The smaller/closer the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct concluding that the data fits that particular distribution given.
For a fraction of the form , the number in front of the division () is the numerator. The number after the division () is the denominator.
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A positive fraction () is less than as long as the numerator is smaller than the denominator (that is, .) The reason is that as long as :
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For example, in the fraction , is the numerator while is the denominator. Both the numerator and the denominator are positive, while the numerator is smaller than the denominator . Therefore, would be less than .