Skip to content

Explore Courses | Elder Research | Contact | LMS Login

Statistics.com Logo
  • Courses
    • See All Courses
    • Calendar
    • Intro stats for college credit
    • Faculty
    • Group training
    • Credit & Credentialing
    • Teach With Us
  • Programs/Degrees
    • Certificates
      • Analytics for Data Science
      • Biostatistics
      • Programming For Data Science – Python (Experienced)
      • Programming For Data Science – Python (Novice)
      • Programming For Data Science – R (Experienced)
      • Programming For Data Science – R (Novice)
      • Social Science
    • Undergraduate Degree Programs
    • Graduate Degree Programs
    • Massive Open Online Courses (MOOC)
  • Partnerships
    • Higher Education
    • Enterprise
  • Resources
    • About Us
    • Blog
    • Word Of The Week
    • News and Announcements
    • Newsletter signup
    • Glossary
    • Statistical Symbols
    • FAQs & Knowledge Base
    • Testimonials
    • Test Yourself
Menu
  • Courses
    • See All Courses
    • Calendar
    • Intro stats for college credit
    • Faculty
    • Group training
    • Credit & Credentialing
    • Teach With Us
  • Programs/Degrees
    • Certificates
      • Analytics for Data Science
      • Biostatistics
      • Programming For Data Science – Python (Experienced)
      • Programming For Data Science – Python (Novice)
      • Programming For Data Science – R (Experienced)
      • Programming For Data Science – R (Novice)
      • Social Science
    • Undergraduate Degree Programs
    • Graduate Degree Programs
    • Massive Open Online Courses (MOOC)
  • Partnerships
    • Higher Education
    • Enterprise
  • Resources
    • About Us
    • Blog
    • Word Of The Week
    • News and Announcements
    • Newsletter signup
    • Glossary
    • Statistical Symbols
    • FAQs & Knowledge Base
    • Testimonials
    • Test Yourself
Student Login

Chi-Square Test

Chi-Square Test

Chi-Square Test:

Chi-square test (or Math image -test) is a statistical test for testing the null hypothesis that the distribution of a discrete random variable coincides with a given distribution. It is one of the most popular goodness-of-fit tests .

For example, in a supermarket, relative frequencies of purchasing 4 brands of tee have been 0.1, 0.4, 0.2, and 0.3 during the last year; during the last week the number of packets sold have been 31, 41, 22, 18 for the 4 brands, respectively. Has the preference changed - i.e. probabilities of purchasing now differs from the last year average preferences, or the deviations in the observed relative frequencies is caused by chance alone?

The chi-square test, besides discrete variables, is often applied to problems involving continuous random variables . In this case, the values of a continuous variable are transformed to a discrete variable with a finite number of values - e.g. the whole range of possible values is split into a finite number of intervals, and every such interval is considered as a discrete value (e.g. age groups "20...29", "30...39", etc). Then the chi-square test is applied to the new discrete variable.

For small samples, the classical chi-square test is not very accurate - because the sampling distribution of the statistic of the test differs from the chi-square distribution . In such cases, Monte Carlo simulation is a more reasonable approach. In many cases such simulation can be carried out by creating an artificial sample with the given proportion of values and applying a resampling procedure to this sample. Besides the one-sample chi-square test, there are variants of the test for comparison of the distribution of two or several samples. For these variants, a permutation version of the test is more accurate when at least one sample is small. See more on the use of resampling and permutation in short online courses

Resampling ,

and in the online book Resampling: The New Statistics

The chi-square test is typically used in categorical data analysis , e.g. to check if two such variables are independent random variables ).

The chi-square test is based on the chi-square statistic .

Browse Other Glossary Entries

Courses Using This Term

Loading...
Biostatistics 1 – For Medical Science and Public Health
This course will teach you the principal statistical concepts used in medical and health sciences. Basic concepts common to all statistical analysis are reviewed, and those concepts with specific importance in medicine and health are covered in detail.
Categorical Data Analysis
This course will teach you the analysis of contingency table data. Topics include tests for independence, comparing proportions as well as chi-square, exact methods, and treatment of ordered data. Both 2-way and 3-way tables are covered.
Survey Analysis
This course will teach you how to analyze data gathered in surveys.
Return to Glossary Search

About Statistics.com

Statistics.com offers academic and professional education in statistics, analytics, and data science at beginner, intermediate, and advanced levels of instruction. Statistics.com is a part of Elder Research, a data science consultancy with 25 years of experience in data analytics.

 The Institute for Statistics Education is certified to operate by the State Council of Higher Education for Virginia (SCHEV)

Our Links

  • Contact Us
  • Site Map
  • Explore Courses
  • About Us
  • Management Team
  • Contact Us
  • Site Map
  • Explore Courses
  • About Us
  • Management Team

Social Networks

Facebook Twitter Youtube Linkedin

Contact

The Institute for Statistics Education
2107 Wilson Blvd
Suite 850 
Arlington, VA 22201
(571) 281-8817

ourcourses@statistics.com

  • Contact Us
  • Site Map
  • Explore Courses
  • About Us
  • Management Team

© Copyright 2023 - Statistics.com, LLC | All Rights Reserved | Privacy Policy | Terms of Use

By continuing to use this website, you consent to the use of cookies in accordance with our Cookie Policy.

Accept