Statistical Topics

This topics list provides access to definitions, explanations, and examples for each of the major concepts covered in Statistics 101-103.

Describing and displaying data

Graphical displays: stemplots, histograms, boxplots,scatterplots.
Numerical Summaries: mean, median, quantiles, variance, standard deviation.
Normal Distributions: assessing normality, normal probability plots.
Categorical Data: two-way tables, bar graphs, segmented bar graphs.

Linear regression and correlation

Linear regression: least-squares, residuals, outliers and influential observations, extrapolation.
Correlation: correlation coefficient, r².
Inference in Linear Regression: confidence intervals for intercept and slope, significance tests, mean response and prediction intervals.
Multiple Linear Regression: confidence intervals, tests of significance, squared multiple correlation.
ANOVA for Regression: analysis of variance calculations for simple and multiple regression, F statistics.

Experiments and sampling

Experimental Design: experimentation, control, randomization, replication.
Sampling: simple, stratified, and multistage random sampling.
Sampling in Statistical Inference: sampling distributions, bias, variability.

Probability

Probability Models: components of probability models, basic rules of probability.
Conditional Probability: probabilities of intersections of events, Bayes's formula.
Random variables: discrete, continuous, density functions.
Mean and Variance of Random Variables: definitions, properties.
Binomial Distributions: counts, proportions, normal approximation.
Sample Means: mean, variance, distribution, Central Limit Theorem.

Hypothesis tests and confidence intervals

Confidence Intervals: inference about population mean, z and t critical values.
Tests of Significance: null and alternative hypotheses for population mean, one-sided and two-sided z and t tests, levels of significance, matched pairs analysis.
Comparison of Two Means: confidence intervals and significance tests, z and t statistics, pooled t procedures.
Inference for Categorical Data: confidence intervals and significance tests for a single proportion, comparison of two proportions.
Chi-square Goodness of Fit Test: chi-square test statistics, tests for discrete and continuous distributions.
Two-Way tables and the Chi-Square test: categorical data analysis for two variables, tests of association.