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Posts: 58

# Statistics for comparing a population with a subset of that population

Hi SAS Users,

I am conducting an analysis that requires comparing mean differences between a population vs. a subset of the sample population. For example, let us assume that we are looking at test scores from different states in the USA. What I am looking to compare is the weighted mean across the whole of USA vs. mean for Massachusetts. The issue is that t-test (paired or unpaired) is not appropriate as Massachusetts scores contribute to the weighted mean across USA. Any suggestions and/or appropriate resourceswill be much appreciated.

Best,

Pronabesh

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Solution
‎03-25-2015 08:43 PM
Contributor
Posts: 58

## Re: Statistics for comparing a population with a subset of that population

I found the solution in Peter Westfall's book "Multiple comparisons and multiple tests". We can use analysis of mean to compare the above mentioned. Such comparisons are similar to comparisons with controls, in that there are fewer comparisons; but they differ in that there is no prespecified control. Instead the comparison is with the overall average, which is computed as a weighted average of individual means, the weight for each being inversely proportional to the variance. This analysis is known as "Analysis of Means" or ANOM.

proc glm data=have;

class group;

model outcome=group;

lsmeans group/tdiff=anom;

run;

In case anyone finds this interesting!

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Solution
‎03-25-2015 08:43 PM
Contributor
Posts: 58

## Re: Statistics for comparing a population with a subset of that population

I found the solution in Peter Westfall's book "Multiple comparisons and multiple tests". We can use analysis of mean to compare the above mentioned. Such comparisons are similar to comparisons with controls, in that there are fewer comparisons; but they differ in that there is no prespecified control. Instead the comparison is with the overall average, which is computed as a weighted average of individual means, the weight for each being inversely proportional to the variance. This analysis is known as "Analysis of Means" or ANOM.

proc glm data=have;

class group;

model outcome=group;

lsmeans group/tdiff=anom;

run;

In case anyone finds this interesting!

Established User
Posts: 1

## Re: Statistics for comparing a population with a subset of that population

Thank you very much for the reference provided and sas codes. It is very helpful. Do you know any alternatives to this command for binary outcomes? For example, if we want to know whether people with knee pain at baseline were more likely to reply to the follow-up questionnaire. Then we have the total population at baseline and subset of responders. Outcome is binary (knee pain y/n).

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