The Logic of Sampling

‘92 Election Results
How many interviews were conducted?

• Fewer than 2000 to estimate a hundred million voters
• The key is selecting the right 2000 people to interview
• The estimates are close but seldom exact
• The amount of error due to using a sample is
  sampling error

Literary Digest Poll

• Warren Harding vs. James Cox
• 1920
• postcards sent to six states
• names selected from telephone books and automobile registrations
• correctly predicted that Harding would win
• correct prediction in 1924, 1928, 1932

1936 election

• Most ambitious poll
• ten million ballots were mailed out
• names selected from telephone books and automobile registrations
• over 2 million ballots were returned
• Alf Landon 57% Franklin Roosevelt 43%
• Roosevelt won in a landslide

What were the errors?

• Only 22% return rate
• were the people who returned the postcards different from those that didn’t return the postcards?
• Sample frame
• were the right people sent postcards?
• names selected from telephone books and automobile registrations
• disproportionately wealthy sample

Gallup Poll

• George Gallup
• American Institute of Public Opinion
• used quota sampling
• select sample based on demographics
• right in the 1936, 1940, and 1944 election

In 1948 he predicted that Thomas Dewey would beat Harry Truman

• polls stopped early in October
• quotas bast on 1940 census
• shift in population to the cities

Today

• Sampling is based on laws of mathematics
• probability sampling
• primary sampling method used in social science
• Why does probability sampling work?

Census

• Increase the sample size until it is equal to the size of the total audience
• We ask everyone
• the sample is exact
• there is not sampling error
• there may be some
• clerical error
• measurement error

Media usage of the Old order Amish

• How many hours of Television do you watch?
• We could assume that it would zero hours

How many Amish would we need to ask?

• One would be sufficient
• The Amish are perfectly homogenous on the variable of watching television
• My survey would be perfectly accurate

The Amish do watch TV

• The Old Order Amish don’t own TVs or have electricity
• They can’t own cars but maybe you’ve seen them riding in someone else's car or van
• They can watch TV in someone else’s home
• We found one women while working as a cleaning lady for the non Amish watched General Hospital everyday.

 Two factor control the size of the sampling error

• Homogeneity of the audience
• sample size

What if?

• The sample is smaller than the audience
• the audience is not homogeneous

Sample distribution

• Random Samples have a normal distribution
• the mean of the sample distribution equal the mean of the population distribution
• the mean of one sample may not mach the population mean
• the difference between the population mean and one sample mean is call sampling error
• the standard error estimates the size of the sampling error

Standard Error

• The sampling error is estimated by the standard error
• directly proportionate to the dispersion of the sample
• indirectly proportionate to the sample size
• standard error is the standard deviation of the sample distribution

Standard error for interval data

• Income for employees

 Confidence interval

• With a certain degree of probability
• The statistical results from our sample will fall within an interval from the population perimeters