Scotland Β· SQASyllabus
Statistics syllabus, dot point by dot point
Every dot point in the Scotland Statisticssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Data Analysis and Modelling
Module overview β- How do you measure and model the linear relationship between two variables?Analyse bivariate data using scatter plots, the sums of squares and products, the product-moment correlation coefficient, and the least-squares regression line, and assess the model with residual plots and the limitations of extrapolation.13 min answer β
- How do you model a continuous measurement, and how do you find probabilities from a normal distribution?Work with continuous random variables and the normal distribution, standardise to find probabilities, combine independent normal variables, and use the normal approximation to the binomial and Poisson distributions with a continuity correction.13 min answer β
- How do you model a count with a discrete random variable and find its expected value and variance?Work with discrete probability distributions, calculate the expectation and variance of a discrete random variable and apply the laws of expectation and variance, and use the binomial, Poisson and geometric distributions as models.13 min answer β
- How do you design a study and collect data so that the conclusions you draw are valid and free from bias?Describe the principles of experimental design, distinguish observational studies from designed experiments, identify sources of bias, and explain control, randomisation, replication and blocking when planning data collection.11 min answer β
- How do you summarise and display a data set so its centre, spread and shape are clear?Calculate and interpret measures of location and dispersion, including the mean, median, quartiles, interquartile range, variance and standard deviation, and use stem-and-leaf plots, boxplots and measures of skewness to describe the shape of a distribution.12 min answer β
- How do you calculate probabilities for combined, conditional and independent events?Apply the addition and multiplication laws of probability, calculate conditional probabilities and use tree diagrams, the total probability rule and Bayes' theorem, and test events for independence and mutual exclusivity.12 min answer β
Hypothesis Testing
Module overview β- How do you test whether categorical data fit a model or whether two categorical variables are associated?Carry out the chi-squared goodness-of-fit test and the chi-squared test for association in a contingency table, computing expected frequencies, the chi-squared statistic and degrees of freedom, and interpreting the result against the assumptions.13 min answer β
- How do you set up a hypothesis test and decide whether to reject the null hypothesis?Set up null and alternative hypotheses, choose a significance level, compute and use a test statistic and p-value, decide between one- and two-tailed tests, identify the critical region, and distinguish Type I and Type II errors.12 min answer β
- How do you test for a difference when the data are not normal or are ranks?Carry out the main non-parametric tests, including the Mann-Whitney U test for two independent samples and the Wilcoxon signed-rank test for paired or single samples, explaining when a non-parametric test is preferred over a t-test.13 min answer β
- How do you test a claim about a population proportion, or compare two proportions?Carry out hypothesis tests for a single population proportion and for the difference between two proportions, using the normal approximation, stating the hypotheses, computing the test statistic and interpreting the result.12 min answer β
- How do you test claims about one or two population means when the standard deviation is unknown?Carry out the one-sample, two-sample (independent) and paired t-tests for population means, stating the hypotheses, computing the test statistic, using degrees of freedom, and interpreting the result, while checking the normality assumption.13 min answer β
Statistical Inference
Module overview β- How do you estimate a population mean from a sample and express how confident you are?Calculate point estimates of a population mean and variance, construct and interpret confidence intervals for a population mean using the normal and Student's t-distributions, and construct a confidence interval for a population proportion.13 min answer β
- How does the sample mean vary from sample to sample, and why is it approximately normal?Describe the sampling distribution of the sample mean, calculate its mean and standard error, and state and apply the central limit theorem to find probabilities for a sample mean.12 min answer β
- How do you choose a representative sample from a population, and why does the method matter?Describe and apply the main sampling methods, including simple random, systematic and stratified sampling, distinguish a sample from a population and a statistic from a parameter, and explain how a poor sampling method introduces bias.11 min answer β
- How do you plan, carry out and communicate a complete statistical investigation?Conduct a statistical investigation that draws together the skills of the course: pose a question, plan and collect data, select and apply appropriate analysis, and communicate justified conclusions with their limitations.10 min answer β