Essential Mathematics and Statistics for Science

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, chi 2 . 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, r S , and Wilcoxon Lower Limit, W L . Appendix VI: Mann-Whitney Lower Limit, U L , at 0.05 (95 #)Significance. Short Answers to 'Q' Questions. Index.