Never confuse "sensitivity" and "specificity" again!
Here's how I keep them straight. π
First some background. There are four categories of test results:
[Skip this tweet if you already know this part!]
TP: Tested positive, Infected
FP: Tested positive, Uninfected
FN: Tested negative, Infected
TN: Tested negative, Uninfected.
Sensitivity is how "sensitive" the test is meaning "does it pick up all the cases?" What's another name for the cases detected by the test? The true positives! Therefore, another name for the sensitivity is the *true positive* rate. It's the percent of cases detected by the test.
Now ask yourself, what's the easiest way of making sure you pick up all the cases? Just say everything is a positive! Why is that bad? Because it would lead to a bunch of false positives. A good test needs to be *specific*. So specificity and *false positives* are linked.
So just to recap: 1. The sensitivity is about being sensitive enough to pick up all the cases 2. The specificity is about making sure the test is *specific* to the cases and doesn't pick up a lot of non-cases as well
If you don't care about the math. You can stop here.
There's a twist that you just have to memorize. The specificity *is* related to the false positive rate (FPR)* but* it's 1 - FPR. In my opinion, it's misnamed, but it does technically contain all the information we need to see how specific the test is.
OK. So sensitivity is the TPR and specificity is 1-FPR. What can we do with that? Well if you memorize just one more thing. You can write down the formulas for each pretty quickly.
Here's my trick for remembering the TPR, FPR, etc. First, the numerator will always just be the named category. So for TPR, the numerator is "TP". Second, the denominator is always the named category plus its complete opposite (T to F and P to N). So the denominator is TP+FN.
This is a general trick. As soon as I see FPR, I know FP will be in the numerator right away. I can immediately follow that up by writing FP in the denominator plus the complete opposite of FP which is TN.
Now that I have the FPR. I can get specificity since it's just 1-FPR. So, that's it. That's my thought process for quickly remembering the difference between specificity and sensitivity, and writing down the formulas.
Extra Credit: If you simplify the formula for 1-FPR, you might notice it's the same as the formula for the TNR. The negative sign in 1-FPR means we should reverse the categories. The T becomes an F and the P becomes an N. Therefore, TNR = 1-FPR. (This is another general rule).
Once you realize the specificity is just the TNR, we can use our trick again to quickly write down the formula (which is the same as the specificity).
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Your rapid test is positive. Does that mean you have covid?
Here's the math you need to figure it out. A thread. π§΅
Let's define some terms that you might have heard of.
A "true positive" means the test result was positive and the person tested does indeed have covid.
A "false positive" means the test was positive but the person doesn't have covid.
A "true negative" means the test was negative and the person tested doesn't have covid.
A "false negative" means the test was negative but the person does have covid.
Got it? Good!
Imagine somebody tweets that they think men on dating apps are jerks.
A commenter asks, "Do you have any peer-reviewed publications to back up your claim?"
The tweeter says they don't.
The commenter then accuses them of knowingly spreading misinformation.
I call this kind of thing a "claim escalation" and I think it's usually a jerk move. The original person tweets something that we all know to take with a pinch of salt. But responders pretend the the tweeter's claim is more than it is as a way of silencing their perspective.
Here's another example. Imagine somebody says that when they have a tummy ache, they find that warm soup stock often helps. If this person has no medical basis for this claim, would we be justified in calling them out for spreading potentially dangerous medical misinformation?
How did I get this poll with almost 29k responses to balance perfectly? A thread. π
Assuming most people didn't secretly flip a coin, where's the randomness in the poll coming from? I think it comes from three sources:
1. Some folks were genuinely picking randomly
2. Based on the comments, even for folks who used a system, the method they used was very unique to them and therefore really random relative to other people
Hereβs the result of yesterdayβs statistics experiment!
The poll is significantly π biased!
WHY???
A thread.π
Hereβs my plot of the responses as they came in.
With 7291 responses, this is *really* baised. The chances of it being a βfair coin flipβ are basically 0. π Whatβs going on?
As a good data scientists, we can use our qualitative data to help us understand our quantitative data! What qualitative data? The comments! Apparently, some folks tried to think one step ahead of the other respondents.
For a lot of people, mathematics is true in the same way that "Kermit The Frog and Miss Piggy are a couple" is true. It's true in an imaginary world where we have agreed upon rules. If that's how you think about math then it's pretty obvious that "2+2=4".
To me, "2+2=4" means that "2 things + 2 things will always be 4 things no matter what the things are". Turns out this is not technically true. You can create all kinds of mathematical systems and physical situations where 2 things + 2 things is not 4 things.
Just found this. Not sure if @michaelshermer is confusing @nhannahjones with me or somebody else because I never said most of that stuff either. What I will say is I learned from my (mostly white) grad school professors how to construct mathematical systems where 2+2 isn't 4.
If that seems contrary to reason to you then I humbly suggest that maybe you don't understand reason as well as you think you do. I know many of us probably learned in grade school that 2+2=4 but the relevant context is it's basic math that they teach to kids.
My race seems to suggest to people that this is a race thing somehow. It's not. Check out the link for a PhD who's not black and who also agrees that 2+2 is not always 4. As Dr. Hossenfelder puts it, "It's not woke. It's math."