Mathematical and statistical skills
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AS and A Level mathematical requirements
M.1—Prefixes, units, symbols and standard form
Use biological units and prefixes including G, M, k, m, micro and n; select appropriate units; use decimal and standard form; interpret symbols such as less than, greater than, less than or equal to, greater than or equal to, proportional to, solidus in units and sum notation.
M.2—Calculator use, estimations and significant figures
Use a calculator for arithmetic, squares, square roots, reciprocals, logarithms and means; estimate calculation results; record experimental data with appropriate precision; keep justified significant figures in calculated quantities.
M.3—Magnification, actual size and geometry
Calculate magnifications and actual sizes; calculate areas of triangles, rectangles and circles; calculate perimeters and circumferences; calculate surface areas and volumes of cuboids and cylinders.
M.4—Averages, ratios, percentages and experimental error
Calculate mean, median, mode and range; recognise and use ratios; calculate percentages and percentage changes; express errors in experimental work as percentage errors.
M.5—Graphs, data transformation and rates of change
Translate information between graphical, numerical and algebraic forms; construct and interpret line graphs, pie charts, bar charts and histograms; choose suitable graph types; orient and scale axes correctly; choose straight joins or best-fit lines; calculate rates of change from gradients and tangents.
A Level only mathematical and statistical requirements
M.6—Probability, sampling and chance
Relate genetic ratios to probabilities; understand sampling in biological situations and data; explain the importance of chance and probability when interpreting biological evidence.
M.7—Hardy-Weinberg, Lincoln index and Simpson diversity
Use Hardy-Weinberg equations for allele and genotype frequencies; use the Lincoln index to estimate population size from mark-release-recapture data; calculate Simpson’s index of diversity.
M.8—Distributions, descriptive statistics and error bars
Distinguish normal and non-normal distributions; use mean, median, mode, range, standard deviation, standard error and 95% confidence intervals; calculate sample standard deviation, standard error and 95% confidence intervals when formulae are provided; plot error bars using standard deviation, standard error or confidence intervals.
M.9—Chi-squared test and t-test
Calculate chi-squared and t-test results using provided formulae; calculate degrees of freedom without being given formulae; use critical values and probability tables to judge significance; connect statistical decisions to biological conclusions.
M.10—Correlation, causation, Pearson and Spearman
Explain the difference between correlation and causation; use Pearson’s linear correlation and Spearman’s rank correlation; understand correlation coefficients from -1 to +1; choose appropriate statistical tests and state conditions for their valid use.
A Level formula reference and statistics notes
Formula reference—Hardy-Weinberg equations
Use p + q = 1 and p^2 + 2pq + q^2 = 1, where p and q are allele frequencies and p^2, 2pq and q^2 are genotype frequencies. Formulae are provided in the examination when needed.
Formula reference—Lincoln index and Simpson diversity
Use the Lincoln index N = (n1 x n2) / m2 for mark-release-recapture estimates and Simpson’s index of diversity D = 1 - sum((n / N)^2) for biodiversity. Formulae are provided in the examination when needed.
Formula reference—Chi-squared, sample standard deviation, standard error and 95% CI
Use chi-squared = sum((O - E)^2 / E), sample standard deviation, standard error and 95% confidence interval formulae when provided; interpret the result rather than memorising the formula symbols only.
Formula reference—t-test, Pearson, Spearman and degrees of freedom
Use provided formulae for t-test, Pearson’s linear correlation and Spearman’s rank correlation; know how to calculate degrees of freedom for chi-squared and t-tests; judge significance using critical values.
Statistics notes—Choosing valid statistical methods
Know when chi-squared, t-test, Pearson’s linear correlation and Spearman’s rank correlation are appropriate; connect data type, distribution, independence, sample size and correlation pattern to the choice of method.