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 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 k th 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?”