Transcript What is Statistics?

Section 5.1
Observational Study vs. Experiment
In an observational study, we observe
individuals and measure variables of
interest but do not attempt to influence
the responses.
 In an experiment, we deliberately
impose some treatment on (that is, do
something to) individuals in order to
observe their responses.

Variables
A response variable measures an
outcome of a study.
 An explanatory variable helps explain or
influences changes in a response
variable.

Population and Sample

The population in a statistical study is
the entire group of individuals about
which we want information.

A sample is a part of the population that
we actually examine in order to gather
information.
Sampling

A census attempts to include everyone in
the population.

Unlike a census, sampling involves studying a
part in order to gain information about the
whole.

Sampling techniques include: voluntary
response, convenience, simple random,
stratified, systematic, and cluster.

The sampling method is biased if it
systematically favors certain outcomes.
The Idea of a Sample Survey

Conclusions about a whole population are often drawn
on the basis of a sample.

Choosing a representative sample is not easy. Careful
planning must take place.


What population do we want to describe?
What do we want to measure?
Example:


Current Population Survey (CPS)
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
Contact 60,000 household each month.
Produces the monthly unemployment.
Other Examples?
Sampling Poorly

Convenience sampling
 Choosing individuals who are easiest to
reach.
 Where’s the Bias?

Voluntary response
 Consists of people who choose themselves
by responding to a general appeal
 Where’s the Bias?
Sampling Well

Simple Random Sample (SRS)
 A SRS of size n consists of n individuals
from the population chosen in such a way
that every set of n individuals has an equal
chance to be the sample actually selected.
 NOTE: In this instance “random” does not
mean haphazard as in “OMG that’s so
random.” In statistics, random means “due
to chance.”
Other Types of Sampling

Stratified Random Sample
 Divide the population into similar groups (strata).
Then choose a separate SRS in each stratum.

Cluster Sample
 Divide the population into groups, or clusters.
The clusters are randomly selected, then ALL
individuals in the chosen clusters are in the
sample.

Systematic Sample
 Begin by selecting an element from the
population at random and then every kth element
is selected, where k, is the sampling interval.
Sampling Errors

Undercoverage
 Occurs when some groups in the population
are left out of the process of choosing the
sample.

Nonresponse
 Occurs when an individual chosen for the
sample can’t be contacted or does not
cooperate.
Nonsampling Errors

Response Bias
 Giving incorrect responses

Wording of Questions
 Confusing, leading, or order of questions
can influence the outcome of a survey
○ Example:
 “How happy are you with your life in general?
 “How many dates did you have last month?”