ANOVA/One Sample t test question

[noetsi]

It has been too long since I studied this....

I have a statewide variable which can be split into 6 regions (that is the the statewide results can be apportioned into 6 regions). I want to know if the mean of the six regions varies signficantly from the statewide mean. I think you can do this with a one sample t test - just run the HO for that test as what the statewide mean is and see if the regions vary signficantly from that.

I think you would have to generate the state mean by the mean of the individuals (not the mean of all the raw data which will normally lead to different results) because that is how t-test means are generated, but I am not sure. That is Counts/days +counts/days +.... for all individuals rather than sum(counts) divided by sum (days).

I am trying to figure out how you would run this in ANOVA. I don't want to know if the mean of the regions vary from each other, which would be simple. I want to know if the means of the areas vary from the statewide average of which they are a part.

[noetsi]

Perhaps you can merge the SAS question I asked here as it is on the same topic?

After a conversation on that thread I have a more basic question. You have a state mean, based on a sample. You want to know if (from a sample) a region in that state's mean is close enough to the state mean to be said to be the same population. Is there a t-test that even addresses this? I thought a one sample t-test would, but I am less sure now. I am confident an independent t test won't work (they are not impendent) and it would not be a paired t-test because the region would be a subset of the state numbers. Not the same units exactly.

[Dragan]

It has been too long since I studied this....

I am trying to figure out how you would run this in ANOVA. I don't want to know if the mean of the regions vary from each other, which would be simple. I want to know if the means of the areas vary from the statewide average of which they are a part.

I would say an easy way to approach your problem would be to use PROC REG (or GLM) with Effects Coding. This approach will directly answer your question.