Figure 1
A toy example illustrating the effect of the inappropriate choice of null distributions. Null distribution 1 follows the 
and null distribution 2 follows the 
. The observed χ2 value is 10, and the P-values are 0.0404 and 0.2650 for these two null distributions, respectively. Suppose P = 0.05 is the threshold of hypothesis testing. Then P = 0.0404 indicates a significant result, while P = 0.2650 does not. If the true null distribution is , then the use of will give many false positive results.