The χ2\chi^2 value means nothing on its own-it is used to find the probability that, assuming the hypothesis is true, the observed data set could have resulted from random fluctuations. A low probability suggests that the observed data are not consistent with the hypothesis, and thus the hypothesis should be rejected. A standard cutoff point used by biologists is a probability of 0.05(5%). If the probability corresponding to the χ2\chi^2 value is 0.050.05 or less, the differences between observed and expected values are considered statistically significant, and the hypothesis (that the genes are unlinked) should be rejected. If the probability is above 0.050.05, the results are not statistically significant; the observed data are consistent with the hypothesis. To find the probability, locate your χ2\chi^2 value in the χ2\chi^2 Distribution Table in Appendix FF. The "degrees of freedom" (df) of your data set is the number of categories (here, 4 phenotypes) minus 1 , so df=3\mathrm{df}=3. Determine which values on the df=3d f=3 line of the table your calculated χ2\chi^2 value lies between.


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Note that the chi-square value (χ2)(\chi^2) is used to calculate the likelihood that the observed data set may have come from random fluctuations, providing the hypothesis is correct.

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