Dear Steemers, this is my first post in Mathematics and it will be easy to understand and to apply in your everyday life even if you are not good at Math.

I'm doing math in everyday life to analyze the results and I always have to keep one thing in my mind.

Is this something real, or it's just a coincidence?

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This question is not easy to answer and it can be misleading to many people, even to trained scientists.

It's more dangerous if this lack of intuition is used against you by the fraudsters who relly on your uncertainty and fear.

This is the formula:

Source

And this is the Link to practical calculator

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Open it and let's play together!
Type N = 12 (size of the sample) and p = 0.5 (probaility 50-50)

Imagine that you have a very small group, that consists of only 12 members, patients, whatever you imagine.

Twelve is a good number, for example, number of your close relatives.

Imagine that something happens, with the probability of 50 %.

What do you think, what is the probability that something happens to all of you?

Maybe 50 % ? No... It's way too high

Maybe 1 %? No, it's still too high

Maybe 0.1 %? You are close now, but it's even less

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Now let's type the number 9 in the calculator, what do you see?

What is the intuition telling you now?

Something with the 50% probability stoke 10 of 12 people in your group.

It can't be just a chance? Have we done something wrong?

The probability is 2 %. This is relatively difficult to expect by pure chance.

Than 8 of 12 is similar, right?

Wrong!

The probability is 20 % now and you are probably seeing the pure coincidence!

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Additional scenario:

You split into two groups, 5 and 7.

You can choose A or B. Both A and B comes with 50 % of chance.

The smaller group is choosing A and gets 4 positive results from 5 members.

The larger group is choosing B and gets 5 positives out of 7 members.

Both groups can be fooled that they made a good choice!

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For both groups, the probability that they found the pattern where there is no pattern is about 20 %.

It is actually more probable than to roll the dice and get number 6.

What do you think,

is it possible/ probable that the groups are fighting about who is right, and all they are fighting about is pure coincidence?

Let's calculate, 20 % or 0.2 for the First Group and multiply that with 0.2 for the Second group

Probability is 4 % !

It's more probable than to throw two dices and get 6 and 6.

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Bad math shown in this simple text made the hype about the vaccines and autism, 20 years ago

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Wakefield, Andrew J., et al. "RETRACTED: Ileal-lymphoid-nodular hyperplasia, non-specific colitis, and pervasive developmental disorder in children." (1998): 637-641. Link