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Probability Independence and Test of Two Categorical Variables
The idea of independence between two categorical variables may sound familiar as we
spoke of independence when we discussed probability.
Recall that in that lesson we
stated that two events, call them A and B, were independent if P(A)*P(B) = P(A and B).
We apply that reasoning to testing whether two categorical variables are independent.
As
with other hypothesis tests we discusses, the idea is to test whether the difference
produced by our sample is statistically different from the hypothesis (i.e. a rejection of
Ho) or is the difference just due to the error associated with random sampling and thus
the difference is not statistically significant (i.e. we do not reject Ho).
For example,
consider the probability lesson and let P(A) = 0.5, P(B) = 0. 30 and P(A and B) = 0.147
If A and B were independent, then technically P(A and B) should equal 0.15, however is
0.147 close enough?
Again, if these numbers are attained via sampling then a difference

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