# 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.
*Questions, comments, or suggestions for this page?
Please send a message to Michelle Lacey
at lacey@stat.yale.edu*

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