# How to estimate population statistics for each category ?

#### harsh

##### New Member
I have data from a simple random sample having n elements which I’m using to estimate my overall population statistics (mean). My population can be divided into k categories, and I know the composition of my overall population in terms of these categories. As part of my study, I want to estimate the statistic for each category of my population. Unfortunately, I do not have a stratified random sample with me.

Question - Given what I have, is there any way to fairly estimate my population statistic for each category of my population ?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
You say that you have a random sample, which would allow you to have accurate overall population estimates. Next you say you want to calculate this estimate for subgroupings in the population. So is the issue that you do not know which group each person is in within your random sample, correct? If that is the scenario, I cannot see how you could infer the group estimates back to the population sub-groupings. Am I missing anything here?

#### harsh

##### New Member
My question is essentially, since I’m using a random sample (hence unbiased) to estimate the population statistics. Can I use the mean of each sub group within that sample as an unbiased estimate of the respective population subgroups ? The key here is that my estimate should be an unbiased estimate

#### hlsmith

##### Less is more. Stay pure. Stay poor.
If a person has a truly random sample, then yes you can use it for subgroups. If some of the groups are small with some extreme values, you may end-up with a little sampling bias, but not any 'systematic' bias.

P.S., True random sampling can be hard to achieve when respondents have autonomy/choice.

#### galegirly

##### New Member
Is what Harsh is describing here not the very basics of survey data statistical analysis. We group respondents into categories using their answers, and infer that the resultant proportions in each category are a reflection of the true make-up of the entire population - and we put some caveats on it - margin of error, and confidence level?