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Simplest terms: Our sample comes from a true population that we don’t know. Looking at the data we got (primarily the variance and the sample size) we try to i
by throwawayhhakdl 7y ago
Simplest terms:
Our sample comes from a true population that we don’t know. Looking at the data we got (primarily the variance and the sample size) we try to infer what the true population mean is. If the spread is small and the sample size is large, odds are pretty good that our sample mean is close to the population mean. If the sample size is small and the variance in the sample is really high, then odds are good our sample mean is pretty far from the true population mean.
We can quantify that. Basically saying, if the true population mean is x, how improbable would a sample as different as ours have been? When we construct a 95% confidence interval we’re saying “assuming the randomness of my sample is no more improbable than a 1/20 dice roll, the true population should be this far or closer to my sample mean.”
For an intuitive example, consider a 100 sided die going from n to n+100 (e.g. 7 to 107) where we are trying to guess the middle value (n+50) based on a single roll. We get 100. If we want to be 100% confident, the then confidence interval should be 0 to 200 as that’s the range the true value must be in. If we say, nah I’m sure I got it exactly right, your 0% confidence interval is just 100 to 100. If you put on your scientist hat, you say you doubt your particular roll was in the top or bottom 5% of the die, so let’s call it a 90% confidence interval at 5 to 195.
Note that you don’t have any particular reason for that last statement, and you could be wrong.
In other words a 95% interval says here’s the range that the true population mean should be in assuming our particular sample was no more improbable from the truth than 1 in 20. If the null result is in those bounds, in the article, 1.00 (for no effect) then even though your sample mean might be 7%, your data says it wouldn’t be outrageous to get a sample mean of 7% by chance from a true population mean of no effect.