Essential Mathematics and Statistics for Science

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.

• Preface xiOn-line Learning Support xv1 Mathematics and Statistics in Science 11.1 Data and Information 21.2 Experimental Variation and Uncertainty 21.3 Mathematical Models in Science 42 Scientific Data 72.1 Scientific Numbers 82.2 Scientific Quantities 152.3 Chemical Quantities 202.4 Angular Measurements 313 Equations in Science 413.1 Basic Techniques 413.2 Rearranging Simple Equations 533.3 Symbols 633.4 Further Equations 683.5 Quadratic and Simultaneous Equations 784 Linear Relationships 874.1 Straight Line Graph 894.2 Linear Regression 994.3 Linearization 1075 Logarithmic and Exponential Functions 1135.1 Mathematics of e, ln and log 1145.2 Exponential Growth and Decay 1286 Rates of Change 1456.1 Rate of Change 1456.2 Differentiation 1527 Statistics for Science 1617.1 Analysing Replicate Data 1627.2 Describing and Estimating 1687.3 Frequency Statistics 1767.4 Probability 1907.5 Factorials, Permutations and Combinations 2038 Distributions and Uncertainty 2118.1 Normal Distribution 2128.2 Uncertainties in Measurement 2178.3 Presenting Uncertainty 2248.4 Binomial and Poisson Distributions 2309 Scientific Investigation 2439.1 Scientific Systems 2439.2 The ‘Scientific Method’ 2459.3 Decision Making with Statistics 2469.4 Hypothesis Testing 2509.5 Selecting Analyses and Tests 25610 t-tests and F-tests 26110.1 One-sample t-tests 26210.2 Two-sample t-tests 26710.3 Paired t-tests 27210.4 F-tests 27411 ANOVA – Analysis of Variance 27911.1 One-way ANOVA 27911.2 Two-way ANOVA 28611.3 Two-way ANOVA with Replication 29011.4 ANOVA Post Hoc Testing 29612 Non-parametric Tests for Medians 29912.1 One-sample Wilcoxon Test 30112.2 Two-sample Mann–Whitney U-test 30512.3 Paired Wilcoxon Test 30812.4 Kruskal–Wallis and Friedman Tests 31113 Correlation and Regression 31513.1 Linear Correlation 31613.2 Statistics of Correlation and Regression 32013.3 Uncertainty in Linear Calibration 32414 Frequency and Proportion 33114.1 Chi-squared Contingency Table 33214.2 Goodness of Fit 34014.3 Tests for Proportion 34315 Experimental Design 34915.1 Principal Techniques 34915.2 Planning a Research Project 357Appendix I: Microsoft Excel 359Appendix II: Cumulative z-areas for Standard Normal Distribution 363Appendix III: Critical Values: t-statistic and Chi-squared, χ2 365Appendix IV: Critical F-values at 0.05 (95 %) Significance 367Appendix 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 369Appendix VI: Mann–Whitney Lower Limit, UL, at 0.05 (95 %) Significance 371Short Answers to ‘Q’ Questions 373Index 379

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