*HOW WOULD I SET UP UP THIS EXPERIMENT* An example for numerical to categorical

Question

*HOW WOULD I SET UP UP THIS EXPERIMENT*

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.

  

Explanation / Answer

To use the chi-square test we have to categorise the numeric data

the categorical table is as follow;

Here, the in the first cell colour represents the column with categories red and blue while Wavelength in nm represents the wavelength specified in the problem for red and blue colour.

Colour Wavelength in nm 780 to 622 492 to 455 Total Red N1 N3 N1+N3 Blue N2 N4 N2+N4 Total N1+N2 N3+N4 TOTAL=N1+N2+N3+N4

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