This book is a completely revised and updated version of this invaluable text which allows science students to extend necessary skills and techniques, with the topics being developed through examples in science which are easily understood by students from a range of disciplines. The introductory approach eases students into the subject, progressing to cover topics relevant to first and second year study and support data analysis for final year projects.
The revision of the material in the book has been matched, on the accompanying website, with the extensive use of video, providing worked answers to over 200 questions in the book plus additional tutorial support. The second edition has also improved the learning approach for key topic areas to make it even more accessible and user-friendly, making it a perfect resource for students of all abilities. The expanding website provides a wide range of support material, providing a study environment within which students can develop their independent learning skills, in addition to providing resources that can be used by tutors for integration into other science-based programmes.
Preface xi On-line Learning Support xv 1 Mathematics and Statistics in Science 1 1.1 Data and Information 2 1.2 Experimental Variation and Uncertainty 2 1.3 Mathematical Models in Science 4 2 Scientific Data 7 2.1 Scientific Numbers 8 2.2 Scientific Quantities 15 2.3 Chemical Quantities 20 2.4 Angular Measurements 31 3 Equations in Science 41 3.1 Basic Techniques 41 3.2 Rearranging Simple Equations 53 3.3 Symbols 63 3.4 Further Equations 68 3.5 Quadratic and Simultaneous Equations 78 4 Linear Relationships 87 4.1 Straight Line Graph 89 4.2 Linear Regression 99 4.3 Linearization 107 5 Logarithmic and Exponential Functions 113 5.1 Mathematics of e, ln and log 114 5.2 Exponential Growth and Decay 128 6 Rates of Change 145 6.1 Rate of Change 145 6.2 Differentiation 152 7 Statistics for Science 161 7.1 Analysing Replicate Data 162 7.2 Describing and Estimating 168 7.3 Frequency Statistics 176 7.4 Probability 190 7.5 Factorials, Permutations and Combinations 203 8 Distributions and Uncertainty 211 8.1 Normal Distribution 212 8.2 Uncertainties in Measurement 217 8.3 Presenting Uncertainty 224 8.4 Binomial and Poisson Distributions 230 9 Scientific Investigation 243 9.1 Scientific Systems 243 9.2 The ‘Scientific Method’ 245 9.3 Decision Making with Statistics 246 9.4 Hypothesis Testing 250 9.5 Selecting Analyses and Tests 256 10 t-tests and F-tests 261 10.1 One-sample t-tests 262 10.2 Two-sample t-tests 267 10.3 Paired t-tests 272 10.4 F-tests 274 11 ANOVA – Analysis of Variance 279 11.1 One-way ANOVA 279 11.2 Two-way ANOVA 286 11.3 Two-way ANOVA with Replication 290 11.4 ANOVA Post Hoc Testing 296 12 Non-parametric Tests for Medians 299 12.1 One-sample Wilcoxon Test 301 12.2 Two-sample Mann–Whitney U-test 305 12.3 Paired Wilcoxon Test 308 12.4 Kruskal–Wallis and Friedman Tests 311 13 Correlation and Regression 315 13.1 Linear Correlation 316 13.2 Statistics of Correlation and Regression 320 13.3 Uncertainty in Linear Calibration 324 14 Frequency and Proportion 331 14.1 Chi-squared Contingency Table 332 14.2 Goodness of Fit 340 14.3 Tests for Proportion 343 15 Experimental Design 349 15.1 Principal Techniques 349 15.2 Planning a Research Project 357 Appendix I: Microsoft Excel 359 Appendix II: Cumulative z-areas for Standard Normal Distribution 363 Appendix III: Critical Values: t-statistic and Chi-squared, χ2 365 Appendix IV: Critical F-values at 0.05 (95 %) Significance 367 Appendix V: Critical Values at 0.05 (95 %) Significance for: Pearson’s Correlation Coefficient, r, Spearman’s Rank Correlation Coefficient, rS , and Wilcoxon Lower Limit, WL 369 Appendix VI: Mann–Whitney Lower Limit, UL, at 0.05 (95 %) Significance 371 Short Answers to ‘Q’ Questions 373 Index 379
Graham Currell was a Principal Lecturer in physics at the University of the West of England until his retirement in 2009. During his career, he was involved in the preparation of specialist training programs to support staff in university science laboratories in Asia, the Middle East, Africa and Central America. Since 2000, he has concentrated on the development of data analysis modules and self-study materials for students. Antony Dowman is the author of Essential Mathematics and Statistics for Science, 2nd Edition, published by Wiley.
