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Mathematical and statistical skills

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  1. AS and A Level mathematical requirements

    1. 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.

    2. 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.

    3. 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.

    4. Calculate mean, median, mode and range; recognise and use ratios; calculate percentages and percentage changes; express errors in experimental work as percentage errors.

    5. 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.

  2. A Level only mathematical and statistical requirements

    1. Relate genetic ratios to probabilities; understand sampling in biological situations and data; explain the importance of chance and probability when interpreting biological evidence.

    2. 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.

    3. 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.

    4. 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.

    5. 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.

  3. A Level formula reference and statistics notes

    1. 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.

    2. 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.

    3. 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.

    4. 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.

    5. 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.