AS Statistics

Introduction Key to symbols in this book Z1 Unit 1 1 Exploring data Looking at the data Stem-and-leaf diagrams Categorical or qualitative data Numerical or quantitative data Measures of central tendancy Frequency distributions Grouped data Measures of spread Linear coding 2 Data presentation and related measures of centre and spread Bar charts and vertical line charts Pie charts Histograms Measures of central tendancy and of spread using quartiles Cumulative frequency curves 3 Probability Measuring probability Estimating probability Expectation The probability of either one event or another The probability of events from two trials Conditional probability 4 Discrete random variables Discrete random variables Expectation and variance 5 Further probability Factorials Permutations Combinations The bonomial coefficients, nCr Calculating probabilities in less simple cases 6 The binomial distribution The binomial distribution The expectation of B(n, p) Using the binomial distribution Does the binomial distribution really work? 7 Hypothesis testing using the binomial distribution Defining terms Hypothesis testing checklist Choosing the significance level Critical values and critical regions 1-tailed and 2-tailed tests Asymmetrical cases Z2 Unit 2 8 The Poisson distribution Conditions for modelling data with a Poisson distribution The sum of two or more Poisson distributions The Poisson approximation to the binomial distribution 9 The Normal distribution The key features of a Normal distribution The sum and difference of Normal variables 10 The chi-squared test The X2 test for association Degrees of freedom Goodness of fit tests 11 Using the Normal distribution to interpret sample data A hypothesis test for the mean using the Normal distribution Confidence intervals for a population mean 12 Small samples and the t distribution The t distribution Confidence intervals from small samples 13 The Wilcoxon signed rank test The Wilcoxon signed rank test for a single sample Z3 Unit 3 14 Sampling and experimental design Sampling Experiments and surveys Sampling methods Experimental design Design of experiments 15 Hypothesis tests on paired samples Paired and unpaired experiments The paired-sample t test The Wilcoxon signed rank test for paired samples 16 Hypothesis tests on unpaired samples Selecting the appropriate test for unpaired samples The Normal test for unpaired samples The t test for unpaired samples The Wilcoxon rank sum test 17 Correlation Bivariate data Interpreting scatter diagrams Pearson's product moment correlation coefficient The meaning of a sample correlation coefficient Interpreting correlation Rank correlation Spearman's rank correlation coefficient Appendices 1 The derivation of the alternative form of the sum of squares, Sxx 2 The binomial theorem Answers Index