DESIGNING SAMPLES

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)

○ Contact 60,000 household each month. ○ Produces the monthly unemployment.

Other Examples?

Sampling Poorly

Convenience samplingChoosing individuals who are easiest to

reach.Where’s the Bias?

Voluntary responseConsists of people who choose themselves

by responding to a general appealWhere’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 SampleDivide the population into groups, or clusters. The

clusters are randomly selected, then ALL individuals in the chosen clusters are in the sample.

Systematic SampleBegin by selecting an element from the population

at random and then every kth element is selected, where k, is the sampling interval.

Sampling Errors

UndercoverageOccurs when some groups in the population

are left out of the process of choosing the sample.

NonresponseOccurs when an individual chosen for the

sample can’t be contacted or does not cooperate.

Nonsampling Errors

Response BiasGiving incorrect responses

Wording of QuestionsConfusing, 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?”