Some of the most common **misconceptions about confidence intervals** are:
* “There is a 95% chance that the true population mean falls within the confidence interval.” *(FALSE)*
* “The mean will fall within the confidence interval 95% of the time.” *(FALSE)*
While I do know the true definition of confidence intervals, I wonder why the above are not true?
In: Mathematics
The true population mean doesn’t fall within the CI you just calculated 95% of the time. Rather, if you repeated your procedure many times, you would find that in 95% of cases, the population mean fell within the CI you calculated in that instance.
For instance, if I simulate many samples of 10 data points that I draw from a Normal distribution with mean 0 and variance 1, and for each sample I calculate a CI around my sample mean, I will find that in approximately 95% of samples, the calculated CI contains 0 (the more samples I draw, the closer this proportion will be to exactly 95%).
Latest Answers