A geologist collects hand specimen sized pieces of limestone

A geologist collects hand specimen sized pieces of limestone from a particular area. A qualitative assessment of both texture and color is made with the following results. Is there evidence of association between color and texture for these limestones? Explain your answer.

Color

Texture Light Medium Dark

Fine 4 20 8

Medium 5 23 12

Coarse 21 23 4

Solution

?² = 17.727,     df = 4,     ?²/df = 4.43 ,         P(?² > 17.727) = 0.0014

warning:  some observed or expected frequencies are less than 5; thus the Central Limit Theorem may not apply and the resultant ?² may be invalid

As p value is very small reject null hypothesis

There is no evidence of association between colour and texture