CONCEPTUAL TOOLS

by Neil E. Cotter

Research Assistant Professor

Last Updated: 11/23/21

(† = missing, * = article)

Statistics

Sample estimation distributions

Gallery of distributions | pdf

Sample statistics

†Random sample

Median and mode

Example 1 | (pdf)

†Percentiles

†Quartiles

Sample mean

Example 1 | (pdf)

Sample variance and stdev

Definitions | (pdf)

Derivation | (pdf)

Example 1 | (pdf)

Data plots

Histogram

Example 1 | (pdf)

Box and whisker plot

Example 1 (pdf)

Quantile plot

Example 1 | (pdf)

†Normal quantile plot

†Parzen windows

Central limit theorem

Theorem statement | (pdf)

Proof for Bernoulli trials | (pdf)

Example 1 | (pdf)

†Parameter estimates

Method of Moments | (pdf)

Maximum Likelihood Method | (pdf)

T-distribution or student's distribution

Derivation | (pdf)

Distribution of sample mean | (pdf)

Distribution of sample variance | (pdf)

Independence of Z and ² | (pdf)

Critical value tables

Normal and t-distribution

table (pdf)

χ²-distribution

table (pdf)

F-distribution

table

α = 0.01 (pdf)

α = 0.05 (pdf)

Cumulative t-distribution tables

Table

ν = 3 (pdf)

ν = 8 (pdf)

Confidence intervals

Gallery (pdf)

Background (pdf)

Procedure (pdf)

Key equations (pdf)

Test of mean

Example 1 (pdf)

Example 2 (pdf)

Example 3 (pdf)

Example 4 (pdf)

Test of var

Example 1 (pdf)

Hypothesis testing

Gallery (pdf)

Test of mean

Example 1 (pdf)

Example 2 (pdf)

Test of variance

example 1 (pdf)

Difference of means

example 1 (pdf)

Test on one proportion

theory (pdf)

example 1 (pdf)

p-value of test

example 1 (pdf)

ANOVA

One Way

Calculations | (pdf)

Example 1 | (pdf)

Bartlett's test

Calculations | (pdf)

Example 1 | (pdf)

Control charts

chart

Example 1 | (pdf)

Nonparametric statistics

Sign test

†Derivation | (pdf)

†Example 1 | (pdf)

Signed-rank test

Derivation | (pdf)

Example 1 | (pdf)

Rank-sum test

†Example 1 | (pdf)