AP Statistics Unit 3: Sampling and Experimental Design

Simple Random Sample

1. Every individual has an equal chance at being chosen

2. Every set of n individuals has an equal chance at being chosen

Stratified Random Sample

Population is divided into homogeneous groups called strata and then stratified random samples are pulled from each stratum.

Systematic Random Sample

Select sample by following a systematic approach; randomly select where to begin between 1 and n, and then survey every nth person after that.

Cluster Random Sample

Randomly pick a location and sample all from those locations.

Population

The entire group of people we want information about

Cenus

a complete count of the population

Sample

a part of the population we actually examine in order to gather information

Sampling Desing

the method used to choose the sample from the population

Sampling Frames

a list of every individual in the population

Multistage Sample

Any combination of different sampling techniques; select successively smaller groups within the population in stages.

Simple Random Sample Hat Method

1. Put the names of all [population] on slips of paper and put them in a large hat and mix the names.

2. Randomly choose [sample size] without replacement.

3. Survey those [sample size] [population unit].

Simple Random Sample RNG Method

1. Number all [population] [range of population size]

2. Use a random number generator to select [sample size] unique numbers between [range of population size]

3. Survey the [sample size] [population unit] that correspond with those numbers

Systematic Random Sample RNG Method

1. Number all [population] [range of population size]

2. Use a random number generator to select a number between 1 and [population size/sample size]

3. Survey the person with the corresponding number

4. Survey every [population size/sample size]th [population unit] on the list after that

Cluster Random Sample Hat Method

1. The clusters will be [location units]

2. Put the names of all [# of locations] [location units] in a hat and mix

3. Select [population size/size in each location] [location names] from the hat without replacement and survey all [population units] in those [location units]

Stratified Random Sample Hat Method

1. Sort all [population units] into strata based on [characteristic]

2. Put names of al the [one of the characteristics] in one hat and mix

3. Select [sample size/ # of characteristics] names without replacement and survey those [population units]

4. Repeat the same process for the other [# of characteristics left] [characteristics]

Stratified Random Sample RNG Method

1. Sort all [population units] into strata based on [characteristic]

2. Number the [one of the characteristics] [population size/ # of characteristics]

3. Use a RNG to select [sample size/ # of characteristics] unique numbers from [range of population size] and survey the corresponding [population units]

4. Repeat the same process for the other [# of characteristics left] [characteristics]

Voluntary Response Bias

people "select" themselves to participate in the study; they are not randomly selected

Nonresponse Bias

occurs when individuals randomly chosen for the sample can't be contacted or refuse to cooperate

Convenience Sampling

when you ask people who are easy to ask; it's convenient but not random and produces biased results

Under Coverage Bias

some groups are left out of the selection process (accidentally or purposely)

Response Bias

occurs when the behavior of the respondent or interviewer causes you to get incorrect answers

Wording of the Question Bias

occurs when the wording of the question influences the answers that are given; a type of response bias

Observational Study

observe outcomes without imposing any treatment

Experiment

actively impose a randomly assigned treatment in order to observe the response

Experimental Unit

the single individual (person

Factor (Explanatory Variable)

what we test/what we change/give experimental units to

Level

a specific value or types for the factor

Response Variable

what you measure or record at the end of the experiment

Treatment

a specific experimental condition applied to the units; same as levels when there are multiple factors

Control Group

a group that is used to compare the factor against; can be a placebo or the "old"/ or current item; counts as one of the levels

Placebo

a "dummy" treatment that can have no physical affect; not required in every experiment

Blinding

method used to that the units or evaluators do not know which treatment the units are getting

Double Blind

neither the units nor the evaluator know which treatment a subject received

Confounding Variable

A third variable that potentially affects both the factor and the response variable. It is the pre-existing condition that makes the subject choose the factor and influences the response.

Control

the effects of extraneous variables on the response

Randomization

the use of chance to assign subjects to treatments

Replication

redoing the experiment on many subjects to quantify the natural variation in the experiment

Completely Randomized Design

experimental units are assigned completely at random to treatments (no sorting beforehand)

Randomized Block Design

experimental units are blocked into homogenous groups and then randomly assigned to treatments (units should be blocked based on a variable that affects the response)

Matched Pairs Design

a special type of block design; 1. match up experimental unites according to similar characteristics and randomly assign one to treatment A and the other gets treatment B automatically; 2. have each unit do both treatments in a random order.

Completely Randomized Design Hat Method

1. Number the [population units] [range of population size]

2. Put the numbers [range of population size] on pieces of paper and put them in a hat. Mix the numbers

3. Randomly select [population size/ # of treatments] [population units] without replacement. the [population size/ # of treatments] [population units] with the corresponding numbers will get treatment one

4. The next [population size/ # of treatments] drawn will get treatment two

5. The remaining [population units] will get treatment three

6. Measure the [response variable] for each [population unit] and compare treatments

Completely Randomized Design RNG Method

1. Number the [population units] [range of sample size]

2. Use a random number generator to select [sample size/ # of treatments] unique numbers between [range of sample size]. The corresponding [population units] get treatment one

3. Select [sample size/ # of treatments] more unique number with the RNG and those [population units] will get treatment two

4. The remaining [population units] will get treatment three

5. Measure the [response variable] for each [population unit] and compare treatments

Randomized Block Design Hat Method

1. Put the [population units] into blocks based on [characteristic]. The [lower half of sample size] will be in one block and the [upper half of sample size] will be in the second block

2. Number the treatments [range of # of treatments]. Put [half of sample size/ # of treatments] 1’s in a hat, [half of sample size/ # of treatments] 2’s in a hat, and [half of sample size/ # of treatments] 3’s in a hat. Mix the numbers

3. For each [population unit] in the [first characteristic] block select one slop of paper without replacement. That rabbit will get that treatment

4. Repeat that process for the [second characteristic] block

5. Compare the [response variable] within the blocks and then overall

Randomized Block Design RNG Method

1. Put the [population units] into blocks based on [characteristic]. The [upper half of sample size] will be in block one and the [lower half of sample size] will be in the second block

2. Number the [population units] in the [second characteristic] block [range of half of sample size]

3. Use RNG to pick [block size/ # of treatments] unique numbers from [range of half of sample size]. The corresponding [population units] get treatment one

4. Pick [block size/ # of treatments] more unique numbers from [range of half of sample size]. These corresponding [population units] get treatment two

5. The remaining [block size/ # of treatments] [population units] get treatment three

6. Repeat the process for the [other characteristic] block

7. Compare the [response variable] within the blocks and then overall