interpretation confidence intervals for proportions

[mjkop56]

I'm conducting an analysis of survey data. The below tables (note - data is made up!!) shows, of each education category, the percentage of males and females. For example, of those with high school degree, 40% are male and 60% are female (40%+60% = 100%). The table also shows the standard errors and confidence intervals. The goal is really to just try to get at the reliability of the proportions. Two questions:

1. I'm not very familiar with SEs and CIs around proportions. Does it make sense to show the SEs and CIs around the proportions of females and males each individually when the proportion of female+male = 100%? Is there anything inherently wrong with this table?

2. Does it make sense to compare the CIs across any of these categories? I'm under the impression that one needs a statistical test to deduce statistical significance.

3. Thanks in advance for any help. (Note - cross posted to statsexchange but no responses)

	Male			Female
Education	Weighted proportion	SE	95% CI	Weighted proportion	SE	95% CI
Graduate or professional	70%	2.0%	64%-75%	30%	1.3%	25%-35%
Bachelors	65%	1.0%	45%-70%	35%	1.0%	30%-40%
Associate’s	55%	1.2%	50%-65%	45%	1.6%	40%-50%
Some college, no degree	45%	2.0%	40%-50%	55%	1.7%	50%-60%
HS graduate	40%	1.3%	30%-50%	60%	1.2%	55%-65%

[ballardw · Accepted solution]

I would expect to see such detail if I had 3 or more categories such as with race or age groups. If you have a strictly binomial proportion then would would expect the P of 1 to be 1-P of the other and the confidence limits to be similar. There might be just be sufficient rounding but I would expect for the first row with a CI of (64%-75%) to have the (25%-36%) for females and would disbelieve the 2nd, 3rd and 5th row CIs because of differences. The upper limit of one should be very close to 1-lowerlimit of the other.

[mjkop56]

Thank you. The actual data in the table was made up, I was just trying to get feedback on the way of presenting the data. Does it make sense to show the CIs for both males and females here for each category of education? Is there anything wrong with this way of presenting the data? Is it better just to show the data for females only for example? (since you can deduce from that the data for males?)

[SAS_Rob]

>>>2.Does it make sense to compare the CIs across any of these categories? I'm under the impression that one needs a statistical test to deduce statistical significance.

No, you should not compare the confidence intervals to see if they intersect when wanting to test for differences.  If you want to test for differences then you can use one of the approaches in this usage note

22565 - Testing for differences in a two-way table with a significant chi-square (sas.com)

[mjkop56]

thank you!