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8.11 : Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.

The test statistic for a test of independence is similar to that of a goodness-of-fit test:

Equation1

where:

  • O = observed values
  • E = expected values (which should be at least 5)

A test of independence determines whether two factors are independent or not. The test of independence is always right-tailed because of the calculation of the test statistic. If the expected and observed values are not close together, then the test statistic is very large and way out in the right tail of the chi-square curve, as it is in a goodness-of-fit.

The number of degrees of freedom for the test of independence is:

Equation2

The following formula calculates the expected number (E):

Equation3

This text is adapted from Openstax, Introductory Statistics, Section 11.3 Test of Independence

Tags
Test Of IndependenceChi square TestContingency TableObserved ValuesExpected ValuesTest StatisticGoodness of fit TestDegrees Of FreedomProbabilityStatistical Independence

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8.11 : Introduction to Test of Independence

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8.1 : Distributions to Estimate Population Parameter

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8.2 : Degrees of Freedom

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8.3 : Student t Distribution

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8.4 : Choosing Between z and t Distribution

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8.5 : Chi-square Distribution

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8.6 : Finding Critical Values for Chi-Square

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8.7 : Estimating Population Standard Deviation

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8.8 : Goodness-of-Fit Test

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8.9 : Expected Frequencies in Goodness-of-Fit Tests

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8.10 : Contingency Table

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8.12 : Hypothesis Test for Test of Independence

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8.13 : Determination of Expected Frequency

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8.14 : Test for Homogeneity

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8.15 : F Distribution

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