This may seem pedantic, but given that this post is on the importance of precision:
“Some likely died.”
Should be
“Likely, some died”.
Also, I think you should more clearly distinguish between the two means, such as saying “sample average” rather than “your average”. Or use x bar and mu.
The whole concept of confidence is rather problematic, because it’s on the one hand one of the most common statistical measures presented to the public, but on the other hand it’s one of the most difficult concepts to understand.
What makes the concept of CI so hard to explain is that pretty every time the public is presented with it, they are presented with one particular confidence interval, and then given the 95%, but the 95% is not a property of the particular confidence interval, it’s a property of the process that generated it. The public understands “95% confidence interval” as being an interval that has a 95% chance of containing the true mean, but actually a 95% confidence interval is an interval generated by a process, where the process has a 95% chance of generating a confidence interval that contains the true mean.
the concept of CI so hard to explain is that pretty every time the public is presented with it
Not just the public, but scientists and medical professionals have trouble with it.
People tend to interpret frequentist statistics as if they were the Bayesian equivalents e.g. they interpret confidence intervals as Credible Intervals.
I don’t get this (and I don’t get Benquo’s OP either. I don’t really know any statistics. Only some basic probability theory.).
“the process has a 95% chance of generating a confidence interval that contains the true mean”. I understand this to mean that if I run the process 100 times, 95 times the resulting CI contains the true mean. Therefore, if I look at random CI amongst those 100 there is a 95% chance that the CI contains the true mean.
[A]ctually a 95% confidence interval is an interval generated by a process, where the process has a 95% chance of generating a confidence interval that contains the true mean.
Is it incorrect for a Bayesian to gloss this as follow?
Given (only) that this CI was generated by process X with input 0.95, this CI has a 95% chance of containing the true mean.
I could imagine a frequentist being uncomfortable with talk of the “chance” that the true mean (a certain fixed number) is between two other fixed numbers. “The true mean either is or is not in the CI. There’s no chance about it.” But is there a deeper reason why a Bayesian would also object to that formulation?
This may seem pedantic, but given that this post is on the importance of precision:
“Some likely died.”
Should be
“Likely, some died”.
Also, I think you should more clearly distinguish between the two means, such as saying “sample average” rather than “your average”. Or use x bar and mu.
The whole concept of confidence is rather problematic, because it’s on the one hand one of the most common statistical measures presented to the public, but on the other hand it’s one of the most difficult concepts to understand.
What makes the concept of CI so hard to explain is that pretty every time the public is presented with it, they are presented with one particular confidence interval, and then given the 95%, but the 95% is not a property of the particular confidence interval, it’s a property of the process that generated it. The public understands “95% confidence interval” as being an interval that has a 95% chance of containing the true mean, but actually a 95% confidence interval is an interval generated by a process, where the process has a 95% chance of generating a confidence interval that contains the true mean.
Not just the public, but scientists and medical professionals have trouble with it.
People tend to interpret frequentist statistics as if they were the Bayesian equivalents e.g. they interpret confidence intervals as Credible Intervals.
I don’t get this (and I don’t get Benquo’s OP either. I don’t really know any statistics. Only some basic probability theory.).
“the process has a 95% chance of generating a confidence interval that contains the true mean”. I understand this to mean that if I run the process 100 times, 95 times the resulting CI contains the true mean. Therefore, if I look at random CI amongst those 100 there is a 95% chance that the CI contains the true mean.
Is it incorrect for a Bayesian to gloss this as follow?
I could imagine a frequentist being uncomfortable with talk of the “chance” that the true mean (a certain fixed number) is between two other fixed numbers. “The true mean either is or is not in the CI. There’s no chance about it.” But is there a deeper reason why a Bayesian would also object to that formulation?