The x² 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 x² value is 0.05 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 0.05 , the results are not statistically significant; the observed data are consistent with the hypothesis. To find the probability, locate your X² value in the X² Distribution Table in Appendix F . The "degrees of freedom" (df) of your data set is the number of categories (here, 4 phenotypes) minus 1, so df -3 .
(a) Determine which values on the df -3 line of the table your calculated X² value lies between.