R Tutorial: Counts vs. proportions

Key Takeaways

you may have noticed in the last exercises that sometimes raw accounts of cases can be useful but often it's the proportions that are more interesting we can do our best to compute those proportions in our head or we could do it explicitly let's return to our table of counts of cases by identity and alignment if we wanted to instead get a sense of the proportion of all cases that fell into each category we can take the original table of counts saved as tab underscore CNT and provided as input to the prop table function we see here that the single largest category is characters that are bad and secret at about 29 percent of characters also note that because these are all proportions out of the whole data set the sum of all these proportions is 1 if we're curious about the systematic associations between variables we should look to conditional proportions an example of a conditional proportion is the proportion of public identity characters that are good to build a table of these conditional proportions add a 1 as the second argument specifying that you'd like to condition on the rows we see here that around 57% of all secret characters are bad because we're conditioning on identity it's every road that now sums to 1 to condition on the columns instead you can change that argument to 2 now it's the columns that sum to 1 and we learn for example that the proportion of bad characters that are secret is around 63% as the number of cells in these tables gets large it becomes much easier to make sense of your data using graphics the bar chart is still a good choice but we're going to need to add some options here's the code for the bar chart based on comps we want to condition on whatever's on the x-axis and then stretch those bars to each add up to a total proportion of 1 so we add the position equals fill option to the Giambi our function let's add one additional layer it changed to our y-axis to indicate that we're looking at proportions when we run this code at the console we get a plot that reflects our table of proportions after we had conditioned on ID while the proportion of secret characters that are bad is still large it actually it's actually less than the proportion of bad care ders and those that are listed as unknown we get a very different picture if we condition instead on alignment the only change needed in the code is to swap the positions of the names of the variables this results in a plot where we've conditioned on alignment and we learned that within characters that are bad the greatest proportion of those are indeed secret this might seem paradoxical but it's just a result of having different numbers of cases in each level okay now you try experimenting with conditional proportions