unit 4 experimental design

Simple Random Sample (SRS)

• no characteristic of concern

• random # generator

• random digit table

• every member of the population has an equal chance of being chosen

Systematic Sample

• no characteristic of concern

• ordered list

• every kth person

  • k is a random # between (N/n) and 1

Stratified Random Sample

• characteristic of concern

• homogenous sample

  • (e.g. everyone in ap stats, sample some from each ap stats class)

• random sample of some from each strata

  • strata = groups created on similar characteristics

Cluster Sampling

• characteristic of concern

• heterogenous sample

  • lunch periods that consist of different grade levels

• random sample of clusters and choose all people in that sample

Bias

• state the direction

• one outcome is systematically favored

Convenience sampling

• insufficient, bias risk

• participants chosen based on accessibility

• not random or representative

Voluntary response sampling

• participants voluntarily respond

• not random or representative

• insufficient, bias risk

Undercoverage

• sampling error in which there is insufficient data

• not representative

  • e.g. doing a political phone survey but only on landline phones

Nonresponse

• sampling error in which participants do not respond

• results in underrepresentation, under-coverage, and potential bias

• insufficient data

Response bias

• participant lies

• participant misinterprets question

• poorly worded question

• results in biased answers

Random sampling

• establish an association or inference about the population from which the sample was selected

• use a chance process to select a sample of n individuals

Random assignment

• establish cause and effect for the group or experimental units

Response variable

• dependent variable

• quantity that someone wants to measure

Explanatory variable

• independent variable

• factor that is manipulated or observed to see effect on response variable

Experimental units

• units that recieve the treatment

  • e.g. single plant, person, whole classroom

Observational study

• association

• measures a variable of interest without the researcher attempting to influence a response

  • standing back and watching it happen

Experiment

• cause and effect (only for experimental units in the trial)

• researcher uses a treatment to cause a change in the response variable

• deliberately imposes a treatment to measure a response

Components of a well-designed experiment

• comparison

• control

• repetition/replication

• random assignment

Randomized block design

• assignment of experimental units to blocks is not random

• samesies

Single/double blind

• participants are unaware which treatment they are receiving

• both participants and researchers are unaware who is receiving the treatment and who is receiving the placebo

  • third party is necessary

Placebo

• inactive treatment

  • e.g. sugar pill

• used to measure effect of active treatment

NO confounding variable

• completely randomized design

Confounding varible present

• randomized block design

Matched pairs design

• 2 treatments

• ideal when there is a potential confounding variable

• blocks of size 2 and each experimental unit gets 1 treatment

  • e.g. stage makeup FRQ

• blocks of size 1 and every experimental unit gets both treatments

  • e.g. MP3 player MCQ, boots FRQ

Population vs. sample

1. any group we desire to gather information about

2. representative and a subset of a population

e.g. all registered voters vs. 1000 registered voters selected by a news organization for this election

Stratified random sample example

• population: all HSHS student body

  • divide students by grade level

    • take 10 students (an SRS) from each grade level

Cluster sample example

• divide students by lunch period

  • chose a random lunch periods (e.g. 5th)

    • everyone in 5th period becomes a sample

Systematic random sample example

• obtain an ordered list of everyone in the population

  • chose every kth person in the sample (k should be a random constant)

• N=500, n=25

  • 500/25=20

  • random # 1<k<20

Control group

• no treatment

• allows for a baseline comparison

• placebo —> inactive treatment

• current treatment

Placebo effect

• an experimental unit responds to an inactive treatment

Confounding variable

• an outside factor impacts the response in such a way that we cannot tell if observed differences in the response are due to the treatments or the confounding variable

Procedure for a matched pairs experiment FRQ

1. identify the confounding variable and how it impacts experiment (proximity to light affects the amount of shine on an actor’s face)

2. using a block design, group actors into blocks of 2 based on position on stage and proximity to light (list blocks)

3. using a fair coin, assign heads to (new treatment) and tails to (current treatment)

4. flip the coin and assign the corresponding treatment to the actor with an even number. assign the other treatment to the other actor.

5. repeat the same exact process for each block

6. (after time period) within each block, compare the effect on _____ for each experimental unit (measure shine)

Observational studies to establish causation

• association is strong

• association is consistent

• large amounts of exp. variables lead to stronger response