Using two different sampling methods when comparing means. A no go?

#1
Madam:
Sir:
I am currently teaching an introduction course in statistics, and a student asked me a question that confuses me. Let’s say we wish to compare the mean income of residents of two cities. We sample randomly residents in City A while we sample systematically in City B. Can we compare reliably the means of these cities? I would say yes as long as the samples represent well each of their respective cities. Do you agree with this answer?

Best regards,

Yves Claveau
Part-time teacher
Department of Geography, Planning and Environment
Concordia University
 

Karabiner

TS Contributor
#2
Why should you not be able to compare the means? The crucial point is, what is the reason for
differences (or non-differences) between A and B? Is it (non-)differences between the cities, or
the sampling scheme, or a combination of both?
 
#4
Why should you not be able to compare the means? The crucial point is, what is the reason for
differences (or non-differences) between A and B? Is it (non-)differences between the cities, or
the sampling scheme, or a combination of both?
Good Morning Karabiner:
Thank you for your answer.

In your answer you ask why I shouldn’t be able to compare the means. The reason is that the sampling schemes could give a different picture of the cities. As a result, a difference between cities could be attributable to the sampling scheme.

I am asking this question because I am not sure if different sampling scheme could give a different picture of the cities. In order to make things as simple as possible, I specified that each sampling scheme gives an appropriate picture of their respective cities.

Yves
 

Karabiner

TS Contributor
#5
In your answer you ask why I shouldn’t be able to compare the means. The reason is that the sampling schemes could give a different picture of the cities. As a result, a difference between cities could be attributable to the sampling scheme.
Yes, of course. So you can compare the means, but the influence of the sampling scheme will possibly be unknown.

With kind regards

Karabiner
 

fed2

Active Member
#6
I specified that each sampling scheme gives an appropriate picture of their respective cities.
I will prove that the sampling schemes are appropriate:

By hypothesis the sampling schemes are appropriate.
But this implies that the sampling schemes are appropriate.

This completes the proof.