Let be Statistan a country of approximately 20 million farmers. I want to draw a representative sample of the farmer population in order to survey them, in particular with the goal of capturing their yield (as defined by kilograms per cultivated hectare) and understanding what makes yield varying across the country.
Statistan is a very diverse country.
- Its cultivated land is 50% rainfed and 50% irrigated;
- Environmental conditions change a lot through the country with 33% of the cultivated land in mountainous regions (very steep fields), 33% in tropical regions and 33% in arid regions;
- Social conditions also differ with 50% of the farmers living in regions with of high per capita income and 50% of the farmers living in region of low per capita income.
Should I take into consideration these categories when drawing the sample? Of course these are all important factors in determining each farmer's yield. It seems that if I sub-group my total population before sampling it I dramatically reduce the overall representativeness of the sample. But also if I don't I won't have many observations from less populated areas (like arid regions) where the potential of relevant findings is higher.
How can I better understand the trade-off between sub-grouping and representativeness of the sample population given the number of observation I will collect with the survey?