Question

*HOW WOULD I SET THIS UP IN A CHI-SQUARE TEST*

An example for numerical to categorical data off the top of my head: Light of different color has different wavelengths, but certain ranges of wavelengths qualify as certain shades/hues/tints/etc. You can generalize and say a certain range can be called "blue" or "red". Red is usually attributed to light that has a wavelength between 780 and 622 nanometers, whereas blue light is between 492 and 455 nm. To the average person, "red" and "blue" obviously mean more than a given wavelength of light, so a categorical/qualitative description might be of more use in such a context.

            Another example would be grading scales. Certain ranges of scores will qualify as an A, a B, and so on. Suppose you want to examine the grades of high school students admitted into a prestigious university. Students that fall in the A/B range tend to have a better chance of being admitted, while those at the other end of the spectrum are "significantly" less likely to enroll. ("Significant" here can take on the statistical meaning of the word.

Answer 1