Statistics

Video 2

variable, categorical variable, numerical variable, discrete and continuous variables, levels of measurement, operational definition, measurement accuracy and precision and binary indicator

Builds on Introduction to Statistics.

Video 3

data provenance, data dictionary, missing value, missingness mechanism, complete-case analysis, duplicate records, outlier and data cleaning log

Builds on Types of Data and Measurement.

Video 4

frequency table, relative frequency, bar chart, contingency table, conditional percentage, cumulative frequency and multiple-response question

Builds on Types of Data and Measurement and Data Tables, Missing Values and Data Quality.

Video 5

distribution, dot plot, histogram, bin, frequency density, symmetry, skewness and modality

Builds on Frequency Tables and Categorical Charts. Also uses area of a rectangle.

Video 6

mean, median, mode, weighted mean, balance point and resistance

Builds on Types of Data and Measurement and Dot Plots, Histograms and Distribution Shape.

Video 7

deviation, population variance, sample variance, standard deviation and degrees of freedom

Builds on Mean, Median, Mode and Weighted Averages. Also uses arithmetic with signed numbers and square roots.

Video 8

percentile, quartile, interquartile range, five-number summary, box plot, outlier fence, median absolute deviation and trimmed mean

Builds on Dot Plots, Histograms and Distribution Shape, Mean, Median, Mode and Weighted Averages and Variance and Standard Deviation.

Video 9

z-score, standardization, linear transformation, shift, change of scale and unit conversion

Builds on Mean, Median, Mode and Weighted Averages and Variance and Standard Deviation.

Video 10

common scale, baseline, absolute change, relative change, percentage point and misleading graph

Builds on Frequency Tables and Categorical Charts, Dot Plots, Histograms and Distribution Shape, Percentiles, Quartiles and Box Plots and Z-Scores and Changes of Scale.

Video 11

scatter plot, sample covariance, Pearson correlation, linear association, influential observation, range restriction, Spearman rank correlation and monotonic association

Builds on Mean, Median, Mode and Weighted Averages, Variance and Standard Deviation and Comparing Distributions and Reading Graphs. Also uses points on a coordinate graph.

Video 12

marginal percentage, conditional association, aggregation, Simpson's paradox and standardized rate

Builds on Frequency Tables and Categorical Charts and Scatter Plots, Covariance and Correlation.

Video 13

target population, sampling frame, selection bias, undercoverage, nonresponse bias, voluntary response bias, measurement bias and representative sample

Builds on Introduction to Statistics, Types of Data and Measurement and Data Tables, Missing Values and Data Quality.

Video 14

simple random sample, stratified sampling, cluster sampling, systematic sampling, probability sample, inclusion probability, survey weight and design effect

Builds on Sampling Bias and Representativeness.

Video 15

observational study, explanatory variable, response variable, causal effect, confounding and reverse causation

Builds on Sampling Bias and Representativeness, Scatter Plots, Covariance and Correlation and Two-Way Tables and Simpson's Paradox.

Video 16

random assignment, control group, placebo, blinding, blocking, matched pairs design, experimental unit and random sampling versus random assignment

Builds on Random Sampling Methods and Observational Studies, Confounding and Causation.

Video 17

sample space, event, complement rule, union, intersection, disjoint events, addition rule and long-run relative frequency

Builds on Introduction to Statistics and Frequency Tables and Categorical Charts.

Video 18

conditional probability, joint probability, marginal probability, multiplication rule, independent events and law of total probability

Builds on Probability Rules and Events and Two-Way Tables and Simpson's Paradox.

Video 19

Bayes' theorem, base rate, prior probability, posterior probability, sensitivity, specificity, positive predictive value and natural frequencies

Builds on Conditional Probability and Independence.

Video 20

multiplication principle, factorial, permutation, combination, equally likely outcomes, sampling with replacement and sampling without replacement

Builds on Probability Rules and Events, Conditional Probability and Independence and Random Sampling Methods.

Video 21

random variable, discrete random variable, support, probability distribution, probability mass function and cumulative distribution function

Builds on Probability Rules and Events.

Video 22

expected value, variance of a random variable, second moment, linearity of expectation, independent random variables, covariance of random variables and variance of a sum

Builds on Discrete Random Variables and Probability Distributions, Mean, Median, Mode and Weighted Averages, Variance and Standard Deviation and Scatter Plots, Covariance and Correlation.

Video 23

Bernoulli trial, Bernoulli distribution, binomial setting, binomial distribution, binomial mean and variance and hypergeometric distribution

Builds on Conditional Probability and Independence, Counting and Sampling Without Replacement and Expected Value, Variance and Sums of Random Variables.

Video 24

Poisson distribution, exposure, event rate, Poisson parameter, independent increments, mean-variance equality and overdispersion

Builds on Bernoulli, Binomial and Hypergeometric Models.

Video 25

continuous random variable, probability density function, probability as area, uniform distribution, exponential distribution, survival probability and memorylessness

Builds on Discrete Random Variables and Probability Distributions and Expected Value, Variance and Sums of Random Variables.

Video 26

normal distribution, standard normal distribution, tail probability, normal quantile and empirical rule

Builds on Z-Scores and Changes of Scale and Continuous Distributions, Density and Cumulative Probability.

Video 27

normal approximation, continuity correction, success-failure condition, approximation error and exact binomial probability

Builds on Bernoulli, Binomial and Hypergeometric Models and Normal Distributions and Quantiles.

Video 28

simulation, Monte Carlo method, simulation replication, random seed, Monte Carlo error, Monte Carlo standard error and model error

Builds on Probability Rules and Events, Discrete Random Variables and Probability Distributions and Normal Distributions and Quantiles.

Video 29

population distribution, sampling distribution, repeated sampling, sampling distribution of the sample mean, sampling distribution of the sample proportion and finite population correction

Builds on Random Sampling Methods, Variance and Standard Deviation, Discrete Random Variables and Probability Distributions and Bernoulli, Binomial and Hypergeometric Models.

Video 30

standard error, standard error of the mean, estimated standard error, effective sample size and cluster dependence

Builds on Sampling Distributions of Means and Proportions, Variance and Standard Deviation and Expected Value, Variance and Sums of Random Variables.

Video 31

law of large numbers, independent and identically distributed, convergence in probability and gambler's fallacy

Builds on Sampling Distributions of Means and Proportions and Standard Deviation and Standard Error.

Video 32

central limit theorem, standardized sample mean, finite positive variance, normal approximation for a sample mean and heavy-tailed distribution

Builds on Normal Distributions and Quantiles, Sampling Distributions of Means and Proportions, Standard Deviation and Standard Error and The Law of Large Numbers.

Video 33

reference distribution, chi-square distribution, Student's t distribution, F distribution and critical value

Builds on Normal Distributions and Quantiles, The Central Limit Theorem and Variance and Standard Deviation.

Video 34

estimator, estimate, bias, variance of an estimator, mean squared error, bias-variance decomposition and consistency

Builds on Sampling Distributions of Means and Proportions, Standard Deviation and Standard Error and The Law of Large Numbers.

Video 35

statistical model, likelihood function, likelihood ratio, maximum likelihood estimate, log-likelihood and boundary estimate

Builds on Discrete Random Variables and Probability Distributions, Bernoulli, Binomial and Hypergeometric Models and Estimation, Bias, Precision and Mean Squared Error.

Video 36

confidence interval, confidence level, coverage probability, margin of error and repeated-sampling interpretation

Builds on Standard Deviation and Standard Error, Estimation, Bias, Precision and Mean Squared Error and The Central Limit Theorem.

Video 37

one-sample t interval, t critical value, normal sampling model and departures from normality

Builds on Confidence Intervals and Coverage and Student's t, Chi-Square and F Distributions.

Video 38

Wald interval, Wilson interval, Clopper-Pearson interval, boundary proportion and nominal and actual coverage

Builds on Bernoulli, Binomial and Hypergeometric Models, Confidence Intervals and Coverage and Normal Approximations and Their Limits.

Video 39

bootstrap, bootstrap sample, bootstrap standard error, percentile interval, resampling unit and bootstrap bias

Builds on Simulation and Monte Carlo Error, Estimation, Bias, Precision and Mean Squared Error, Confidence Intervals and Coverage, Confidence Intervals for a Mean and Confidence Intervals for a Proportion.

Video 40

sample-size planning, conservative proportion, pilot estimate and nonresponse allowance

Builds on Random Sampling Methods, Standard Deviation and Standard Error, Confidence Intervals for a Mean and Confidence Intervals for a Proportion.

Video 41

null hypothesis, alternative hypothesis, test statistic, null distribution, p-value, one-sided and two-sided tests, significance level and pre-specification

Builds on Simulation and Monte Carlo Error, Confidence Intervals and Coverage and Student's t, Chi-Square and F Distributions.

Video 42

type I error, type II error, power, power analysis, minimum detectable effect and optional stopping

Builds on Sample Size and Margin of Error and Hypothesis Tests and P-Values.

Video 43

statistical significance, practical importance, effect size, smallest meaningful effect, equivalence margin and absence of evidence

Builds on Confidence Intervals and Coverage, Hypothesis Tests and P-Values and Type I Error, Type II Error and Power.

Video 44

randomization test, permutation test, permutation distribution, sharp null hypothesis, exchangeability, restricted permutation, Monte Carlo p-value and plus-one correction

Builds on Randomized Experiments, Blocking and Matched Pairs, Simulation and Monte Carlo Error and Hypothesis Tests and P-Values.

Video 45

one-sample t test, t statistic, standardized mean difference and duality of tests and confidence intervals

Builds on Confidence Intervals for a Mean, Hypothesis Tests and P-Values and Statistical Significance and Practical Importance.

Video 46

exact binomial test, one-proportion z test, null standard error and discrete p-value

Builds on Bernoulli, Binomial and Hypergeometric Models, Confidence Intervals for a Proportion and Hypothesis Tests and P-Values.

Video 47

independent samples, standard error of a difference, Welch t test, Welch confidence interval, Welch-Satterthwaite degrees of freedom, pooled variance and equal-variance t test

Builds on Standard Deviation and Standard Error and One-Sample t-Tests.

Video 48

paired data, within-pair difference, paired t test, paired confidence interval and before-after design

Builds on Randomized Experiments, Blocking and Matched Pairs, One-Sample t-Tests and Comparing Two Independent Means.

Video 49

difference in proportions, two-proportion z test, pooled proportion, unpooled confidence interval and A/B test

Builds on Confidence Intervals for a Proportion, One-Proportion Tests and Comparing Two Independent Means.

Video 50

sign test, Wilcoxon signed-rank test, signed rank, zero differences, tied ranks and distribution-free method

Builds on Percentiles, Quartiles and Box Plots, Bernoulli, Binomial and Hypergeometric Models, Hypothesis Tests and P-Values and Paired t-Tests and Before-After Data.

Video 51

rank sum, Wilcoxon rank-sum test, Mann-Whitney U statistic, probability of superiority, location-shift model and exact permutation distribution

Builds on Comparing Two Independent Means, Sign Tests and Wilcoxon Signed-Rank Tests and Randomization and Permutation Tests.

Video 52

risk, risk difference, risk ratio, odds, odds ratio, baseline risk, case-control study and log-scale interval for a ratio

Builds on Conditional Probability and Independence, Confidence Intervals for a Proportion and Comparing Two Proportions.

Video 53

goodness-of-fit test, expected frequency, chi-square statistic, multinomial model and degrees of freedom for estimated parameters

Builds on Discrete Random Variables and Probability Distributions, Hypothesis Tests and P-Values and Student's t, Chi-Square and F Distributions.

Video 54

chi-square test of independence, chi-square test of homogeneity, expected count, Pearson residual and Cramér's V

Builds on Two-Way Tables and Simpson's Paradox, Risk, Odds and Relative Effects and Chi-Square Goodness-of-Fit Tests.

Video 55

Fisher's exact test, fixed margins, conditional inference, two-sided exact p-value, paired binary data, McNemar test, discordant pair and marginal homogeneity

Builds on Bernoulli, Binomial and Hypergeometric Models, Paired t-Tests and Before-After Data, Chi-Square Independence and Homogeneity and Risk, Odds and Relative Effects.

Video 56

one-way ANOVA, between-group sum of squares, within-group sum of squares, mean square, F statistic and Welch ANOVA

Builds on Comparing Two Independent Means and Student's t, Chi-Square and F Distributions.

Video 57

factor, factorial design, cell mean, main effect, simple effect, interaction, randomized block design and replication

Builds on Randomized Experiments, Blocking and Matched Pairs and One-Way ANOVA and Welch ANOVA.

Video 58

planned contrast, post-hoc comparison, family-wise error rate, Bonferroni correction, Holm procedure, false discovery rate, Benjamini-Hochberg procedure and Tukey procedure

Builds on Type I Error, Type II Error and Power, One-Way ANOVA and Welch ANOVA and Factorial Designs, Blocking and Interactions.

Video 59

Kruskal-Wallis test, pooled ranks, omnibus test, identical-distribution null hypothesis, tie correction and chi-square approximation

Builds on Mann-Whitney Tests and Rank-Based Comparisons, One-Way ANOVA and Welch ANOVA and Planned Contrasts, Post-Hoc Comparisons and Multiple Testing.

Video 60

chi-square pivot, confidence interval for a standard deviation, F test for two variances, Levene test, Brown-Forsythe test and sensitivity to nonnormality

Builds on Variance and Standard Deviation, Confidence Intervals for a Mean, Student's t, Chi-Square and F Distributions and One-Way ANOVA and Welch ANOVA.

Video 61

predictor, least-squares line, slope, intercept, fitted value, residual, residual sum of squares and R-squared

Builds on Scatter Plots, Covariance and Correlation and Estimation, Bias, Precision and Mean Squared Error. Also uses equation of a straight line.

Video 62

residual plot, linear conditional mean, constant variance, heteroscedasticity, independent errors, Q-Q plot, hat value and Cook's distance

Builds on Least Squares and R-Squared, Observational Studies, Confounding and Causation and Student's t, Chi-Square and F Distributions.

Video 63

simple linear regression model, error term, residual standard deviation, standard error of the slope, t test for a slope and confidence interval for a slope

Builds on Least Squares and R-Squared, Regression Assumptions, Residuals and Influence and One-Sample t-Tests.

Video 64

mean response, confidence interval for a mean response, prediction interval, prediction error and extrapolation

Builds on Inference for a Regression Slope and Confidence Intervals and Coverage.

Video 65

multiple regression, partial regression coefficient, adjusted association, indicator variable, reference group and omitted variable

Builds on Least Squares and R-Squared, Regression Assumptions, Residuals and Influence and Inference for a Regression Slope.

Video 66

categorical predictor, reference coding, interaction term, conditional effect and model hierarchy

Builds on Multiple Regression and Adjusted Associations and Factorial Designs, Blocking and Interactions.

Video 67

polynomial regression, linear in the coefficients, log transformation, back-transformation, conditional median and lognormal error

Builds on Multiple Regression and Adjusted Associations and Categorical Predictors and Interactions.

Video 68

nested models, partial F test, adjusted R-squared, multicollinearity, variance inflation factor, identifiability and model selection

Builds on Multiple Regression and Adjusted Associations, Categorical Predictors and Interactions, Transformations and Curved Relationships and Planned Contrasts, Post-Hoc Comparisons and Multiple Testing.

Video 69

logistic regression, logit, logistic function, odds ratio for a predictor, complete separation, calibration and predicted probability

Builds on Risk, Odds and Relative Effects, Multiple Regression and Adjusted Associations and Likelihood and Maximum Likelihood Estimation.

Video 70

training data, test data, loss function, overfitting, cross-validation, data leakage and distribution shift

Builds on Least Squares and R-Squared, Regression Assumptions, Residuals and Influence, Multiple Regression and Adjusted Associations and Logistic Regression.

Video 71

Bayesian updating, prior distribution, posterior distribution, normalizing constant, prior odds, posterior odds and Bayes factor

Builds on Bayes' Theorem and Base Rates and Likelihood and Maximum Likelihood Estimation.

Video 72

beta distribution, beta-binomial conjugacy, posterior mean, posterior median, credible interval and equal-tailed credible interval

Builds on Prior, Likelihood and Posterior, Confidence Intervals and Coverage, Confidence Intervals for a Proportion and Continuous Distributions, Density and Cumulative Probability.

Video 73

posterior predictive distribution, conditional independence, beta-binomial predictive distribution, prior sensitivity, prior predictive check and posterior predictive check

Builds on Bayesian Estimation and Credible Intervals and Logistic Regression.

Video 74

repeated measures, cluster, pseudoreplication, intraclass correlation, design effect for clustered data, cluster bootstrap and random-intercept mixed model

Builds on Random Sampling Methods, Randomized Experiments, Blocking and Matched Pairs, Standard Deviation and Standard Error, Paired t-Tests and Before-After Data and Multiple Regression and Adjusted Associations.

Video 75

time series, trend, seasonality, lag, autocorrelation and stationarity

Builds on Scatter Plots, Covariance and Correlation, Regression Assumptions, Residuals and Influence and Repeated Measures, Clusters and Independence.

Video 76

naive forecast, seasonal naive forecast, moving average, exponential smoothing, forecast horizon, rolling-origin evaluation, temporal leakage and forecast interval

Builds on Validation, Overfitting and Honest Prediction and Time Series, Trend, Seasonality and Autocorrelation.

Video 77

estimand, analysis plan, preregistration, planned versus exploratory analysis, selective reporting, sensitivity analysis and reproducibility

Builds on Planned Contrasts, Post-Hoc Comparisons and Multiple Testing, Validation, Overfitting and Honest Prediction, Sparse Tables, Fisher's Exact Test and Paired Binary Data, Inference for Variance and Comparing Spread, Posterior Prediction and Prior Sensitivity, Repeated Measures, Clusters and Independence and Smoothing, Forecasting and Time-Aware Validation.

Video 78

statistical investigation, research question, study design, primary and secondary outcomes, exploratory data analysis, method selection, model checking and reproducible report

Builds on Selecting Methods and Reporting Statistical Results.