Inference for Sampling

Inference for Sampling
The purpose of a sample is to give us
information about a larger population.
 The process of drawing conclusions about
a population on the basis of sample data is
called inference.

Why should we rely on random sampling?
1)To eliminate bias in selecting samples from the list of available
individuals.
2)The laws of probability allow trustworthy inference about the
population
• Results from random samples come with a margin of error
that sets bounds on the size of the likely error. (It tells us
how much variability to expect.)
• Larger random samples give better information about the
population than smaller samples.
Important Note on Bias
Bias
is introduced by the way in
which a sample is selected or by the
way in which the data are collected
from the sample. Increasing the size
of the sample does nothing to
reduce the bias!

Sample Surveys: What Can Go Wrong?
Most sample surveys are affected by errors
in addition to sampling variability.
 Good sampling technique includes the art of
reducing all sources of error.

Sampling Error

Mistakes made in the process of taking a
sample that could lead to inaccurate
information about the population
Voluntary response
 Convenience sampling
 Undercoverage

Undercoverage
Undercoverage occurs when some groups
in the population are left out of the process
of choosing the sample.
EXAMPLE:
A sample survey of households will miss
homeless persons, prison inmates, students
living in dorms, etc.
Nonsampling Error
Can plague even a census
 Nonresponse
 Response Bias
 Poor wording of questions

Nonresponse
Nonresponse occurs when an individual
chosen for the sample can’t be contacted
or refuses to participate.
NOTE: This differs from “voluntary
response” because in a voluntary response
survey the individuals have all opted to
take part in the survey. In nonresponse,
those chosen for the sample do not
participate.
Voluntary response vs. Nonresponse

Voluntary response is sampling error
since it has to do with choosing the
sample.

Nonresponse is nonsampling error since
it occurs after the sample has been
chosen.
Response Bias

A systematic pattern of incorrect
responses
EXAMPLE:
 People know they should vote, so when
asked by an interviewer if they voted in
the last election, they will say that they
did.
 Faulty memory: “Have you visited the
dentist in the last 6 months?”
Wording of Questions

Confusing or leading questions can
introduce strong bias
EXAMPLE: The same sample was asked both
of these questions:
 “Should illegal immigrants be prosecuted and
deported for being in the U.S. illegally, or
shouldn’t they?” (69% favored deportation)
 “Should illegal immigrants who have been in
the U.S. for two years be given the chance to
keep their jobs and eventually apply for legal
status?” (62% responded “yes”)
Does order matter?
Suppose college students were asked these
questions:
1.
2.
“How happy are you with your life in
general?” (Scale of 1 to 5)
“How many dates did you have last
month?”