topic Re: CLM too large? does it make sense? in Statistical Procedures

CLM too large? does it make sense?

smsm15 — Mon, 13 Nov 2023 20:17:40 GMT

hello,

taking the mean of a variable that is 5 level 0,25,50,75,100 for specific populations.

In this population there are only two people with the exposure so n=2 out of 500 and therefore only they can have a mean variable (variable I taking the mean of is amount of outcome per exposure). using proc means clm I am getting such a large confidence interval for this population while the rest are fine. does this statistically make sense due to how small the population is? it just seems outrageous.

CI: (-292.66, 342.66)

mean= 25, obs1=0, obs=50. standard dev=35.36 standard error =25

Re: CLM too large? does it make sense?

PaigeMiller — Mon, 13 Nov 2023 22:06:53 GMT

I get those answers too!

data have;
    x=0; output;
    x=50; output;
run;

proc means data=have n mean std stderr clm;
    var x;
run;

According to Wikipedia and many (all?) textbooks, the formula for a confidence interval for the mean is

so I leave it up to you to plug the numbers in, plus determine the value of c from appropriate t-distribution tables, and compute for yourself if those numbers are correct, and why (or why not). If you think it is wrong, show us your calculations.

Re: CLM too large? does it make sense?

ballardw — Mon, 13 Nov 2023 22:07:08 GMT

Small sample => wide confidence limit to be confident. So two values of 0 and 50 will generate that result.

The large limits are coming from the t-score portion of the calculation which is pretty large for that sample size.

Re: CLM too large? does it make sense?

SteveDenham — Tue, 14 Nov 2023 19:04:26 GMT

As @ballardw says, it comes from the t distribution part. I get 12.71 for a two-tailed t value of 0.05. With a standard error of 25, then a half interval is 12.71*25 =317.25, so your confidence bounds around a mean of 25 would look like -292.25 to 342.25. A more precise t value will yield what you are seeing.

SteveDenham