In the definitional formula, $x^{2}=\sum_{i=1}^{k} \frac{\left(f_{0}-f_{e}\right)^{2}}{f_{e}}$ , and the computational formula, $x^{2}=\sum_{i=1}^{k} \frac{\left(f_{o}^{2}\right)}{f_{e}}-n$ , squaring the numerator ensures that ______.

Question

Quizplus · Accepted Answer

Squaring the numerator in both the definitional and computational formulas for the Chi-square statistic ensures that the value is never less than zero, as squaring any real number (positive or negative) results in a non-negative value.

In the Definitional Formula x2=∑i=1k(f0−fe)2fex^{2}=\sum_{i=1}^{k} \frac{\left(f_{0}-f_{e}\right)^{2}}{f_{e}}x2=∑i=1k​fe​(f0​−fe​)2​ , and the Computational Formula x2=∑i=1k(fo2)fe−nx^{2}=\sum_{i=1}^{k} \frac{\left(f_{o}^{2}\right)}{f_{e}}-nx2=∑i=1k​fe​(fo2​)​−n

In the Definitional Formula $x^{2}=\sum_{i=1}^{k} \frac{\left(f_{0}-f_{e}\right)^{2}}{f_{e}}$ , and the Computational Formula $x^{2}=\sum_{i=1}^{k} \frac{\left(f_{o}^{2}\right)}{f_{e}}-n$