# Statistics

## A Level Statistics Edexcel

### Specification link A level Statistics

Year 1 Statistics

Numerical Measures: Measures of location, measures of spread, outliers and scaling, comparing distributions, suitability of numerical measures. Probability Theory: Venn diagrams and set notation, 2-way tables, tree diagrams, mutually exclusive and independent events, conditional probability.
Data Representation and Interpretation: Reading and interpreting statistical diagrams, misrepresentation and the suitability of statistical diagrams, spreadsheets and databases. Normal Distribution: Calculation of probabilities, inverse normal, finding µ, σ or both, distribution of the sample mean, binomial to normal approximation.
Discrete Random Variables: Tabulating probabilities, mean, median, mode, variance, standard deviation.

Sampling Methods: Simple Random, Stratified, Systematic, Cluster, Convenience, Snowball Suitability of Sampling Methods

Binomial Distribution: Calculation of probabilities, mean, variance, suitability of binomial model, comparing distributions. Bivariate Data: Product Moment and Spearman’s Rank Correlation Coefficient, Regression Line, Hypothesis Testing for PMCC and Spearman’s rank.
Contingency Tables: Calculation of expected values and hypothesis test for independence. Hypothesis Testing: For population mean µ, for binomial proportion p.
Statistical Enquiry Cycle: to include initial planning, data collection, data processing and presentation,  interpretation of results, evaluation and review. Non parametric Hypothesis Tests: Single and paired sample sign test, single and paired sample Wilcoxon Test, Wilcoxon Rank Sum Test.

### Year 3 Statistics

Poisson: Calculation of probabilities, mean, variance, suitability of poisson model, sum of 2 poisson distributions. Linear Combinations of Normal Variables: Adding and subtracting normal variables, multiplying normal variables by a constant.
Confidence Intervals and Hypothesis Tests for population mean µ: to include z and t distribution and central limit theorem. Concepts in Hypothesis Testing: Type I and type II errors, critical regions for normal and proportion, calculating type II errors and power of test.
Rectangular and Exponential Distributions: Calculation of probabilities, mean, variance. Hypothesis Tests between two parameters: difference between two population means (z and t), difference between two population proportions
Goodness of Fit: Ratio, proportion, binomial, poisson, normal, exponential Bayes Theorem: Extension of conditional probability from year 1.
Experimental Design: Terminology and paired t test. ANOVA: 1 factor and 2 factor, effect size, cohen’s d.