Essential Mathematics and Statistics for Science, 2nd Edition

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, 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