Inferential Statistics Course

Lesson 1 • Sampling Distributions Explained

Introduces the sampling distribution as the bridge between sample statistics and population parameters. Demonstrates how repeated sampling produces predictable distributional patterns.

Lesson 2 • Types of Error and Uncertainty

Distinguishes sampling error, non-sampling error, and bias. Prepares students to evaluate the quality of inferences before applying formal tests.

Lesson 3 • Probability Review for Inference

Reviews essential probability rules needed to interpret inferential results. Connects probability theory directly to uncertainty quantification in estimation.

Lesson 4 • Populations, Samples, and Parameters

Defines population, sample, parameter, and statistic with concrete examples. Establishes the vocabulary used throughout all subsequent inferential methods.

Lesson 1 • Point Estimation Principles

Covers properties of good estimators: unbiasedness, consistency, and efficiency. Grounds interval estimation in the logic of point estimation.

Lesson 2 • Sample Size Determination

Derives formulas for choosing sample size to achieve desired margin of error. Applies calculations to means and proportions in planning contexts.

Lesson 3 • Interpreting Confidence Level and Width

Clarifies the frequentist meaning of confidence level and factors affecting interval width. Corrects common misinterpretations that undermine valid inference.

Lesson 4 • Confidence Intervals for Means

Constructs z-based and t-based confidence intervals for population means. Addresses when to use each distribution based on sample size and known variance.

Lesson 1 • Type I and Type II Errors

Distinguishes false positives and false negatives and their consequences. Quantifies alpha, beta, and the power of a test.

Lesson 2 • Null and Alternative Hypotheses

Formulates null and alternative hypotheses for one- and two-tailed tests. Connects hypothesis structure to the research question being investigated.

Lesson 3 • Statistical Power Analysis

Calculates power as a function of effect size, sample size, and alpha. Enables students to design studies with adequate power before data collection.

Lesson 4 • p-Values: Calculation and Meaning

Defines the p-value as the probability of observing results at least as extreme under the null. Teaches correct calculation for z- and t-tests.

Lesson 1 • Paired-Sample t-Test

Analyses matched or repeated-measures data using the paired t-test. Explains when pairing increases power relative to independent-samples designs.

Lesson 2 • Assumption Verification and Remedies

Systematically checks normality, independence, and variance assumptions for all t-tests. Introduces nonparametric alternatives when assumptions are violated.

Lesson 3 • One-Sample z-Test and t-Test

Executes one-sample tests for means under known and unknown variance conditions. Reinforces assumption checking before test execution.

Lesson 4 • Independent Two-Sample t-Tests

Compares means from two independent groups using pooled and Welch t-tests. Teaches the equal-variance assumption test and its implications.

Lesson 1 • ANOVA Assumption Checks and Alternatives

Tests homogeneity of variance and normality within ANOVA contexts. Introduces Welch ANOVA and Kruskal-Wallis as robust alternatives.

Lesson 2 • Post-Hoc Multiple Comparison Tests

Applies Tukey, Bonferroni, and Scheffé corrections to control familywise error. Selects the appropriate post-hoc method based on study design.

Lesson 3 • Two-Way ANOVA and Interaction Effects

Extends ANOVA to two factors and tests main effects and their interaction. Interprets interaction plots to understand conditional group differences.

Lesson 4 • One-Way ANOVA Logic and Setup

Decomposes total variance into between-group and within-group components. Establishes the F-ratio as the test statistic for group mean equality.

Lesson 1 • McNemar's Test for Paired Proportions

Tests change in proportions for matched or repeated categorical data. Distinguishes McNemar's test from the standard chi-square independence test.

Lesson 2 • Measures of Association for Categorical Data

Quantifies the strength of association beyond statistical significance. Applies Cramér's V, phi coefficient, and odds ratios to contingency tables.

Lesson 3 • Chi-Square Test of Independence

Evaluates whether two categorical variables are statistically independent in a contingency table. Constructs and interprets two-way frequency tables.

Lesson 4 • Chi-Square Goodness-of-Fit Test

Tests whether observed frequencies match a hypothesised distribution. Calculates expected frequencies and the chi-square statistic from categorical data.

Lesson 1 • Prediction and Model Evaluation

Generates point predictions and prediction intervals from the fitted model. Evaluates model quality using R², RMSE, and residual standard error.

Lesson 2 • Pearson Correlation Coefficient

Measures the strength and direction of linear association between two continuous variables. Tests the significance of the correlation and interprets its magnitude.

Lesson 3 • Regression Diagnostics

Evaluates linearity, homoscedasticity, normality of residuals, and independence. Identifies influential observations using leverage and Cook's distance.

Lesson 4 • Inference for Regression Coefficients

Constructs confidence intervals and hypothesis tests for slope and intercept. Uses the t-distribution to assess coefficient significance.

Lesson 1 • Model Selection Strategies

Compares stepwise, best-subset, and theory-driven model selection approaches. Evaluates models using AIC, BIC, and cross-validation criteria.

Lesson 2 • Multiple Linear Regression Fundamentals

Adds multiple predictors to the regression model and interprets partial slopes. Distinguishes marginal from conditional effects of each predictor.

Lesson 3 • Multicollinearity Detection and Remedies

Identifies multicollinearity using VIF and condition indices and explains its effects on inference. Applies centering, ridge regression, and variable removal as remedies.

Lesson 4 • Logistic Regression for Binary Outcomes

Models binary outcomes using logistic regression and interprets log-odds and odds ratios. Tests model fit with the Hosmer-Lemeshow test and likelihood ratio test.