Statistical Thinking for Data Analysis

Explore data types of variables and datasets, including categorical and quantitative, nominal and ordinal, discrete and continuous, and learn how sample statistics estimate population parameters using random versus convenient sampling.

Explore how small samples, confounding factors, and convenient samples affect conclusions from observational studies on the MMR vaccine and Covid testing, emphasizing data quality and garbage in, garbage out.

Load the Nhanes CSV into a data frame, subset to adults, and use tidyverse pipes to select education, race, gender, and income for exploratory analysis.

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 hospital example, visualize relationships with a Venn diagram, and learn the rule P(B|A) = P(A∩B)/P(A) while distinguishing independence and disjoint events.

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.

Explore how sample means follow a normal sampling distribution under the central limit theorem, using pregnancy duration to compute z-scores and a 64-woman sample's probability of exceeding 270 days.

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.

Compute hypothesis tests for population means using height and cholesterol data, interpret p values, and decide to reject or fail to reject the null at 0.05.

Explore what the p value really means in hypothesis testing, including type I error, significance levels, and reporting exact p values alongside confidence intervals for the population parameter.

Compare mean differences in hippocampal volume across three group comparisons (controls, players with concussion, players without concussion) using Cohen's d, p values, and 95% confidence intervals.

Apply a chi-square test of independence on a two-by-two table to compare proportions, interpret p-values, and assess association between gender and breathlessness in the National Youth Fitness Survey.

Compare proportions in a two-by-two table by examining the power pose study: high vs low power poses influence gambling risk, with 86% vs 60% and a near-significant p-value under 0.05.

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.

Explore how researchers plan hypothesis tests by balancing Type I and Type II errors, selecting effect sizes, significance levels, and power to determine sample size, illustrated with mask and hydroxychloroquine studies.

Learn to perform a two-group means comparison in R using t.test, evaluate sample sizes, means, and sds, and interpret the 95% confidence interval for income differences by education and race.

Use scatter plots to assess linear relationships between quantitative variables. Measure strength and direction with the sample correlation coefficient, mindful of outliers and unit independence.

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.