Skip to content Skip to navigation

Connexions

You are here: Home » Content » The Chi-Square Distribution: Summary of Formulas

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

      A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

      What is in a lens?

      Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

      Who can create a lens?

      Any individual Connexions member, a community, or a respected organization.

    • External bookmarks
  • E-mail the authors

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

This content is ...

In these lenses

  • Printable Books

    This module is included inLens: Connexions Books Available for Print on Demand
    By: ConnexionsAs a part of collection:"Collaborative Statistics"

    Comments:

    "This book was purchased from the authors by the Maxfield Foundation and provided to the community as an open textbook available freely online and in PDF format. Bound copies of the book can also […]"

    Click the "Printable Books" link to see all content selected in this lens.

  • Bio 502 at CSUDH

    This module is included inLens: Bio 502
    By: Terrence McGlynnAs a part of collection:"Collaborative Statistics"

    Comments:

    "This is the course textbook for Biology 502 at CSU Dominguez Hills"

    Click the "Bio 502 at CSUDH" link to see all content selected in this lens.

Recently Viewed

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

The Chi-Square Distribution: Summary of Formulas

Module by: Dr. Barbara Illowsky, Susan Dean

Summary: This module provides an summary on formulas used in Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

formula 1: The Chi-square Probability Distribution

μ=dfμ=df and σ=2⋅dfσ=2⋅df

formula 2: Goodness-of-Fit Hypothesis Test

  • Use goodness-of-fit to test whether a data set fits a particular probability distribution.
  • The degrees of freedom are number of cells or categories - 1number of cells or categories - 1.
  • The test statistic is Σ n ( O − E ) 2 E Σ n ( O − E ) 2 E , where OO = observed values (data), EE = expected values (from theory), and nn = the number of different data cells or categories.
  • The test is right-tailed.

formula 3: Test of Independence

  • Use the test of independence to test whether two factors are independent or not.
  • The degrees of freedom are equal to (number of columns - 1)(number of rows - 1)(number of columns - 1)(number of rows - 1).
  • The test statistic is Σ ( i ⋅ j ) ( O - E ) 2 E Σ ( i ⋅ j ) ( O - E ) 2 E where OO = observed values, EE = expected values, ii = the number of rows in the table, and jj = the number of columns in the table.
  • The test is right-tailed.
  • If the null hypothesis is true, the expected number E = (row total)(column total) total surveyed E= (row total)(column total) total surveyed .

formula 4: Test of a Single Variance

  • Use the test to determine variation.
  • The degrees of freedom are the number of samples - 1.
  • The test statistic is ( n - 1 ) ⋅ s 2 σ 2 ( n - 1 ) ⋅ s 2 σ 2 , where nn = the total number of data, s2s2 = sample variance, and σ2σ2 = population variance.
  • The test may be left, right, or two-tailed.

Comments, questions, feedback, criticisms?

Send feedback