
Brief Overview
Randomized experiments isolate treatment effects in a migraine study example, using random assignment, placebo control, and double blinding to average out confounding factors and assess efficacy.
Explore a multicenter, blind, placebo-controlled randomized trial of hydroxychloroquine for covid-19, showing no day-14 improvement, and analyze randomization checks, p-values, and statistical thinking about sample versus population.
Define probability and explain its role in statistics, focusing on conditional probability and hypothesis testing, including p-values, with examples from coin tosses and diastolic blood pressure data.
Explore conditional probability through a blood pressure and cholesterol example, computing intersection and conditional probabilities, assessing independence, and applying Bayes rule concepts.
Learn the normal distribution and standard normal concepts, apply the empirical rule (68% within one standard deviation, 95% within two), compute z-scores, and interpret probabilities from heights data.
Explore ggplot in R to create bar charts, histograms, box plots, and scatter plots using the Nhanes data, with aesthetic mappings and bin width adjustments.
Explore sample proportions, election polling, and coin-toss examples, and learn how the sampling distribution, central limit theorem, and standard error describe variation around population parameters.
Explore how sample means of height approximate a normal distribution around the population mean, using standard error and varying sample sizes to illustrate the central limit theorem for height data.
Construct a 95% confidence interval for the population mean cholesterol using a heart disease data example, applying the sampling distribution, standard error, and t-distribution considerations.
Explore how to estimate population proportions using composites for the National Youth Fitness Survey and election polling, constructing confidence intervals from sample proportions and standard errors.
Test hypothesis on population proportion using a coin toss, starting from the null hypothesis toward the alternative and using the p-value and 0.05 significance level to reject the null.
Explore type one and type two errors, power, and sample size in hypothesis testing. Learn to set population effect sizes and alpha levels, and interpret uncertainty about null and alternative.
Compute confidence intervals and perform a model utility test for the population slope of the line of best fit, using National Youth Fitness Survey data on BMI and met scores.
Explore running a simple linear regression in R with ggplot and pipe syntax, using height to predict weight from NHANES data, including residuals and outlier handling.
Analyze the vioxx study's reported relative risk of heart attack versus naproxen, the questionable reporting and Merck's role, and relate to OxyContin and the opioid crisis.
Course Description
This is a university level course taught by a professor with 16 years of teaching experience at Columbia University and other institutions including New York University, Yale University, and Berkeley. Providing the broader audience with the opportunity to truly understand important statistical concepts at the foundation is what motivates me to keep teaching this material.
It is a clear and concise version of my Columbia University course titled “Introduction to Statistical Reasoning”. It is the companion course to the third edition of my book “Statistical Thinking through Media Examples” published by Cognella. You can preview and purchase my book from their website (google book title) .
My course and book provides you with the statistical intuition and understanding you need, through media, research, and real-world data examples. I communicate the statistical concepts in my course and book in a language you will understand with a minimum of calculations. You will learn to go beyond the news headlines to critique the quality of the research for yourself, including polls and surveys. You will learn how to conduct statistical analysis and how to interpret the results.
With a solid foundational understanding of statistics, you can build on that foundation with confidence. You can become a statistical analyst or data scientist with the statistical intuition to properly conduct research and interpret the results. Join me and start building that necessary foundation today!