The main reason for this is that the true sampling distribution for the X 2 statistic is actually discrete (because you’re dealing with categorical data!) but the χ2 distribution is continuous. Specif...The main reason for this is that the true sampling distribution for the X 2 statistic is actually discrete (because you’re dealing with categorical data!) but the χ2 distribution is continuous. Specifically, when N is small and when df=1, the goodness of fit statistic tends to be “too big”, meaning that you actually have a bigger α value than you think (or, equivalently, the p values are a bit too small).
The main reason for this is that the true sampling distribution for the X 2 statistic is actually discrete (because you’re dealing with categorical data!) but the χ2 distribution is continuous. Specif...The main reason for this is that the true sampling distribution for the X 2 statistic is actually discrete (because you’re dealing with categorical data!) but the χ2 distribution is continuous. Specifically, when N is small and when df=1, the goodness of fit statistic tends to be “too big”, meaning that you actually have a bigger α value than you think (or, equivalently, the p values are a bit too small).
