Hello, Mr. Tarrou again.
Ok, we are going to take a look at "Simpson's Paradox".
This is going to finish our discussion of
Umm, Kind of analyzing two way tables.
Uh. I say kind of analyzing two way tables because we will. Uh.
When we analyze two way tables, and we're looking for a relationship between two categorical variables
We're not actually going to be able to test, that there is an association between those variables until
we get to much, much later in the textbook, and we learn something called "chi-squared goodness of fit test"
So, um, you know we just got done with a video. We did a bunch of row and column percents
and conditional probabilities. And just sort of looked at them
And, you know, noticed that there was some patterns maybe going on between a couple of categorical variables
Where you might say like, in the last video. It seemed that the higher your education level was, the more money you made overall.
Which, we certainly hope is true since we're in college and in honors math classes.
So, that does lead us into though, you know. We talked about lurking variables.
Where there is the common response lurking variable, and the confounding lurking variable.
If you don't remember those, you should go look them up because they're some vocab words you're still supposed to know.
Well. This idea of, um, lurking variable kind of comes up in something called "Simpson's Paradox".
That's when you're looking at a two way table. At least that's the way I'm going to define it.
And there's an observed association, you might noticed something going on.
And, uh. Let's say. I pulled some information off the internet, on the wiki site.
About, uh. Success of removing kidney stones, and I'll have that reference on my description of this video>
And, you know theres two types of treatments. I didn't discuss what that really was.
But we're looking at removing kidney stones and "Treatment A" has a success rate of 78%.
And "Treatment B" has a success rate of 82%. Well, now doing column percents of course
because we believe that the treatment method is going to help determine, or explain, whether or not the removal of the stones was successful.
So we're doing problem percents. Uh, 273 divided by 350 is 78%, and so on to get 82%.
Well if i just looked at this. I would say I want "Treatment B" cause that looks better.
Well, we have an observed association in a two way table, uh. And that is observed association is reversed when a lurking variable is revealed in a three way table.
Now, a three way table is simply just two, two way tables.
and by the way, a two way table again. We have a type of treatment, and a success. Or a success rate.
Those are you're two variables. Hence the name "Two way table."
Now if I come over here and cover that, and I reveal this three way table. Now what's the three way table?
Well. We've got now the variable of, is it a large or small stone we have.
And so under the small stone we're going to have
our original two variables of treatment type and
whether or not there was a success or failure.
And we're going to have that same two way table
or, different numbers, but the same type of design
the same, two way table under large kidney stones.
So we're making a two way table of just treatment and success rate into a three way table
being the size of the stone, the treatment type, and then the success rate. So we have three variables in this table.
Hence, it's called a three way table. Well under small stones "Treatment A." Again we expect the treatment to help explain the success rate.
So we're doing column percents.
Of we had 87 patients get "Treatment A"
And 81 out of 87 were successful. So that 93%.
And in "B" we had 270 patients. 234 were successful
and that's 86.7%. Uh, same thing with the large.
We have 73% success rate for the large stones
for "Treatment A."
And we have a 69% success rate for removing those
large kidney stones for "Treatment B"
Now, look at these success rates, and how in the three way table "Treatment A" is better for the small stones
Or at least it has a higher success rate. And it's also higher for the large stones.
Which, of course, are going to be tougher to remove. Hence the lower rates overall.
Compared to the two way table we just looked at a second ago. Where when we clumped it all together
and we had all the stones, both large and small, in the same grouping. And we're kind of hiding that variable.
That lurking variable. It would appear to be a lurking variable in this table. "Treatment B" is better, has a higher success rate.
That's "Simpson's Paradox". You observe something in a two way table, and all those results reverse when you reveal that lurking variable in a three way table.
WHOOOOOOOO!!! BAM!
Hope these are helping. Go do your homework.
Mr. Tarrou out.