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Chi squared test
A significant difference from your null hypothesis (i.e. difference from your expectation) is indicated when your calculated X^{2} value is greater than the c^{2 }value shown in the 0.05 column of this table (i.e. there is only a 5% probability that your calculated X^{2}value would occur by chance). You can be even more confident if your calculated value exceeds the c^{2} values in the 0.01 or 0.001 probability columns. If your calculated X^{2} value is equal to, or less than, the tabulated c^{2 }value for 0.95 then your results give you no reason to reject the null hypothesis. In a few special circumstances (though not generally) a calculated X^{2 }value lower than the c^{2}value in the 0.95 or 0.99 columns provides evidence that your results agree well with a null hypothesis.

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