Nature of the Chi-Square Distribution

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Title:

Nature of the Chi-Square Distribution

Url:

https://serc.carleton.edu/sp/cause/cooperative/examples/18171.html

Creator:

Smith, Brian

Publisher:

Science Education Resource Center

Description: In this activity, students learn the true nature of the chi-square and F distributions in lecture notes (PowerPoint file) and an Excel simulation. This leads to a discussion of the properties of the two distributions. Once the sum of squares aspect is understood, it is only a short logical step to explain why a sample variance has a chi-square distribution and a ratio of two variances has an F-distribution. In a subsequent activity, instances of when the chi-square and F-distributions are related to the normal or t-distributions (e.g. Chi-square = z2, F = t2) will be illustrated. Finally, the activity will conclude with a brief overview of important applications of chi-square and F distributions, such as goodness-of-fit tests and analysis of variance.

LC Classification:

Science -- Mathematics -- Mathematical statistics -- Study and teaching. Research
Science -- Mathematics -- Mathematical statistics -- Testing of hypotheses -- Chi-square test

GEM Subject:

Mathematics -- Instructional issues
Mathematics -- Statistics

Key Concept:

Mathematics -- Chi square
Mathematics -- Statistics

Date Issued:

2007

Resource Type:

Instructional Material
Instructional Material -- Demonstration
Instructional Material -- Lesson/Lesson Plan

Format:

Document -- DOC
Document -- PPT
Document -- XLS
Document -- HTML

Audience:

Educator
Learner

Education Level:

High School
Higher Education
Higher Education -- Undergraduate (Lower Division)
Higher Education -- Undergraduate (Upper Division)
Higher Education -- Technical Education (Upper Division)
Higher Education -- Technical Education (Lower Division)
Vocational/Professional Development Education

Language:

English

Access Rights:

Free access

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Source:

CAUSEweb

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