Notes

 A population is a large group of individuals you want information about.  An individual is defined to include people, animals, or objects that are described by data.  Realistically, though, would we able to survey everyone in the United States to find out something?  For example, could we ask every American what their favorite food is or who they plan to vote for in an election?

Example: US Census every 10 years Example: A phone poll asking who you will vote for in an upcoming election  A CENSUS ◦ a survey of an entire population ◦ very expensive ◦ time-consuming  A SAMPLE ◦ a group chosen to represent an entire population ◦ less expensive ◦ can be designed to take much less time than a census

Population = entire group Sample = chosen group  What is the population? ◦ The population is the group of 250 computers.  What is the sample? ◦ The sample is the group of 25 computers he inspects.

 Convenience Sample: chooses individuals who are easiest to reach ◦ Example: asking people leaving a grocery store who they are going to vote for in an election  Voluntary Response Sample: individuals respond to a general request ◦ Example: people respond to a survey they received in the mail

In other words, they are biased.

 A population might be UNDERREPRESENTED. ◦ one or more parts of a population are left out when choosing the sample  A population might be OVERREPRESENTED. ◦ an emphasis is placed on one or more of the parts of a population

Scenario #1Scenario #2  A survey is conducted by calling 100 people randomly chosen from the phone book and asking them what there favorite kind of toothpaste is.  A restaurant owner wants to know how often families in his area go out for dinner. He surveys 30 families who eat at his restaurant on Tuesday night.

Scenario #1 is BIASEDScenario #2 is BIASED  The random people chosen from the phone book are not necessarily representative of the entire city’s population.  People who aren’t listed in the phone book are excluded.  The sample is a convenience sample, which probably isn’t representative of the entire area’s population.  Families already eating out may eat out more often than other families in the are.

 Imposes a treatment on individuals  Collects data on their response to the treatment

 Observes individuals and measures variables without controlling the individuals or their environment in any way

This is an observational study, because the researcher isn’t controlling the students or applying a treatment. This is an experiment, because the cosmetologist applies a treatment to some individuals.  A researcher asks students the average number of hours they spend studying for a test to see if there is a relationship between studying and grades.  A cosmetologist wants to know whether nail polish A lasts longer than nail polish B, so she paints two sets of nails with each polish.

 For experiments to be useful, they must be carefully thought out and designed.  A CONTROLLED EXPERIMENT sets up a control group and a treatment group so that two groups can be studied under conditions that are identical except for one variable.  A RANDOMIZED COMPARATIVE EXPERIMENT is one in which individuals are assigned to the control group or the treatment group randomly in an effort to minimize bias.

At a local elementary school, 150 randomly chosen students were given milk at lunch for a year. 150 other randomly chosen students were given other drinks at lunch for a year. At the end of the year, students in the milk group had 22% fewer calories than the students in the other group.  Randomized Comparative Experiment  Treatment is drinking milk at lunch  Treatment group drank milk  Control group drank other beverages

 Which would be better: an experiment or an observational study?  In this case, an observational study would be best, because it wouldn’t be fair to ask a treatment group to possibly ruin its hearing if the individuals don’t already listen to music with headphones.  To be effective, randomly choose one group of people that already listens to an iPod™ with headphones for more than two hours a day. Then, randomly choose one group of people that doesn’t listen to music with headphones.  Monitor the hearing of both groups regularly and record results.