Chi-Square Test Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
For a chi-square test with observed=15, expected=20 for one category, calculate that category's contribution to the ฯ‡2\chi^2 statistic.

Solution

  1. 1
    Contribution: (Oโˆ’E)2E=(15โˆ’20)220=2520=1.25\frac{(O-E)^2}{E} = \frac{(15-20)^2}{20} = \frac{25}{20} = 1.25

Answer

Contribution =(15โˆ’20)220=1.25= \frac{(15-20)^2}{20} = 1.25.
Each cell contributes (Oโˆ’E)2/E(O-E)^2/E to the chi-square statistic. Larger deviations between observed and expected contribute more. The total ฯ‡2\chi^2 is the sum of all cells' contributions.

About Chi-Square Test

A hypothesis test that compares observed frequencies to expected frequencies using the chi-square statistic to assess independence or goodness of fit.

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More Chi-Square Test Examples

Example 1 medium

A die is rolled 60 times. Observed: 1โ†’8, 2โ†’12, 3โ†’9, 4โ†’11, 5โ†’13, 6โ†’7. Conduct a chi-square goodness-o

Example 2 hard

A 2ร—2 table: Men: 30 prefer A, 20 prefer B. Women: 15 prefer A, 35 prefer B. Test independence of ge

Example 4 hard

A survey of movie preferences across three age groups produces a 3ร—4 contingency table (3 age groups

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