Friday, January 28, 2011

Myths and Misconceptions in Survey Sampling - 2 (SRS is the "safest" sampling scheme)

In the first of this series, we looked at what SRS is. It certainly is the simplest sampling scheme. But not the safest.

Think of a population of 100 people made up of 50 girls and 50 boys. Your task is to sample 10 persons. You go ahead and take a SRS sample expecting that you'll anyway get a "representative sample" expecting 5 girls and 5 boys. But do not be very surprised if you get 3 girls and 7 boys. Why? Chance. For the same reason that you do not always get one head and one tail exactly when you toss a coin twice. Best way to understand this is to conduct a small simulation in R:

#create a population of boys, girls and total  
pb <-  rep("B", 50)                             
pg <- rep("G", 50)                           
pt <-  c(pg, pb)
#create an empty list to store results of sampling
s1 <-- rep(list(rep("NA",10)),1000) 
#take 1000 samples of 10 persons each (with replacement)
for (i in 1:1000) {
     s1[[i]] <- sample(pt, 10)
#calculate % of boys selected in each sample of 10 and plot results  
s2 <- sapply(s1, function(x) length(x[x=="B"])*10)
Created by Pretty R at

Of course, practically we would do this exercise just once and not 1000 times. But the above histogram illustrates that there is a chance (though small) that you can end up having even 2 boys in a sample of 10 individuals. A better approach in this case is to stratify the population into girls and boys and choose 5 out of 50 from each.
Bottomline: SRS is not the safest sampling scheme. Stratification is an insurance against chance.

Yet, there are times when you might need to use SRS:
1) You have nothing but a list of elements but no extra information on them. e.g drawing a sample from a list of voters in an area
2) When being correct might weaken your case (such is life). Sharon Lohr in her book gives the example of a legal case where a complicated sampling scheme might seem like "you are making the number up".


Rahul Bagdia said...
This comment has been removed by a blog administrator.
Rahul Bagdia said...

Hey Sharan,

Coincidentally landed up to TAM's page and recollected you and our few interactions when at UofM. How are things. I am running a startup in CleanTech and IT space from Nagpur Drop me email as you seem to have concealed your identity at all locations..:)

BTW, this is no real comment, but to handshake with you and get your coordinates.

Rahul Bagdia

Sharan Sharma said...

Hi Rahul,
Good to hear from you! Will drop a line...ciao, Sharan