#SIGMAPLOT 11 DO NOT TEST BONFERRONI CODE#

(If you run the code below youвЂ™ll probably get a slightly different but similar answer.)ДЁ-sample test for equality of proportions without continuity correction We get about 20%, confirming our calculations. R treats TRUE and FALSE as 0 or 1, so calling mean on results returns the proportion of TRUEs in the vector. This returns a vector we save as вЂњresultsвЂќ that contains TRUE or FALSE for each replicate. We then apply a function to each column of the matrix that runs 10 one-sample proportion tests using the prop.test function and saves a TRUE/FALSE value if any of the p-values are less than 0.05 (we talk more about the prop.test function below). This produces a 10 x 1000 matrix of results that we save as вЂњcoin.flipsвЂќ. First we replicate 1,000 times the act of flipping 10 fair coins 10 times each and counting the number of heads using the rbinom function. In other words, do we get any p-values less than, say, 0.05? Flip 10 coins 10 times each, get the proportion of heads for each coin, and use 10 one-sample proportion tests to statistically determine if the results we got are consistent with a fair coin. We can think of this as doing multiple hypothesis tests. The probability of observing 0, 1, 9 or 10 heads when flipping a fair coin 10 times is about 2% which can be calculated in R as follows:ДЎ - (1 - pbinom(q = 1, size = 10, prob = 0.5) * 2)^10 As we said, the chance of this happening is low in a single trial, but we increase our chances of it happening by conducting multiple trials. It just so happened we were very unlucky to witness such an unusual event. If it happened to us we may conclude the coin is unfair, but that would be the wrong conclusion if the coin truly was fair. Think of flipping a fair coin 10 times and getting 9 or 10 heads (or 0 or 1 heads). When we run a hypothesis test, we always run a risk of finding something that isnвЂ™t there. rejecting a null hypothesis that should not have been rejected. Making multiple comparisons leads to an increased chance of making a false discovery, i.e. The outcome of these pairwise comparisons will hopefully tell us which schools have significantly different proportions of students flossing. But where are the differences? This leads us to pairwise comparisons of proportions, where we make multiple comparisons. If we reject the null, we have evidence of differences. The null would be no difference between the proportions versus some difference. An obvious first step would be to conduct a hypothesis test for any differences between these proportions. When finished weвЂ™ll have 8 proportions of students who answered вЂњYesвЂќ. LetвЂ™s say we go to 8 high schools in an area, survey 30 students at each school, and ask them whether or not they floss their teeth at least once a day. We sometimes want to make pairwise comparisons to see where differences occur.

Sigmaplot 11 do not test bonferroni