How to compare the mean difference between two groups if the value of each individual is percent

[SteveDenham · Accepted solution]

Well, if you know both the numerator and denominator for each estimate, and since the numerators are all > 40, then you could use:

proc genmod data=yourdata;
class group;
model numerator1/denominator1 = group /dist=binomial type3;
lsmeans group/diff ilink;
run;

Where numerator1 and denominator1 are the values for activity_1, and would be replaced by numerator2 and denominator2 for activity_2.  Since it seems from your communications that the denominator would be the same for both activities because it is the enrollment at the school, you could simplify a little bit.

SteveDenham

[SAS-questioner]

Thank you so much! I have one last silly question, do you know what's this test called? It's clearly not a T-test, is it binomial test?

[SteveDenham]

It is a generalized linear model with a binomial distribution and a logit link.

Or

Logistic regression.

SteveDenham

[SAS-questioner]

Hi, Steve, I am wondering could you please tell me what is different from this methods that you posted to 'dist=poisson"? If the rate is the thing that I want to compare, when should I use "binomial" and when should I use "poisson"?

[SteveDenham]

Binomial distribution: bounded below by zero, above by 1 (inclusive at both bounds). It is the proportion (or rate) of subjects (or trials) having a given characteristic divided by the number of subjects (or trials) observed (N). The variance is a function of the proportion (=N*p*(1-p)).

Poisson distribution: bounded below by zero (inclusive). It is the count of subjects having a given characteristic. The population variance is equal to the population mean.

SteveDenham

[Ksharp]

Steve,
I think Poisson Distribution is used for low probability event,like insurance's claim probability.
While Logistic Regression is used for normal probability(not too small), otherwise need EXACT logistic model or Penalty Logistic model .

[SAS-questioner]

Like I replied above, the activity_1_rate is computed by using the number of students who participated in activity 1 divides the total number of students.

[Ksharp]

Then you can use Non-parameter method Wilcoxon test in PROC NPAR1WAY .

[Ksharp]

https://support.sas.com/kb/24/188.html