Fisher's Exact Test

all right our next lecture is going to be looking at the Fisher's exact test which is another statistical test that we use for nominal data when we pull up our decision tree diagram here we can see that we use a Fisher's exact test when we have two groups of nominal data that's unpaired and when we decide we're deciding between using a chi-square and a Fisher's exact test we look at the expected count so this would be those expected frequencies that we calculated back in the chi-square picture and we would use the Fisher's exact if we had an expected count of greater than or equal to five in less than 80 percent of the cells and so we'll get into this a little bit more when we go through the lecture what this exactly means our objective as always is to appraise if the specific Fisher's exact test can be used for analyzing data provided in a scientific journal or if it was appropriate for use in analyzing data provided in a scientific journal so like I mentioned before the Fisher's exact test is used for nominal data however it is used in the following cases so it can be used when total number of patients is small so less than 20 with the two-by-two matrix or it can be used if we have more than 20 subjects but the expected cell count is 5 or greater in less than 80 percent of the cells the other 5 assumptions of the chi-square still apply the calculation of the Fisher's exact test involves a direct calculation of the probability P for one tailed test however most of the online statistical calculators will give you a two-tailed option and that's what we're going to be using today it's important to keep in mind that if one were to be calculating this by hand since the distribution of probabilities of data matrices is usually not symmetric it's kind of considered controversial whether it is appropriate to double the calculated p-value when the test is two-tailed if you're calculating it for a one tailed there's also some controversy to that the Fisher's exact test is on the conservative side as well but it is important to be able to differentiate between when you should maybe use it compared to a chi-square test and so I'll give you an example of that so again you are a clinical pharmacist working in an outpatient pain clinic and you're interested in assessing based on gender the distribution of patients you have that are on pain medication a versus pain medication B so again we have our two rows here one for male one for female and we're looking at associations between specific pain medication use and gender assignment here so we have pain medication a in the first column here and pain medication B in the second column here so to begin with we want to make sure that no assumptions are violated so kind of the two that we look after fisher's exact or right here so total number of patients is less than 20 with a 2x2 matrix so we have 22 patients here so this isn't the case or we have an N greater than 20 that's what we have here but the expected cell count is 5 or greater and less than 80 percent of the cells here I've put the expected frequencies that I've calculated in brackets in red here and we calculate these expected frequencies in the same way that we do for the chi-square so we can see we have an expected frequency of 6.5 here that's greater than 5 we have 9.5 here that's greater than 5 but the other two are less than 5 so that means that we have a cell count of 5 or greater and only 50% of the cells so we would use the Fisher's exact in this case if they were all greater than 5 then perhaps we should be using the chi-square we want to state the null and alternative hypothesis so the null hypothesis is that there is no association between patient gender and pain medication used the alternative is that there is an association between patient gender and pain medication used we want to state the alpha to 0.05 and in the case of the Fisher's exact test we don't calculate a degrees of freedom we don't need to find a critical chi-square value because the Fisher's exact test allows us to calculate our probability value directly and for this we're going to use a statistical program ok so I've pulled it up here and we just enter our values and the 4 cells here which I've already done okay and we want to use a Fisher's exact and we want to do a two-tailed as well and then we hit calculate and like I mentioned before for the Fisher's exact it directly calculates a p-value so our two-tailed p-value is equal to one and so this is greater than 0.05 and so this means there is no association between gender and medication use and so it's considered to not be statistically significant so again since our p-value is equal to one which is greater than 0.05 there is not a statistically significant association between gender and pain medication used and our next set of lectures we're going to look at the McNamara and Cochran Q test

Channel: Katrina McGonigal

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Length: 5min 12sec (312 seconds)

Published: Mon Feb 02 2015