So I’m presenting an example today similar to the one that I’m also giving at an elementary school showing students exactly what the heck do biostatisticians do. And that is using something called a Fisher’s exact test to see if the distribution of categories between two groups are the same or not. Now, I’m using candy bars for my elementary school presentation but I’m going to use something here that is even more fun and yummy. An example from my trilogy!! Oh, come on! You just know that’s more fun and yummy. Don’t lie! So say, we have Tina again and we again want to determine the kind of dimension she is in. And if she’s in a good dimension, she’s probably working at that computer store in that shopping center with the cool Barnes & Nobel where she can order the Order of The Dimension series. But if she’s in a bad dimension, she’s probably doing something like basking in the sun at a tropical resort. Now, let’s say that in 5 out of 6 good dimensions, she’s at the shopping center but in the last good dimension, she’s also at an island resort on the weekend. But in 18 out of 20 bad dimensions, she’s at the resort — which might be nice — if that’s your cup of tea — but in the other 2 dimensions, she’s also at a shopping center, ordering a series of … you know. So comparing the numbers that she is at the resort on the weekend, we have 1/6 vs. 18/20 and applying the Fisher’s exact test, using the fancy formula given here, we get a p-value 0.03 which is less than 0.05. Which means the chances of being at the resort versus the shopping center between the good and bad dimensions appear to be significantly different. But we’ll cover more on significance and the p-value next time. Till then, don’t you just want to go to that Barnes & Nobel at your local shopping center and order your very own series of Order of The Dimensions or would you really prefer to spend your weekend here?
Yeah. Though so! B&N for the win! Don’t lie!
So now we know how to map values from one matrix to another, we might want to see mapping one column could effect mapping another column. The problem is that sometimes we don’t know how the columns interact with each other though. In other words, we don’t know their joint distribution. We might have a hunch about the joint distribution if we look at the pairwise correlation between two variables. So, say Randy wants to get the 411 on which dimension he is in based on where Tina is employed — if she is employed in that realm. So say he looks at the Houston and Indianapolis realms and sees that she’s employed at a computer store or a printer store. And since she works at those stores in justified dimensions, he can further deduce that it is a good dimension and Tina is in fact employed by good Anton. Or is he … meaning Anton being good or … well, you know how to find out by now! And yeah, Tina might have a more exciting life in the unjustified dimension … but does she have access to a nearby Chipotle there? Or a Barnes & Noble where she could order a copy of the Order of The Dimensions series? Or an AMC theater showing the Order of the Dimensions movie or … yeah, I’ll stop. But anyway, the point is working at a computer or printer store at a shopping center has its benefits. Like she’s most likely near a CVS or Walgreens where they may also carry DVDs of … well, you get the picture. But still, you can always check out the Order of The Dimensions series at Barnes & Nobel until next time!
So finally we get to cover the gist Barton and Schruben stuff! Or so I hope … Anyway, lets saw Randy narrowed Anton being down to Phoenix, Houston, New Orleans, and Atlanta. What? So what if I mentioned Phoenix and New Orleans like last time? Randy can catch Anton as part of promotion APS-tied in’d … whatever. Moving on … lets say Randy further got word that scientists then narrowed down Anton’s location to Houston or New Orleans and the exact location can be pinpointed from the relative distance of Phoenix (designated as a 0) and Atlanta (designated as a 1), depending on a number. So lets say the number was 1/4 which is closer to 0 which is closer to Phoenix. Well, Houston is closer to Phoenix than New Orleans is so Anton just have been in Houston. But if the number was 3/4, or closer to 1, or closer to Atlanta … and New Orleans to closer to Atlanta than Houston is … Anton would probably be in New Orleans! Of course Houston and New Orleans are closer to each other than to either Phoenix or Atlanta and not all the distances are equidistant as the eCDF predicts and you’re getting confused again, aren’t you? Sorry! But basically since the cities are not equidistant to each other, we can map their actual location using another distribution, say a normal distribution concentrated on the center. But more about that next time. So where exactly does Randy find Anton? Well, not gonna tell ya but since Mardi Gras is coming up, thought I’d leave you with this pic of gold ole Bourbon Street.
Now, who wants some gumbo?