I heard a statistic the other night. I’m not sure of its source, but I wanted to demonstrate a logical fallacy.
The statistic I heard was that 70% of women with metastatic breast cancer were diagnosed with metastatic cancer at initial diagnosis. What this means is that 70% of the women living with metastatic breast cancer were metastatic when diagnosed. What this does not mean is that 30% of women diagnosed with breast cancer are early stage. It also does not mean that 30% of women who are diagnosed early stage will become metastatic.
You see, in each case the denominator is changing. They are independent statistics. In the first you are saying that of all the women with mets today, 70% had mets when they were diagnosed.
The second statistic is about all women. So the numbers are in no way related to one another.
The third statistic is about all women who were diagnosed with early stage breast cancer. So again, the numbers are in no way related to another another.
Each statistics is fundamentally different – they have different denominators. One of the numbers tells you nothing about the other numbers, because the groups involved are fundamentally different.
So, it leaves me wondering, where does the 30% of all breast cancers will progress to metastatic come from? This is a great mystery, but I found myself wondering, is it simply a matter of someone not understanding the math? Someone not understanding that 70% of something does not imply 30% of something different, even if that something different kinda sounds like the opposite of the 70%?
I don’t know, but I’ve learned to be careful when I hear numbers thrown around. So I make no promises that any of the numbers that I’ve stated above are in any way correct numbers. I just wanted to demonstrate the point that it is easy to think numbers are related to one another, when in fact they are completely different statistics.