keepcalmandstudyon
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Below is my understanding of the chisquare test - I would like to check if my understanding is correct:
For Paper A, we can use the chisquare test only if all expected frequencies are >= 5 (or if all expected frequencies are >1 and not more than 20% of the expected frequencies are less than 5).
This is because if we divide by very small e_i values, the resulting numbers for (f_i – e_i )^2/e_i could be rather large and erratic (because the numbers would basically be just squares of the observed frequencies). So then distribution of the test statistic may not match the chisquare distribution very well.
In Paper A, we would get around this problem by combining some categories.
But in Paper B, we don't need to combine any categories because R can get around this by using "simulate.p.value=TRUE":
chisq.test(observedfrequencies,p=expectedprobabilities,simulate.p.value=TRUE)
The above is what I understand from Example 10.14 of the CS1 Paper B Online Resources. Is my understanding correct? If correct, why does simulating the p-value get around the problem of expected frequencies being less than 5?
For Paper A, we can use the chisquare test only if all expected frequencies are >= 5 (or if all expected frequencies are >1 and not more than 20% of the expected frequencies are less than 5).
This is because if we divide by very small e_i values, the resulting numbers for (f_i – e_i )^2/e_i could be rather large and erratic (because the numbers would basically be just squares of the observed frequencies). So then distribution of the test statistic may not match the chisquare distribution very well.
In Paper A, we would get around this problem by combining some categories.
But in Paper B, we don't need to combine any categories because R can get around this by using "simulate.p.value=TRUE":
chisq.test(observedfrequencies,p=expectedprobabilities,simulate.p.value=TRUE)
The above is what I understand from Example 10.14 of the CS1 Paper B Online Resources. Is my understanding correct? If correct, why does simulating the p-value get around the problem of expected frequencies being less than 5?