Calculate Std Error of Percent manually

[Barkat]

Below is a table from SAS result. What formula was used to calculate the "Std Err of Percent" in this table?

I know, SE of percent = (True percent - observed percent)/True percent. I believe the "Percent" column has the observed percent (correct me if I am wrong). I thought true percent for Male-Negative is 1*100/9=11.1%. So, SE of percent=(11.1-7.5605)/11,1=0.3189. But the table shows 7.5159. My brain is not working. Please help.

Gender	Result	Frequency	Weighted Frequency	Std Err of Wgt Freq	Percent	Std Err of Percent	95% Confidence Limits for Percent
Male	Negative	1	16.20746	16.20746	7.5605	7.5259	0.0000	22.6253
	Positive	4	64.82982	31.56546	30.2419	14.4387	1.3398	59.1441
	Total	5	81.03728	34.96896	37.8024	15.9078	5.9594	69.6454
Fem	Negative	3	100.00000	56.73086	46.6482	18.0779	10.4613	82.8350
	Positive	1	33.33333	33.33333	15.5494	14.1520	0.0000	43.8778
	Total	4	133.33333	64.91964	62.1976	15.9078	30.3546	94.0406
Total	Negative	4	116.20746	58.52508	54.2087	17.5366	19.1054	89.3120
	Positive	5	98.16316	45.08850	45.7913	17.5366	10.6880	80.8946
	Total	9	214.37061	71.16743	100.0000

[ballardw]

Show starting data in the form of a data step.

Show the code for creating that output.

Then we have some clue of what is going on.

[Barkat]

Example of a starting data and SAS code are mentioned below. Actually, I am curious, what formula was used to calculate the "Std Err of Percent" in the back end?

data have;                      
   input ID Gender $ Result $;     
   datalines; 
1 Male  Positive
2 Male Negative
3 Female Negative
4 Female  Negative
5 Male  Positive
6 Male Positive
7 Female Positive
8 Female  Negative
9 Male  Positive
;  

Data have; set have;
if Gender="Male" then Prob=0.0617;
if Gender="Female" then Prob=0.0300;
Wt=1/Prob;
run;

proc surveyfreq data=have;
table Gender*Result  /  cl; 
Weight wt;
run;

[SAS_Rob]

This appears to be output from Proc SURVEYFREQ which means the standard errors are calculated factoring in the design effect (strata, cluster and weight).  There are a number of different methods (controlled by the VARMETHOD= option on the SURVEYFREQ statement) for calculating them so I would suggest you reference the documentation:

SAS Help Center: Proportions