t-test for dependent samples

[mandan414]

Hello,

I'm estimating the health indicators among provincial populations, and would like to compare them with the estimations from total population in Canada. So, the populations samples would be dependent, since the provincial populations are included in the total sample size. Is there any t-test I can do in SAS? Or in SUDAAN?

Thank you,

Mandana

[PaigeMiller]

Are you assuming that the national numbers are known, and you are estimating the provincial numbers from your sample of the population? 

Or are you estimating both national and provincial numbers from a sample?

[mandan414]

I have the national numbers and then categorize it to the provincial samples by an index.  

[PaigeMiller]

Yes, but are the national numbers from the same study as the provincial numbers? Or can you assume that wherever these national numbers come from, they are "fixed" or "known"?

[mandan414]

We have a sample represents national number and we disaggregate it using an index. In this way, we are comparing sub sample vs sample or doing overlapping comparison. Thanks. 

[PaigeMiller]

I don't know what this means:

We have a sample represents national number and we disaggregate it using an index.

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Can you explain how the study was conducted and how the statistics are arrived at?

[mandan414]

Let's say it in this way:

we have a sample of a population and then disaggregate it to sub samples.  How to do the test of significant between the estimations for sample vs subsample? For example, we have a sample of population and calculate the average blood pressure for the population. Then, we disaggregate the population by age and estimate the average blood pressure for each age group. Finally, we would like to test whether the difference in average blood pressure between each age group vs the total population is significant.  Thank you.

[PaigeMiller]

A common test is the One-way Analysis of Variance test, where you compare each group's mean to the overall mean. However, since you are working with survey data, I think PROC SURVEYMEANS would work. Here is an example that is similar to yours: https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_surveymeans_examples06.htm

I believe you can also get the exact statistical tests you want from PROC SURVEYREG with a CLASS statement and the SOLUTION option in the MODEL statement.

[mandan414]

Thank you for the response.

The example you sent is the test between the subgroups. I need to test the total group vs the subgroups.

I found this one but not quite sure whether ANOM is for survey data or not.

https://communities.sas.com/t5/Statistical-Procedures/Statistics-for-comparing-a-population-with-a-s...

Thanks again.

[PaigeMiller]

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@mandan414 wrote:

The example you sent is the test between the subgroups. I need to test the total group vs the subgroups.

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I disagree. If you scroll down, you will see plots where clearly each group are compared to the full sample.

I found this one but not quite sure whether ANOM is for survey data or not.

https://communities.sas.com/t5/Statistical-Procedures/Statistics-for-comparing-a-population-with-a-s...

I don't think ANOM exists in the survey case. But  PROC SURVEYREG will produce statistical tests of the group means to the overall mean.

[mandan414]

You mean we can use PROC SURVEYREG for the test of significant for the proportion estimations of total sample vs subsample?

I used PROC SURVEYREG for the test of association before but not for the cases like this. Sorry, I'm not an statistician and my questions may seem basic. 

Thank you.

[PaigeMiller · Accepted solution]

Yes, SURVEYREG should be able to do the statistical test you have asked for.

If you add the SOLUTION option to the MODEL statement, it will compare the regression coefficient to zero ... which in this case, is statistically the same as comparing the mean of a group (province mean) to the overall mean (national mean). Here is an example (but you have to add in the SOLUTION option): 

https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_surveyreg_examples08.htm

[mandan414]

How about I want to do the comparison of proportions as well. For example the proportions of sub populations with university education vs the proportions of total population with university education. Thank you. 

[PaigeMiller]

PROC SURVEYLOGISTIC

[mandan414]

Thank you!