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11.4 The chi-square distribution: summary of formulas

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

    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) .
  • The test statistic is Σ ( i ⋅ j ) ( O - E ) 2 E where O = observed values, E = expected values, i = the number of rows in the table, and j = 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 .
The expected value for each cell needs to be at least 5 in order to use the Independence test.

Glossary

Contingency table

The method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other. The table provides an easy way to calculate conditional probabilities

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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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