Introduction to Statistics Course

Lesson 1 • Populations, Samples, and Variables

Introduces the population-sample distinction and variable classification. Connects proper variable identification to choosing correct analytical methods.

Lesson 2 • Data Collection and Sampling Methods

Explains probability and non-probability sampling strategies and their trade-offs. Connects sampling design to the validity of statistical conclusions.

Lesson 3 • Levels of Measurement

Covers nominal, ordinal, interval, and ratio scales and their analytical implications. Guides students in matching measurement level to appropriate statistical tools.

Lesson 4 • Introduction to Statistical Software

Orients students to common statistical tools and data entry conventions. Prepares learners to execute calculations and organize datasets throughout the course.

Lesson 1 • Frequency Distributions and Tables

Constructs frequency, relative frequency, and cumulative frequency tables. Provides the tabular foundation for all graphical displays covered in this chapter.

Lesson 2 • Graphical Displays for Categorical Data

Covers bar charts, pie charts, and Pareto charts for categorical variables. Teaches selection criteria based on the communication goal and audience.

Lesson 3 • Measures of Variability

Quantifies spread using range, variance, standard deviation, and IQR. Establishes variability concepts essential for probability and inference in later chapters.

Lesson 4 • Graphical Displays for Quantitative Data

Introduces histograms, stem-and-leaf plots, and box plots for numeric data. Links graph shape to distributional properties explored in later chapters.

Lesson 5 • Measures of Central Tendency

Defines mean, median, and mode and explains when each measure is most appropriate. Connects central tendency to the shape of distributions introduced graphically.

Lesson 1 • Introduction to Random Variables

Defines discrete and continuous random variables and their probability distributions. Bridges probability theory to the distribution models covered in the next chapter.

Lesson 2 • Basic Probability Concepts

Defines experiments, sample spaces, and events using set notation. Grounds all subsequent probability rules in a consistent formal framework.

Lesson 3 • Addition and Multiplication Rules

Derives rules for union and intersection of events, including mutually exclusive cases. Enables students to compute compound event probabilities accurately.

Lesson 4 • Counting Techniques

Covers permutations, combinations, and the fundamental counting principle. Supports probability calculations involving large or complex sample spaces.

Lesson 1 • Poisson Distribution

Models rare events occurring over time or space using the Poisson formula. Connects to binomial as a limiting case and supports quality-control applications.

Lesson 2 • Binomial Distribution

Derives the binomial formula from Bernoulli trials and identifies its conditions. Enables probability calculations for fixed-trial, two-outcome scenarios.

Lesson 3 • Normal Distribution Applications

Applies Z-score transformations to find probabilities and percentiles for real data. Reinforces normal distribution mechanics before sampling distributions are introduced.

Lesson 4 • Other Useful Distributions

Surveys uniform, exponential, and t-distributions and their practical contexts. Prepares students to recognize which model fits a given inferential scenario.

Lesson 1 • Concept of a Sampling Distribution

Defines the sampling distribution of a statistic through simulation and theory. Distinguishes sample-to-sample variability from within-sample variability.

Lesson 2 • Central Limit Theorem

States and demonstrates the CLT for non-normal populations with sufficient sample size. Justifies the use of normal-based inference across diverse real-world datasets.

Lesson 3 • Sampling Distribution of the Mean

Derives the mean and standard error of the sample mean for any population. Provides the theoretical basis for confidence intervals and hypothesis tests.

Lesson 4 • Sampling Distribution of a Proportion

Extends sampling distribution logic to categorical outcomes and sample proportions. Prepares students for proportion-based confidence intervals and hypothesis tests.

Lesson 1 • Confidence Intervals for a Mean (Unknown Variance)

Applies the t-distribution when population variance is unknown and samples are small. Connects t-distribution degrees of freedom to interval width.

Lesson 2 • Confidence Intervals for a Proportion

Derives proportion confidence intervals using the normal approximation. Addresses conditions for validity and the Wilson interval as an alternative.

Lesson 3 • Confidence Intervals for a Mean (Known Variance)

Builds Z-based confidence intervals when population variance is known. Introduces margin of error and the interpretation of confidence level.

Lesson 4 • Point Estimation Principles

Defines estimators and desirable properties such as unbiasedness and efficiency. Establishes why point estimates alone are insufficient for decision-making.

Lesson 1 • Logic and Structure of Hypothesis Testing

Explains null and alternative hypotheses, Type I and II errors, and significance levels. Establishes the decision framework used in all subsequent testing procedures.

Lesson 2 • Z-Tests for Means and Proportions

Applies Z-tests to large-sample mean and proportion hypotheses using the p-value approach. Reinforces the connection between confidence intervals and hypothesis tests.

Lesson 3 • Chi-Square Tests

Uses chi-square statistics for goodness-of-fit and tests of independence in tables. Extends hypothesis testing to categorical data beyond proportions.

Lesson 4 • T-Tests for Small Samples

Conducts one-sample and two-sample t-tests when population variance is unknown. Covers assumptions of normality and equal variance for two-sample cases.

Lesson 1 • Simple Linear Regression

Derives the least-squares regression line and interprets slope and intercept. Connects regression to correlation and introduces prediction using the fitted model.

Lesson 2 • Inference in Simple Linear Regression

Tests the significance of the slope and constructs confidence and prediction intervals. Integrates hypothesis testing and estimation into the regression context.

Lesson 3 • Scatter Plots and Correlation

Visualizes bivariate relationships and quantifies linear association with Pearson's r. Establishes the graphical and numerical foundation for regression modeling.

Lesson 4 • Introduction to Multiple Regression

Extends simple regression to multiple predictors and interprets partial coefficients. Introduces adjusted R-squared and multicollinearity as key model evaluation concerns.