Biased and Unbiased Surveys

Date: 11/05/2008 at 17:34:48
From: Caitlin
Subject: 'bias in surveys' 

What does 'biased' and 'unbiased' mean?  Here's an example.  Tell 
weather the sampling method is biased or unbiased: The Tri-State
Soccer League is conducting a survey to determine if the players want
to change the style of soccer shirt.  They will randomly survey all
players who wear size large shirts.

I don't know what 'biased' and 'unbiased' mean.

Date: 11/07/2008 at 01:33:50
From: Doctor Jordan
Subject: Re: 'bias in surveys'

Hi Caitlin,

The basic idea of statistics is to make statements about a set of
things using a subset (a sample) of those things.

A sample is "biased" if some members of the population are more likely
to be included than others.  A sample is "unbiased" if all members of
the population are equally likely to be included.

Here are two examples.  Suppose I want to find out how big a typical
fish is in a lake.  One way of getting a sample of the fish would be
to use a net.  But then I will never catch any of the fish that are
smaller than the holes in the net, so I'll think that all the fish in
the lake are big.  This sample is biased because the big fish are more
likely to be included in my sample; to get an unbiased sample I need
to sample the fish in a different way.

Now suppose I want to know how long a bear sleeps every day on average
during the year.  If I watched it for 10 days in the winter, each day
it would sleep 24 hours since bears hibernate in the winter.  This
sample is biased because in winter the bear sleeps all day while
during the rest of the year it is awake part of the day and asleep
part of the day.  If I want an unbiased sample, I could watch it for 1
day each month for a year, instead of just in the winter.

In your example about the Tri-State Soccer League, there are a lot of
players and we need to take a sample of them to find out if they want
to change the shirts.  If we only sample players who wear large
shirts, this sample is biased because some members (those who wear
large shirts) are more likely to be included.

The problem with this is that maybe the medium shirts are too big but
the small shirts are too small for some players, while the large
shirts fit well.  If we only sample players who wear large shirts, we
will not find out about the fitting problems with the other sized shirts.

Does this make sense?  If you have any questions please write back. 

- Doctor Jordan, The Math Forum
  http://mathforum.org/dr.math/