StatisticsQ&A by dot point

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.