1. Introduction to statistics (week one)
Type of (RVs)
- Numeric (continuous, discrete)
- Categorical (ordinal, nominal)
- Working examples.
Analytical tools for numerical RVs
- Probability mass function
- Probability density function
- Working examples.
Graphical description of RVs
- Pie/bar charts
- Boxplot
- Histogram
- Scatter plot
- Working examples.
Population and sample statistics
- Mean
- Standard deviation
- Covariance/correlation
- Working examples.
Confidence intervals
- Quantiles
- Working examples.
2. Single-factor, single and two-treatment experiments (week two)
Gaussian distribution
- Central limit theorem
- Quantiles and confidence intervals.
Student-T distribution
- Quantiles and confidence intervals.
Single-treatment experiments
- Statistical model
- Single-sample T-test
- Assumptions
- Null hypothesis and upper, lower and two-tail alternative hypotheses
- Test statistic
- Test decision via p-values and rejection regions
- Working examples.
Two-treatment experiments
- Statistical model
- Two-independent-sample and two-sample -paired T-tests
- Assumptions
- Null hypothesis and upper, lower and two-tail alternative hypotheses
- Test statistic
- Test decision via p-values and rejection regions
- Working examples.
- Wilcoxon signed-rank test
- Test decision via p-values
- Working examples.
3. Single-factor, multi-treatment experiments (week three)
F-distribution
- Quantiles and confidence intervals.
Multi-treatment experiments
- Completely randomised designs
- Statistical model
- One-way ANOVA and F-test
- Decomposition of sum of squares
- Assumptions
- Null and alternative hypotheses
- Test decision via test statistic and region regions
- Working examples
- Kruskal-Wallis one-way ANOVA
- Null and alternative hypotheses (no assumptions)
- Null and alternative hypotheses (same shape and scale)
- Test decision via p-values
4. Two-factor experiments I (week four)
Two-factor experiments:
- Experimental and blocking factors
- Treatments, blocks and nuisance factors
- Complete factorial and completely randomised block design experiments
- Statistical model
- Two-way ANOVA and F-tests
- Decomposition of sum of squares
- Assumptions
- Null and alternative hypotheses
- Test decision via test statistic and region regions
- R^2
- Tukey post-hoc analysis
- Working examples.
Course delivery
This microcredential will be presented online and will run over four weeks. Each week will consist of a 2-hour lecture and 1.5-hour PC lab. Theoretical material will be presented in the lecture and students will work on practical problems during the PC labs using the R programming language.
To ensure maximum flexibility for participants working full time, the lectures and PC labs will be pre-recorded in MP4 screencast format for study at a suitable time.
