide to sections 2. Randomisation tests (N. Colegrave, J. Engel and A.B. Plowman) 2.1 The problem 2.2 The solution 2.3 Use of randomisation tests for single case and small samples sizes in a zoo setting 2.4 Limitations of randomisation tests 2.5 Presentation of results 2.6 Software for randomisation tests 3. Multivariate tests (V.A. Melfi, N. Marples and G.D. Ruxton) 3.1 The problem 3.2 Common mistakes 3.3 Solutions 3.4 How is it done? 3.5 How to interpret and present results 4. Analysing activity budgets using G-tests (N. Marples, G.D. Ruxton and N. Colegrave,) 4.1 The problem 4.2 Common mistakes 4.3 Solutions 4.4 Limitations 5. General issues 5.1 Autocorrelation, temporal independence and sampling regime (S. Dow, J. Engel and H. Mitchell) 5.2 Social independence (S. Wehnelt, H. Buchanan-Smith, G.D. Ruxton and N. Colegrave) 5.3 Multiple test corrections (C.A. Caldwell, G.D. Ruxton and N. Colegrave) 5.4 Parametric versus non-parametric tests (C.A. Caldwell) 6. References (S. Pankhurst) 4 1. Introduction A.B. Plowman 1.1 What are these guidelines for? This volume aims to give zoo researchers, particularly students, clear guidelines to enable them to choose the most appropriate statistical tests for the types of datasets typically collected in zoo settings. If the guidelines in this volume are followed then researchers should be confident that they have chosen correct, valid and robust statistical analyses. The guidelines highlight typical challenges in zoo research, offer solutions and give advice on how to present the results of the tests and how to interpret these results in terms of what conclusions may or may not be drawn. With these guidelines we hope to increase not only the quality of zoo research but also the acceptance rate of zoo-based research papers in peer reviewed scientific journals. 1.2 Why are these guidelines needed? Despite a long history of fascinating, innovative and robust research carried out in zoos around the world (e.g. de Waal and van Roosemalen, 1979) many researchers in other fields do not consider zoo research a scientifically worthwhile activity. The most common reasons given for this are that animals in zoo environments are not ‘natural’ and that robust statistical analyses are not possible. The first of these objections is something all researchers should be aware of. However, with recent developments in husbandry methods and naturalistic housing and social groupings, most modern zoos now provide an extremely useful research setting; bridging the gap between highly controlled, but often extremely unnatural, laboratory conditions and the totally natural, but very difficult working conditions of the field. The second objection will hopefully be dispelled by these guidelines, since they demonstrate that valid and robust statistical tests are possible for typical zoo datasets, even studies on a single animal. However, even robust statistics can not make up for low biological validity of a study on a small number of individuals (see section 2.4), but this is a problem in common with many field studies (see Bart et al., 1998) and these guidelines also provide ways to deal with this challenge. In the past the zoo research community has not helped itself to dispel its image of poor statistical procedures and low validity. The typical statistical difficulties encountered (e.g. small samples, lack of independence of data points, non-normal distributions) have been dealt with in many different, more or less appropriate, ways by different researchers. In the published literature featuring zoo research one can find almost as many different statistical procedures applied to very similar datasets as there are papers. Thus, it is not surprising that many researchers find it hard to know which, if any, are correct. In addition to demonstrating which analyses are most appropriate we hope these guidelines will promote greater consistency in the way typical zoo research datasets are analysed and presented. Consensus on, and standardisation of, the methods we use can only be of benefit to all zoo researchers, increasing our own confidence and competence, improving the quality of our research and enhancing the value of our subject among the wider scientific community. 1.3 How to use these guidelines It is vital that the relevant sections of these guidelines are read BEFORE starting research as the tests to be used will strongly influence the way data are collected Sections 2, 3, and 4 of these guidelines provide information on the types of tests recommended in various situations that commonly occur during zoo research. The flowchart below provides a simple way for researchers to find the appropriate section for their experimental situation. Section 5 will be useful for all researchers as it provides general guidance on sampling procedures and how to avoid common statistical pitfalls, which are relevant irrespective of the tests being performed. 5 START Standard Do you have a parametric large sample size Yes (>15) and tests normally see readily available distributed data text books No (see section 5.4)? Are you comparing the same animal(s) in two or more conditions e.g. evaluating enrichment, before and after an Are you focusing enclosure on one move or modification, dependent Randomisation Yes Yes with high and low visitor variable e.g. tests numbers? cortisol level, time spent Section 2 Or are you comparing pacing? two or more animals (or groups) in one condition e.g. males vs females, No adults vs juveniles? Are you investigating No changes in Yes G-tests and several related derivatives dependent Section 4 variables e.g. the whole activity budget, Are you investigating the relationships between many dependent and independent variables e.g. multi-zoo studies Yes Multivariate using existing tests differences in Section 3 husbandry to evaluate their effects on animals, MBA studies? 6 2. Randomisation Tests N. Colegrave, J. Engel and A.B. Plowman 2.1 The problem A frequent problem of studies carried out in a zoo setting is that, due to practical or ethical limitations, they are often based around a limited number of replicates. For example, zoos may be limited in the number of animals that are available to test a hypothesis, or the number of independent enclosures in which animals can be kept while being studied. In multi zoo studies, individual zoos will often be used as the independent data points, creating obvious difficulties in generating large data sets. Small sample size studies present three specific problems: • First, with few data points it is difficult to decide with any confidence whether the data meet the assumptions required for a particular test. For example, most parametric statistical tests assume that the data are drawn from populations with an underlying normal distribution. Determining whether this is the case in a study with only eight replicates is not realistic. • Second, small studies will generally have extremely low statistical power, and since the power of parametric tests will decline rapidly as assumptions are violated, they may be extremely inefficient tools for extracting the maximum information from our data. • Third, despite best intentions, it will often be difficult or impossible to design zoo studies with the idealised sampling regimes envisaged in statistical text books. Instead data will often be collected opportunistically, leading to obvious problems. The most frequent proposed solution to these problems is to use non-parametric tests. However, and despite popular belief, such tests are not assumption free, and also frequently have low statistical power as well as other limitations (e.g.