AP Statistics - Chapter 4

“Bad” Sampling Methods

• Convenience Sample

• Voluntary Response Sample

• Have bias -  the design of a statistical study shows bias if it would consistently underestimate or consistently overestimate the value you want to know

Convenience Sample

• Sample selected by taking from the population individuals that are easy to reach

• 30 students from the school library. Won’t accurately represent the homework habits of all students at the high school because students who hang out in the library tend to be more studious

Voluntary Response Sample

• People decide whether to join a sample by responding to a general invitation

• Call-in, text-in, write-in, and many Internet polls. Attract people who feel strongly about an issue, and who often share the same opinion

• Overestimate bias

 “Good” Sampling Methods

• Simple Random Sample (SRS)

• Stratified Random Sample and Strata

• Cluster Sample and Clusters

• Systematic Random Sample

• Response Error - not everyone answers honestly

• Nonresponse Error - not everyone replied

Simple Random Sample (SRS)

• Sample chosen in such a way that every group of n individuals in the population has an equal chance to be selected as the sample

• Ex - From a town with 100,000 residents, randomly select 1,000 people

Stratified Random Sample and Strata

• Sample obtained by classifying the population into groups of similar individuals, called strata, then choosing a separate SRS in each stratum and combining these SRSs to form the sample

• Ex - A researcher randomly selects and interviews fify male and fifty female teachers from a staff of 500 teachers

• Ex - A market researcher randomly selects 200 drivers under 35 years of age and 100 driver over 35 years of age

Cluster Sample and Clusters

• Sample obtained by classifying the population into groups of individuals that are located near each other, called clusters, and then choosing an SRS of the clusters. All individuals in the chosen clusters are included in the sample

• Ex - All of the teachers from 85 randomly selected nation’s middle schools were interviewed

• Ex - A researcher for an airline interviews all of the passengers on five randomly selected flights

Systematic Random Sample

• Selects a random starting point from the population, then a sample is taken from regular fixed intervals of the population depending on its size

• Every fifth person boarding a plane is search thoroughly - random starting point

Observational Study

volunteers, no randomization, no set thing or treatment people are made to do, watching for patterns

Experiment

• Deliberately imposes some treatment to observe response to see if treatment causes change in response

• Evidence on average (group)

• Causation

• Experimenter has control

Confounding variables

• 2 variables are associated in a way that their effect cannot be distinguished

• Difference between both groups

• Not controlled variables

• Effect entire group

• In observational study

Good experiment

• Comparison - 2 groups are compared

• Randomize who gets what treatment - spinner, flip a coin, names in a hat

• Control all factors only - difference between groups should be treatment

• Repeat - use enough subjects to make conclusion

Placebo

Fake Treatment

Placebo Effect

People respond to anything - response to dummy treatment

Statistically significant

Observed responses so large not by chance

Blocking

NOT stratified

Block

• Group of experimental units that are known before the experient to be similar in some way that is expected to affect response to treatment

• by gender

Randomized block design

Random assignment of experimental units to treatments is carried out separately within each block

Double Blind

• Neither subject or those who interact + measure response know which treatment a subject has

• A third party did the randomization

Single Blind

Either subjects will know treatment and those measuring response variable don’t (or vice versa)

Matched Pairs Design

• Type of randomizes block design for comparing two treatments

• Create blocks by matching pairs of similar experimental units

• Chance is used to determine which unit in each pair gets each treatment

• Sometimes, a “pair” in a matched pair deisgn consists of a single unit that receives both treatment. Since the order of the treatments can influence the response, chance is used to determine with treatments is applied first for each unit

Scope of Inference