Example You want to interview a sample of 50 Stockton residents to see how the Stockton population feels about a proposed law. You decide to visit Sherwood Mall between classes at 11:00 and interview passerbys. Is this a "good" sample?

Math 37 - Lecture 3

Randomization (3.2, 3.3)
How do I select the subjects for the study?

How do I divide subjects into treatment groups?
Selecting Sample from Population:

Goal: Want sample to have the same characteristics as the population, to be representative of the population.

Example: Want to interview a sample of 50 Stockton residents to see how the Stockton population feels about the proposed downtown baseball stadium. You decide to visit Sherwood Mall between classes at 11:00 and interview passerbys.

Example: To inspect the delivery of oranges, you randomly pick 10 oranges from the top of the crate.

Def: Bias = Sample is systematically different from the population.

e.g. selection bias, nonresponse bias

Examples of Improper Sampling:

Convenience Sampling

Voluntary Response

Quota Sampling

Probability Sampling Plans: Every unit has a specified chance of making it into the sample

*Simple Random Sample: Each set of n units has an equal chance of being selected.

Stratified Random Sample: Split population into similar groups (e.g. side of river, building type), take a random sample from each group

Cluster Sample: Split the population into groups (e.g. buildings) take a sample of groups and use everyone in each group.

Multistage Sample: Keep breaking the clusters down (e.g. regions then states then counties then apartment blocks)

Systematic Sample: Select every kth apartment

Taking a Simple Random Sample, SRS (Table B)

1. Label the units (Can "double label"…)

2. Pick a starting point at random

3. Read numbers off the list until you have your sample

Eliminate numbers corresponding to unused labels.

Eliminate repeats.

4. Report the corresponding units

Example A college has 4,000 students. About 55% of the population are women and about 10% are graduate students. We want to obtain a sample of 20 students to analyze their diet. Describe an implementation of each sampling plan. Which do you prefer?

Dividing Subjects into Treatment Groups:

Goal: Want treatment condition to be only difference between groups so need groups as similar as possible before impose treatment(s)

Example: Post a sign asking for volunteers to participate in an alcohol-reaction time study. Assign nondrinkers to "no alcohol" group and remaining drinkers to "alcohol group".

Experimental Designs

Completely Randomized Design (CRD): Randomly assign all experimental units among the treatments

Randomized Block Design (RBD): Separate units into blocks (expect them to behave similarly within the block) and then randomly assign units within each block to the treatments.

Special Case: Match Pairs design: Each unit or pair of units (e.g. identical twins) receives both treatments

Example Want to see if a new gas additive improves mileage.

Acura 3.5RL	Audi A8 Q	Buick Century	Cadillac Catera
Cadillac El Dorado	Chevy Lumina	Chrysler Cirrus	Dodge Stratus
Ford Taurus	Ford T-bird	Hyundai Sonata	Infiniti I30
Infiniti Q45	Lexus GS 300	Lexus LS 400	Lincoln Mark VII
Mazda 626	M Benz E320	M Benz E420	Mits. Diamante
Nissan Maxima	Olds Aurora	RR Silver Spur	Saab 900
Toyota Camry	Volvo 850	Chevy Blazer	Chevy Suburban
Chevy Tahoe	Chrysler T&C	Ford Expedition	Ford Explorer
Geo Tracker	Isuzu Rodeo	Isuzu Trooper	Jeep Gr Cheerokee
Kia Sportag	Ldrover Defender	Ldrover Discovery	Lexus LX 450
Mazda MPV	Mits Montero	Nis Pathfinder	Range Rover
Suzuki Sidekick	Toy Landcruiser	Toyota Rav 4	Toyota 4 Runner

Design an example of each type of experiment.