Chi-Square Statistic Calculation
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Example from:
Chi-Square Independence Test - Quick Introduction
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1. Observed Frequencies
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Middle school or lower
High schoolBachelor'sMaster'sPhD or higher
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Never married1836219690
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Married1236453621150
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Divorced6993330
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Widowed3996330
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3990845433300
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2. Expected Frequencies under Null Hypothesis of Independence
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Middle school or lower
High schoolBachelor'sMaster'sPhD or higher
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Never married11.72725.216.29.990
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Married19.545422716.5150
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Divorced3.998.45.43.330
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Widowed3.998.45.43.330
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3990845433300
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3. Residuals = (Observed - Expected)
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Middle school or lower
High schoolBachelor'sMaster'sPhD or higher
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Never married6.309.00-4.20-7.20-3.900.00
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Married-7.50-9.003.009.004.500.00
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Divorced2.100.000.60-2.40-0.300.00
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Widowed-0.900.60.6-0.30
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0.000.000.000.000.000.00
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4. Chi-Square Points = (Observed - Expected) ^2 / Expected
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Middle school or lower
High schoolBachelor'sMaster'sPhD or higherTotal
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Never married3.393.000.703.201.5411.83
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Married2.881.800.213.001.239.13
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Divorced1.130.000.041.070.032.27
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Widowed0.210.000.040.070.030.34
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7.624.801.007.332.8223.57
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5. Chi-Square Statistic = Sum Chi-Square Points
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23.57
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