How to NOT use statistics

This is sort of an open ended question but I wanna be clear. Given a sufficient population you might be able to learn something (this is the open part) but whatever you learn about your population, when is it ever applicable to a member of the population?

From what I understand of statistics it’s never applicable to a single member of a population, however, all to often I find myself in a discussion where the other person goes “I read that 10% of the world population has this disease” and continue to conclude that every tenth person in the room has this disease.

I understand that ten people in this room is not a big enough sample for the statistic to be relevant but apparently a lot don’t.

Then there’s this thing about large enough samples. You only need to probe a large enough population to get reliable statistics. This though, isn’t it proportional to the complexity of the statistic? If I’m measuring something that’s very rare, doesn’t that mean I need a much bigger sample to be able to determine the relevance for such a statistic?

The thing is, I truly question the validity of any newspaper or article when statistics is involved, they way it’s used to build confidence.

That’s a bit of background.

Back to the question, in what ways can you NOT or may you NOT use statistics to form an argument. I negated the question because I’d like to find out more about common misconceptions regarding statistics.

Answer

To make conclusions about a group based on the population the group must be representative of the population and independent. Others have discussed this, so I will not dwell on this piece.

One other thing to consider is the non-intuitivness of probabilities. Let’s assume that we have a group of 10 people who are independent and representative of the population (random sample) and that we know that in the population 10% have a particular characteristic. Therefore each of the 10 people has a 10% chance of having the characteristic. The common assumption is that it is fairly certain that at least 1 will have the characteristic. But that is a simple binomial problem, we can calculate the probability that none of the 10 have the characteristic, it is about 35% (converges to 1/e for bigger group/smaller probability) which is much higher than most people would guess. There is also a 26% chance that 2 or more people have the characteristic.

Attribution
Source : Link , Question Author : John Leidegren , Answer Author : Greg Snow

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