Using Statistics to Understand the Environment

by Cook; Penny A.

• ISBN13: 9780415198882
• ISBN10: 0415198887
• Edition: 1st
• Format: Nonspecific Binding
• Copyright: 2000-06-15
• Publisher: Routledge

Summary

Evaluating and using statistics is an essential part of environmental science courses from pollution studies to environmental management and ecology. This text focuses on the needs of the researcher and provides a concise student-friendly introduction to this core area of Environmental Studies. Statistics for Environmental Investigationscovers all the basic tests required for environmental projects and points the way to the more advanced techniques.

Table of Contents

Series editors' preface	ix
List of figures	xi
List of tables	xiv
List of boxes	xvi
List of worked examples	xviii
Acknowledgements	xx
Using this book	xxii
Project design	1	(24)
Variables	3	(1)
Populations, samples and individuals	3	(1)
Observations and manipulations	4	(1)
Sampling	5	(2)
Block designs	7	(1)
The block design in manipulative experiments	7	(1)
Sampling people	8	(5)
Questionnaire design	10	(2)
Semi-structured and unstructured interviews	12	(1)
Sample size	13	(1)
Independence of data	14	(1)
Sources of error	15	(3)
Data types	18	(3)
Data records	21	(1)
Summary	22	(1)
Questions	23	(2)
Describing data	25	(25)
Descriptive statistics	25	(14)
Frequency tables	26	(1)
Frequency histograms	26	(4)
Measures of central tendency	30	(2)
Measuring variation of normally distributed data	32	(5)
Reliability of the sample mean	37	(2)
Measuring variation of ordinal or non-normal data	39	(1)
Methods of presenting data	39	(8)
Presenting measures of central tendency	40	(3)
Presenting relationships between variables	43	(1)
Cross-tabulation of data	44	(3)
General guidelines for drawing graphs and charts	47	(1)
Summary	47	(1)
Questions	48	(2)
Using statistics to answer questions	50	(17)
Hypothesis testing	50	(5)
Statistical tests	55	(10)
Transforming data	58	(1)
Square root transformation	59	(1)
Logarithmic transformation	60	(1)
Other transformations to correct skewness	60	(1)
Arcsine transformation	61	(1)
Back-transformation of descriptive statistics	62	(1)
Choosing a statistical test	62	(3)
Summary	65	(1)
Questions	66	(1)
Differences between two samples	67	(22)
Unmatched comparisons	68	(11)
t test	69	(5)
Mann--Whitney U test	74	(5)
Matched-pair tests	79	(6)
Paired t test	80	(3)
Wilcoxon matched-pairs test	83	(2)
Summary	85	(1)
Questions	86	(3)
Relationships between variables	89	(32)
Correlations	92	(8)
Pearson's product moment correlation coefficient	94	(3)
Spearman's rank correlation coefficient	97	(3)
Regression	100	(14)
Testing the significance of the regression line	105	(5)
Using the regression equation as a predictive model	110	(1)
Assumptions of simple linear regression	110	(4)
Fitting a regression line through the origin	114	(1)
Relationships between more than two variables	114	(2)
Correlation matrix	114	(1)
Multiple correlation	115	(1)
Concordance	116	(1)
Multiple regression and logistic regression	116	(1)
Summary	116	(1)
Questions	117	(4)
Analysing frequency data	121	(14)
Associations between frequency distributions	121	(8)
The special case of 2 x 2 contingency tables	127	(2)
Goodness of fit against theoretical distributions	129	(3)
The special case of two-category goodness of fit tests	130	(1)
Goodness of fit against model distributions	131	(1)
Assumptions of chi-square frequency analysis	132	(1)
Fisher's exact test and G tests	132	(1)
Testing for associations between more than two distributions	133	(1)
Summary	133	(1)
Questions	134	(1)
Differences between more than two samples	135	(57)
Parametric one-way analysis of variance	136	(14)
Testing for equality of variances	137	(2)
Calculating the F statistic for ANOVA	139	(5)
Multiple comparison tests with equal sample sizes: the Tukey test	144	(3)
Multiple comparison tests with unequal sample sizes: the Tukey--Kramer test	147	(3)
Kruskal--Wallis one-way anlysis of variance using ranks	150	(9)
Multiple comparison tests with equal sample sizes: the Nemenyi test	154	(2)
Multiple comparison tests with unequal sample sizes: Dunn's test	156	(3)
Parametric two-way analysis of variance	159	(14)
Interpretation of significant interactions	166	(4)
Two-way ANOVA with single observations in each cell	170	(3)
Two-way analysis of variance using ranks	173	(10)
Friedman's matched group analysis of variance using ranks	178	(5)
Testing specific hypotheses	183	(1)
Other models of analysis of variance	183	(3)
More than two independent variables	184	(1)
Analysing Latin square designs	184	(1)
Nested analysis of variance	184	(1)
Analysis of covariance	185	(1)
Multivariate analysis of variance	185	(1)
Summary	186	(1)
Questions	187	(5)
Glossary	192	(13)
Definitions of statistical terms	192	(10)
Mathematical symbols	202	(3)
Appendix A Basic mathematical methods and notation	205	(2)
Appendix B Using statistical software	207	(8)
Appendix C Further reading	215	(2)
Selected texts	215	(1)
Statistical tables	216	(1)
Appendix D Statistical tables	217	(10)
Appendix E Answers to exercises	227	(14)
Chapter 1	227	(2)
Chapter 2	229	(2)
Chapter 3	231	(1)
Chapter 4	232	(1)
Chapter 5	233	(2)
Chapter 6	235	(1)
Chapter 7	236	(5)
References	241	(2)
Index	243	(3)
Key to commonly used statistical tests	246