University Introductory Statistics Two-Sample Inference and Chi-Square Tests — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 7 definitions and 7 theorems, 7 worked examples, 2 diagrams, in 16 printable pages. This page lists what the notes cover. The notes themselves come with the University Introductory Statistics bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Two-Sample Inference and Chi-Square Tests — what the notes cover
8 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Comparing two means from independent samples
- Theorem — Sampling distribution of a difference of two sample means
- Theorem — Large-sample z procedures for a difference of means
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
The pooled two-sample t procedure
- Definition — Pooled estimate of a common variance
- Theorem — Pooled two-sample t procedures
Also in this section: 1 worked example, 1 note on method and common errors.
Paired data and the t procedure on differences
- Definition — Paired data and the sample of differences
- Theorem — Paired t procedures
Also in this section: 1 worked example, 1 note on method and common errors.
Comparing two proportions
- Definition — Pooled sample proportion
- Theorem — Large-sample z procedures for a difference of proportions
Also in this section: 1 worked example, 1 note on method and common errors.
The chi-square goodness-of-fit test
- Definition — Expected counts under a stated model
- Theorem — Chi-square goodness-of-fit test
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Two-way tables and the test of independence
- Definition — Expected counts in a two-way table
- Theorem — Chi-square test of independence
Also in this section: 1 worked example, 1 note on method and common errors.
Association and causation in categorical data
- Definition — Conditional distributions of a two-way table
- Definition — What a rejection of independence licenses
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Introductory Statistics Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Two-Sample Inference and Chi-Square Tests practice worksheet is free and stays free.
Every University Introductory Statistics topic — the complete Solutions Bundle
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- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
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Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet.
Two-Sample Inference and Chi-Square Tests practice worksheet