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Quantitative
Descriptive and summary statistics: measures of central tendency and dispersion; skew and kurtosis; frequency distributions; graphical methods including frequency histograms and cumulative frequency plots; exploratory data analysis including stem and leaf and box and whisker displays. Probability theory: rules for assigning and combining probabilities; the OR rule with mutually exclusive and non-mutually exclusive events; the AND rule with independent and non-independent events; the binomial distribution (and its normal approximation). The normal distribution: z scores and areas under the curve; the sampling distribution of the sample mean. Statistical inference: significance testing (including the null and alternative hypothesis, type 1 and type 2 errors, significance level, power and sample size); effect size and confidence intervals. Z-tests and t-tests of means for single sample, independent samples and related samples designs. Confidence intervals: for the population mean; for the difference between two population means. Mean and error bar graphs. Non-parametric alternatives to t-tests: the sign test; Wilcoxon matched-pairs signed ranks test; Mann-Whitney test. Tests of proportions: chi-squared tests for goodness of fit and for contingency tables. Cramer’s Phi as a measure of association in contingency tables. McNemar’s test of change. Bivariate correlation and linear regression: scatterplots; Pearson’s correlation coefficient; partial correlation; the significance of a correlation coefficient; the linear regression equation and its use in prediction; the accuracy of prediction; Spearman’s and Kendall’s rank order correlation coefficients. The analysis of variance: one factor independent and repeated measures designs; two factor independent, repeated measures and mixed designs; main effects and interaction effects (including graphical presentation); planned (including trend) comparisons; the Bonferroni correction; post hoc comparisons (including the choice between methods); the analysis of simple effects. Non-parametric alternatives to one factor analyses of variance: Kruskal-Wallis, Friedman and Cochran’s Q tests. The choice of an appropriate statistical analysis: the issue of level of measurement (nominal, ordinal, interval and ratio scales); test assumptions (e.g. normality, homogeneity of variance, linearity); transformations of the dependent variable in an attempt to meet assumptions; robustness; power efficiency.
- Practicals (1): A practical in this context is a learning and teaching resource that can be used for instructional purposes within a Higher Education environment. Practicals on this site have been collected from academics who use them regularly within their own teaching. Practicals
- Tutorials (44): A tutorial is a document, software, or other media created for the purpose of instruction for any of a wide variety of tasks. Tutorials usually have the following characteristics:
- A presentation of content, usually with an example or examples, often broken up into discrete modules or sections.
- Some method of review that reinforces or tests understanding of the content in the related module or section.
- A transition to additional modules or sections that builds on the instructions already provided. Tutorials can be linear or branching. Tutorials
- Demos (26): A demo generally sheds light on how to do something. Demos on this site include video-based instruction. Demos
- Other (14): Other quantitative resources. Other
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