# Multi-stage sampling and sample representation

I have used mutli-stage sampling (i.e. cluster and stratified sampling) to select four units within a geographical area. Each unit was selected randomly from a list of that unit. There are only four different types of units in the geographical area, so the unit selected is representative of each unit type. (I established some minimum criteria to ensure the chosen unit is representative of all units of the same type e.g. in terms of size. e.g. the chosen unit must have about 100 people because the the size of all units of a particular type is ranges from 50 to 150 people, so this is sort of an average.)

Note: The geographical area meets basic criteria I have established e.g. it must include all unit types present in the overall area. The geographical area is part of the overall area e.g. a village in one part of a country).

I have then randomly selected people belonging to each unit (e.g. 100 people from unit 1, 100 people from unit 2, 100 people from unit 3, and 100 people from unit 4).

My sample size is then 400 people (belonging to four representative units within the geographical area). I consider this to be a representative sample based on a stratification of unit type.

My problem is that I am unsure how representative the total members of each unit are in regard to the population of the geographical area. i.e, there may be more men in unit 1 but less men in the geographical area. Or, more older people in unit 2, compared to the geographical area.

In this case, is it necessary for the 400 people in my sample to resemble the demographic breakdown of the geographical area. I am unsure how this is possible but feel that it is not possible, as my sample of 400 people is representative of the unit type, not the geographical area.

Note: By "representative", I mean that the sample broadly reflects the population characteristics e.g. if there are 100 males and 90 females in the population, this ratio would be broadly reflected in the sample.

• You first need to figure out if you have a stratified sample or a cluster sample. From your description, it appears that you have a stratified sample. Please clarify. – StasK Oct 18 '12 at 3:27
• Thanks. I have clarified in the question that it is multi-stage sampling. – Amarald Oct 18 '12 at 4:24
• Not by much, actually. First question: did you select the "units" randomly? Did you select one unit from a list of the unit of the corresponding type? Second question: give a definition of "a representative sample". I know what a probability sample is, and how to work with one. "Representative" is a slang term with little meaning. – StasK Oct 18 '12 at 14:02
• If you have done random sampling it should be possible to compute the inclusion probabilities for units in sample. If you have the inclusion probabilities you can compute design weights and construct estimators for your population parameters of interest. – djhurio Oct 26 '12 at 11:38
• Reflection of population is not so important feature for a sample. Other definition of representative sample is sample which allows to estimate population parameters with required precision. – djhurio Oct 26 '12 at 11:42