Statistics Applied to Education Course

Lesson 1 • Role of Statistics in Education

Statistics drives evidence-based decisions in schools and policy. This section frames why quantitative reasoning is essential for educators and researchers.

Lesson 2 • Organising and Displaying Data

Raw data must be structured before analysis. Students construct frequency tables, histograms, and stem-and-leaf plots from student performance data.

Lesson 3 • Types of Variables and Scales

Variable classification determines which analyses are valid. Students categorise nominal, ordinal, interval, and ratio data from real classroom examples.

Lesson 1 • Percentiles and the Normal Distribution

Percentile ranks contextualise individual scores within a group. Students apply normal distribution properties to interpret standardised assessment results.

Lesson 2 • Describing and Reporting Data

Effective reporting translates statistics into actionable insights for stakeholders. Students draft descriptive summaries suitable for teachers, parents, and administrators.

Lesson 3 • Measures of Variability

Variability reveals how spread out student scores are around the centre. Students calculate range, variance, and standard deviation for classroom datasets.

Lesson 4 • Measures of Central Tendency

Mean, median, and mode each capture a different aspect of typical performance. Students compute and compare these measures using test score distributions.

Lesson 1 • Probability Distributions

Discrete and continuous distributions model different types of educational data. Students work with binomial and normal distributions in assessment contexts.

Lesson 2 • Sampling and Sampling Error

Samples differ from populations due to random variation. Students distinguish sampling error from bias and evaluate sample representativeness.

Lesson 3 • Sampling Distributions and Standard Error

The sampling distribution of the mean is central to inference. Students simulate and interpret sampling distributions to understand standard error.

Lesson 1 • p-Values and Statistical Significance

The p-value measures evidence against the null hypothesis. Students interpret p-values correctly and distinguish statistical from practical significance.

Lesson 2 • One-Sample Tests

One-sample tests compare a group mean to a known standard. Students conduct z-tests and t-tests to evaluate school performance benchmarks.

Lesson 3 • Effect Size and Power

Effect size quantifies the magnitude of educational differences beyond significance. Students calculate Cohen's d and conduct basic power analyses.

Lesson 4 • Logic of Hypothesis Testing

Hypothesis testing formalises decision-making under uncertainty. Students formulate null and alternative hypotheses for realistic educational scenarios.

Lesson 1 • One-Way ANOVA

Extends group comparison to three or more independent groups simultaneously. Students partition variance and interpret the F-ratio in educational studies.

Lesson 2 • Non-Parametric Alternatives

Ordinal or non-normal data require distribution-free tests. Students apply Mann-Whitney U and Kruskal-Wallis tests as alternatives to t-tests and ANOVA.

Lesson 3 • Paired Samples t-Test

Analyses pre-test and post-test differences within the same group of students. Students apply the paired t-test to measure instructional impact.

Lesson 4 • Post-Hoc Tests and Multiple Comparisons

Significant ANOVA results require follow-up to identify differing pairs. Students apply Tukey and Bonferroni corrections to control familywise error.

Lesson 1 • Scatterplots and Linear Relationships

Visual inspection of scatterplots reveals direction, form, and strength of association. Students create and annotate scatterplots from student performance data.

Lesson 2 • Pearson Correlation Coefficient

Pearson's r measures the strength of linear association between two continuous variables. Students compute r, test its significance, and interpret its magnitude.

Lesson 3 • Regression Assumptions and Diagnostics

Valid regression inference requires meeting linearity, independence, and homoscedasticity assumptions. Students diagnose violations using residual plots.

Lesson 4 • Simple Linear Regression

Regression models predict one educational outcome from a single predictor. Students derive the least-squares line and evaluate model fit.

Lesson 1 • Model Building Strategies

Predictor selection affects model validity and interpretability. Students compare simultaneous, hierarchical, and stepwise entry methods for educational research.

Lesson 2 • Introduction to Multiple Regression

Multiple regression controls for confounds while estimating each predictor's unique contribution. Students extend simple regression logic to multivariate educational data.

Lesson 3 • Multicollinearity and Model Diagnostics

Highly correlated predictors distort regression estimates. Students detect multicollinearity using VIF and tolerance statistics and apply remedies.

Lesson 4 • Interpreting and Reporting Regression Results

Clear reporting of regression findings supports replication and policy use. Students write results sections including tables, effect sizes, and model comparisons.

Lesson 1 • Introduction to Multilevel Modeling

Students are nested within classrooms and schools, violating independence assumptions. Students recognise when multilevel models are needed and interpret basic two-level output.

Lesson 2 • Selecting and Justifying Statistical Methods

Choosing the right method requires matching research questions, data types, and assumptions. Students build decision frameworks for selecting analyses in educational studies.

Lesson 3 • Chi-Square Tests for Categorical Data

Chi-square tests evaluate relationships among categorical educational variables. Students apply goodness-of-fit and independence tests to enrolment and outcome data.

Lesson 4 • Repeated Measures ANOVA

Repeated measures designs track the same students across multiple time points. Students apply within-subjects ANOVA to longitudinal achievement data.