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. On-line Learning Support.1 Mathematics and Statistics in Science.1.1 Data and Information.1.2 Experimental Variation and Uncertainty.1.3 Mathematical Models in Science.2 Scientific Data.2.1 Scientific Numbers.2.2 Scientific Quantities.2.3 Chemical Quantities.2.4 Angular Measurements.3 Equations in Science.3.1 Basic Techniques.3.2 Rearranging Simple Equations.3.3 Symbols.3.4 Further Equations.3.5 Quadratic and Simultaneous Equations.4 Linear Relationships.4.1 Straight Line Graph.4.2 Linear Regression.4.3 Linearization.5 Logarithmic and Exponential Functions.5.1 Mathematics of e, ln and log.5.2 Exponential Growth and Decay.6 Rates of Change.6.1 Rate of Change.6.2 Differentiation.7 Statistics for Science.7.1 Analysing Replicate Data.7.2 Describing and Estimating.7.3 Frequency Statistics.7.4 Probability.7.5 Factorials, Permutations and Combinations.8 Distributions and Uncertainty.8.1 Normal Distribution.8.2 Uncertainties in Measurement.8.3 Presenting Uncertainty.8.4 Binomial and Poisson Distributions.9 Scientific Investigation.9.1 Scientific Systems.9.2 The ‘Scientific Method’.9.3 Decision Making with Statistics.9.4 Hypothesis Testing.9.5 Selecting Analyses and Tests.10 t -tests and F-tests.10.1 One-sample t -tests.10.2 Two-sample t -tests.10.3 Paired t -tests.10.4 F-tests.11 ANOVA – Analysis of Variance.11.1 One-way ANOVA.11.2 Two-way ANOVA.11.3 Two-way ANOVA with Replication.11.4 ANOVA Post Hoc Testing.12 Non-parametric Tests for Medians.12.1 One-sample Wilcoxon Test.12.2 Two-sample Mann–Whitney U-test.12.3 Paired Wilcoxon Test.12.4 Kruskal–Wallis and Friedman Tests.13 Correlation and Regression.13.1 Linear Correlation.13.2 Statistics of Correlation and Regression.13.3 Uncertainty in Linear Calibration.14 Frequency and Proportion.14.1 Chi-squared Contingency Table.14.2 Goodness of Fit.14.3 Tests for Proportion.15 Experimental Design.15.1 Principal Techniques.15.2 Planning a Research Project.Appendix I: Microsoft Excel.Appendix II: Cumulative z -areas for Standard Normal Distribution.Appendix III: Critical Values: t -statistic and Chi-squared, χ2.Appendix IV: Critical F-values at 0.05 (95 %) Significance.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.Appendix VI: Mann–Whitney Lower Limit, UL, at 0.05 (95 %)Significance.Short Answers to ‘Q’ Questions.Index.