Lectures

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  1. Thinking Statistically

  In our introductory lecture, Professor Leonard presents the fundamentals of statistics, emphasizing that it focuses on understanding and interpreting data to make informed decisions. Key topics include populations and samples, parameters and statistics, descriptive and inferential statistics, data types, measurement levels, and proper data collection. He also discusses observational studies, experiments, statistical integrity, and why correlation does not imply causation. The lecture concludes with an introduction to JASP, the statistical software used throughout the course.
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  2. Describing & Summarizing Data

  In lecture two, we learn to describe and summarize data using measures of center, including the mean, median, and mode, while distinguishing between population parameters and sample statistics. We examine frequency distributions, bar charts, histograms, and scatterplots using JASP and Microsoft Excel, learning that histograms are used for continuous data, while bar charts are used for categorical or discrete data. The lecture concludes with trend lines for prediction and the importance of avoiding misleading graphs, such as truncated axes and deceptive 3D graphics.
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  3. Understanding Data Spread

  In lecture three, we explore measures of spread, including range, variance, standard deviation, and coefficient of variation. We learn to interpret box plots, five-number summaries, outliers, and skewness. The lecture also introduces the empirical rule for normal distributions and z-scores, which show how many standard deviations a value is from the mean and provide a foundation for understanding probability distributions and hypothesis testing.
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  4. Random Variables & Probability

  In lecture four, we explore the fundamentals of random variables and probability distributions, distinguishing between discrete and continuous distributions. We cover expected value, Bernoulli trials, and discrete distributions such as binomial, geometric, and hypergeometric, using practical examples like casino games, water bottle flipping, and poker hands in Microsoft Excel. The lecture concludes by introducing the concept of sampling distributions and previewing how discrete probability distributions will serve as the foundation for understanding continuous probability distributions in subsequent lectures.
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  5. Continuous Probability Distributions

  In lecture five, we transition from discrete to continuous probability distributions, exploring how both are used to find probabilities for their respective random variables. We cover the Poisson distribution as our final discrete example before introducing the normal distribution and explaining how z-scores standardize different normal curves. The lecture concludes with practical applications using JASP to find probabilities and percentiles, while previewing sampling distributions and the central limit theorem.
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  6. Sampling & Statistical Inference

  In lecture six, we study sampling methods and the central limit theorem, focusing on how properly collected random samples allow us to make reliable inferences about populations. We examine techniques such as stratified, cluster, and systematic sampling, while also discussing common sources of bias. The lecture concludes by showing how sampling distributions of sample means center around population parameters, providing the foundation for confidence intervals and hypothesis testing in future lectures.
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  7. Confidence Intervals

  In lecture seven, we explore confidence intervals for estimating population parameters, focusing on the population mean using sample statistics. We learn how 90%, 95%, and 99% confidence intervals provide ranges for the true population parameter, with the margin of error determined by critical z-scores or t-scores. The lecture also introduces the Student’s t distribution, used when the population standard deviation is unknown, and demonstrates constructing confidence intervals with JASP.
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  8. Confidence, Proportions, and Variance

  In our eighth and final lecture, we construct confidence intervals for population proportions and variance. We examine how binomial distributions can be approximated by normal distributions, allowing us to use z-scores to create confidence intervals for proportions, a technique widely used in polls and surveys. We also explore determining sample sizes for desired margins of error. The lecture concludes with the chi-squared distribution for estimating population variance and standard deviation, highlighting how it differs from normal and t-distributions and demonstrating how statistical software can efficiently construct these confidence intervals.