Statistics Course

Lesson 1 • Types of Data and Measurement Scales

Covers nominal, ordinal, interval, and ratio scales and their implications for analysis. Correct scale identification determines which methods are valid throughout the course.

Lesson 2 • Data Collection and Sampling Basics

Introduces populations, samples, and the logic of representative sampling. Proper collection methods prevent bias that would invalidate all downstream analysis.

Lesson 3 • What Statistics Is and Why It Matters

Defines statistics as a discipline and distinguishes descriptive from inferential goals. Anchors the chapter by framing every subsequent topic as a tool for reducing uncertainty.

Lesson 1 • Measures of Central Tendency

Covers mean, median, and mode with conditions favoring each measure. Understanding center is the first step toward comparing groups and detecting shifts.

Lesson 2 • Measures of Variability and Spread

Introduces range, variance, standard deviation, and IQR as complements to center. Spread quantifies uncertainty and is essential for every inferential technique ahead.

Lesson 3 • Shape, Skewness, and Kurtosis

Describes distributional shape through skewness and kurtosis statistics. Shape determines whether parametric assumptions hold in later inferential chapters.

Lesson 4 • Five-Number Summary and Box Plots

Builds the five-number summary and translates it into box plots for comparison. Box plots enable rapid visual comparison of multiple groups simultaneously.

Lesson 1 • Counting Techniques and Combinatorics

Covers permutations, combinations, and the multiplication principle for counting outcomes. Counting methods enable exact probability calculations for discrete sample spaces.

Lesson 2 • Addition and Multiplication Rules

Derives rules for unions and intersections of events, including mutually exclusive cases. These rules are the computational backbone of joint and marginal probabilities.

Lesson 3 • Conditional Probability and Bayes' Theorem

Formalizes how new information updates probability estimates via Bayes' theorem. Conditional reasoning is critical for diagnostic testing and Bayesian inference later.

Lesson 1 • Central Limit Theorem

Proves and demonstrates the CLT for sample means and proportions. The CLT justifies normal-based inference regardless of the original population's shape.

Lesson 2 • Other Key Continuous Distributions

Covers the uniform, exponential, and t-distributions and their use cases. Familiarity with these distributions prepares students for hypothesis testing and regression.

Lesson 3 • Binomial and Poisson Distributions

Derives and applies the binomial and Poisson models for count data. These two distributions cover the majority of discrete real-world scenarios professionals face.

Lesson 4 • Discrete Random Variables and Distributions

Defines random variables and probability mass functions for discrete outcomes. Discrete distributions model count data encountered in quality control and surveys.

Lesson 1 • Sample Size Determination

Derives formulas for minimum sample sizes given desired precision and confidence. Proper sizing prevents underpowered studies and wasteful data collection.

Lesson 2 • Point Estimation Principles

Defines estimators and desirable properties such as unbiasedness and efficiency. Understanding estimator quality prevents reliance on inferior summary statistics.

Lesson 3 • Confidence Intervals for Proportions

Derives the large-sample interval for a population proportion and checks validity conditions. Proportion intervals are essential for survey analysis and quality audits.

Lesson 4 • Confidence Intervals for Variance

Uses the chi-square distribution to build intervals for population variance and standard deviation. Variance intervals support process capability and risk assessment tasks.

Lesson 1 • Logic and Structure of Hypothesis Tests

Establishes null and alternative hypotheses, test statistics, and decision rules. This framework is the template for every specific test introduced in the chapter.

Lesson 2 • Tests for Proportions and Variances

Extends hypothesis testing to two-proportion z-tests and F-tests for variance equality. These tests support quality comparisons and pre-test assumption checking.

Lesson 3 • One-Sample Tests for Means and Proportions

Applies z-tests and t-tests to single-sample mean and proportion problems. One-sample tests are the simplest application of the hypothesis-testing framework.

Lesson 4 • Statistical Power and Effect Size

Quantifies the probability of detecting a true effect and measures practical significance. Power analysis prevents underpowered studies and over-reliance on p-values alone.

Lesson 1 • Regression Assumptions and Diagnostics

Checks linearity, independence, normality, and equal variance through residual analysis. Violated assumptions invalidate inference and must be addressed before reporting.

Lesson 2 • Simple Linear Regression

Derives the least-squares regression line and interprets slope and intercept. Simple regression is the foundation for all multivariate extensions in this chapter.

Lesson 3 • Multiple Linear Regression

Extends regression to multiple predictors and interprets partial regression coefficients. Multiple regression controls for confounders and improves predictive accuracy.

Lesson 4 • Model Selection and Validation

Applies variable selection strategies and cross-validation to build parsimonious models. Rigorous validation prevents overfitting and ensures generalizability of results.

Lesson 1 • One-Way ANOVA

Partitions total variance into between-group and within-group components to test mean equality. ANOVA extends the two-sample t-test to any number of groups simultaneously.

Lesson 2 • Chi-Square Test of Independence

Assesses association between two categorical variables in a contingency table. Independence tests are fundamental for survey analysis and categorical data modeling.

Lesson 3 • Post-Hoc Multiple Comparisons

Controls family-wise error rate using Tukey, Bonferroni, and related procedures after ANOVA. Post-hoc tests identify which specific group pairs differ after a significant F-test.

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

Tests whether observed categorical frequencies match a hypothesized distribution. Goodness-of-fit tests validate distributional assumptions used in other analyses.