Wednesday, January 12, 2011

Myths and Misconceptions in Survey Sampling - 1 (SRS , EPSEM and Self-weighting samples)

1. Misconception 1: SRS , EPSEM and Self-weighting samples are interchangeable terms
Many use these terms interchangeably in conversation or writing. But, for example:
"Similarly we must avoid the common confusion of epsem with simple random sampling (srs). Probably most  survey samples are epsem but very few are srs (outside academic writing)

In fact, even Wikipedia makes that mistake!
"A self-weighting sample, also known as an EPSEM (Equal Probability of Selection Method) sample...

Let's see why these terms are not interchangeable.
1) Simple Random Sampling (SRS)
The basic form of sampling similar to a draw of balls from an urn (aren't you tired of urn examples?).
"Simple Random Sampling is a method of selecting n units out of the N such that even one of the NCn distinct samples has an equal chance of being drawn. In practice a simple random sample is drawn unit by unit.

So, each population frame element has an equal chance of being selected irrespective of how many at a time the sampling is done - individually, pair-wise, three-at-a-time etc. Also,
"We shall restrict the term simple random sampling to situations where the elements are selected individually, hence the elements are also the sampling units. This differs from cluster sampling where the sampling units are clusters containing several elements.

2) EPSEM
"Sample Designs assigning equal probabilities to all individual elements of a frame population are called "epsem" for Equal Probability Selection Method
So,
1) EPSEM is not one specific sampling method but consists of many types as long as they all result in (known) equal selection probabilities
2) SRS is a type of EPSEM but every EPSEM need not be (and usually is not) an SRS. For example,  Probability Proportionate to Size (PPS) is an EPSEM design that is a type of cluster sampling (see above quote from Kish) i.e not SRS.

3) Self-weighting samples:
We collect data from samples not as an end in itself but to learn something about the population from which the samples were drawn. In this process, a weight is attached to each sample element. Why? To correct any possible imbalances that might (will) crop up in the process of implementing the design. For example, say you draw a simple random sample from a list of people. At this stage every person has an equal chance of being selected and thus the same weight.  

Now if each person that was contacted responded to the survey and there were no other survey problems (like the filled-in questionnaire getting lost!), each person would still have the same weight, which would actually be the inverse of his selection probability) . This kind of a sample would be called a self-weighting sample.  

But in practice, you find that the response rate to your survey among the upscale people is lower than the rest and you've ended up getting more responses from the non-upscale folk. This would make your results biased. To compensate for this we would calculate an apply a weight that will upweight an upscale person (and therefore downweight the rest). So what started off as an EPSEM design is no longer a self-weighting sample. In fact, this is actually what ones finds in practice and so:
"Others have used the phrase self-weighting sample, although some eschew this term, given that weighting typically involves nonresponse adjustment and some form of calibration such as ratio adjustment or raking, and these lead to unequal weights even when all elements of the sample have been selected with equal probability.
 Encyclopedia of Survey Research Methods, Ed. Paul Lavrakas. The entry "EQUAL PROBABILITY OF SELECTION"

Summary
1. SRS is an EPSEM method but not every EPSEM is SRS
2. Every SRS is self-weighting (in principle) but every self-weighting sample need not be SRS
3. EPSEM samples are self-weighting in principle but not in practice

2 comments:

Sandeep said...

Dear Mr.Sharma,

I humbly request you to kindly start a new blog for "intellectuals" such as yourselves so that we "lesser mortals" don't feel out of place. It would really help help us hold ourselves in "high esteem" if you "restrain" yourself from showing us "our true position" with such ease.

Thanking you,

yours faithfully,

(Beta) Bhasin

p.s.: Kehne ka tatparya yeh hai ki hamara education system itna ganda hai ki hame yeh sab samajhne layak banaya hi hani hai.

Sharan Sharma said...

arre sir, yeh aapne kya keh diya...i am the lesser mortal here...seriously...aur baat rahi hamari education system ki...well,...