Yates correction factor |
James Dean Brown (University of Hawai'i at Manoa) |
Example 1: Reanalysis of Shimura's 2004 data |
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Calculating X^{2} in two-way analyses
The steps for calculating the X^{2} value in two-way analyses are as follows: |
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None of these calculations are difficult. In fact, they can easily be done by hand, but the calculations are boring and repetitive so I chose to do them using my spreadsheet program. Using a formula, I would represent the X^{2} statistic for the two-way analysis in the 1st Advice contingency table as follows:[ p. 24 ]
We then compare the observed X^{2} statistic of 0.06 with the critical X^{2} value of 3.842 and see that the observed X^{2} is much lower. We must therefore conclude that this X^{2} and the associated comparisons are not statistically significant. Looking at the X^{2} results in Example 1 for the 2nd Advice and 3rd Advice contingency tables, you can see that the resulting observed values of X^{2} turned out to be 2.52 and 4.24, respectively, and that only the one for the 3rd Advice is significant at p < .05 (i.e., the probability is less than 5% that the comparisons being analyzed occurred by chance alone) as indicated by the asterisk which refers to the p < .05 statement just below the table.[ p. 25 ]
So in this case, X^{2}(Yates) turns out to be 0.00, which is the value recorded in Example 1 for 1st Advice. The values found for 2nd Advice and 3rd Advice are 1.75 and 3.25, respectively. To verify that you have understood the calculation of X^{2}(Yates), try calculating the values for yourself for the 2nd and 3rd Advice contingency tables using the above formula. The significance of these values is determined in the same way shown above for a regular X^{2} analysis. Using the same critical value of X^{2} as in the above example (3.842), we find that none of the X^{2}(Yates) values exceed the critical value and so none of them can be considered significant.References
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Brown, J. D. (1988). Understanding research in second language learning: A teacher's guide to statistics and research design. Cambridge: Cambridge University Press.[ p. 27 ]