AP StatisticsAP Statistics

Chapter 5 NotesChapter 5 Notes

Ways to Collect DataWays to Collect Data

SurveySurvey Select a sample, ask questions, record answers.Select a sample, ask questions, record answers.

Observational StudyObservational Study Observe individuals and measure variables of Observe individuals and measure variables of

interest, but do not attempt to influence the interest, but do not attempt to influence the response, (lack of control, often no random response, (lack of control, often no random assignment to experimental groups).assignment to experimental groups).

ExperimentExperiment Study in which we deliberately manipulate and Study in which we deliberately manipulate and

control the sample and measure variables.control the sample and measure variables.

Survey TermsSurvey Terms

Population: The entire group of individuals Population: The entire group of individuals that we want information about.that we want information about.

Sample: A part of the population that we Sample: A part of the population that we actually examine in order to gather actually examine in order to gather information.information. Sampling: The process of choosing and studying a Sampling: The process of choosing and studying a

part, in order to get information about the whole.part, in order to get information about the whole. Census: Attempts to contact every individual Census: Attempts to contact every individual

in the population.in the population.

Bad Sampling MethodsBad Sampling Methods

Voluntary Response SampleVoluntary Response Sample Consists of people who choose themselves by Consists of people who choose themselves by

responding to a general appeal.responding to a general appeal. Convenience SamplingConvenience Sampling

Choosing individuals who are the easiest to Choosing individuals who are the easiest to contact.contact.

Bias….the result of poor samplingBias….the result of poor sampling Systematic favoring of certain outcomesSystematic favoring of certain outcomes

Proper Sampling MethodsProper Sampling Methods

Probability Sample: Sample chosen by chance.Probability Sample: Sample chosen by chance. Simple Random Sample (SRS)Simple Random Sample (SRS)

n individuals from the population chosen in such a way that n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the every set of n individuals has an equal chance to be the sample actually selected.sample actually selected.

Stratified Random SampleStratified Random Sample Population is first divided into groups called strata, that are Population is first divided into groups called strata, that are

similar in a way that is important to the response. SRS is similar in a way that is important to the response. SRS is then taken from each stratum to form the sample. then taken from each stratum to form the sample.

# of individuals taken from the strata should be proportional to the # of individuals taken from the strata should be proportional to the number of individuals in the strata.number of individuals in the strata.

Other Sampling MethodsOther Sampling Methods

Cluster SamplingCluster Sampling Divide population into clustersDivide population into clusters Randomly select some clusters.Randomly select some clusters. All individuals in chosen clusters are included in All individuals in chosen clusters are included in

the samplethe sample Multistage samplingMultistage sampling

Sampling done in steps using a combination of Sampling done in steps using a combination of methods, (used for very large populations).methods, (used for very large populations).

Problems with surveys (even when Problems with surveys (even when sampling methods are good)sampling methods are good)

UndercoverageUndercoverage Some groups in the population are left out of the Some groups in the population are left out of the

process of choosing a sample.process of choosing a sample. NonresponseNonresponse

Individual chosen for the sample can’t be Individual chosen for the sample can’t be contacted or does not cooperatecontacted or does not cooperate

*These problems may or may not cause bias.* *These problems may or may not cause bias.* Bias will result if the people left out are different, Bias will result if the people left out are different,

as a group, than the people included.as a group, than the people included.

Error/BiasError/Bias Sampling ErrorSampling Error

Occurs because the sample rarely reflects the population Occurs because the sample rarely reflects the population perfectly.perfectly.

Can’t be avoided…we just have to account for it in our Can’t be avoided…we just have to account for it in our calculations (example: margin of error).calculations (example: margin of error).

Response BiasResponse Bias Occurs when a respondent does not give an accurate Occurs when a respondent does not give an accurate

response.response. Causes: characteristics of the interviewer, lying, etc.Causes: characteristics of the interviewer, lying, etc.

Poor Question WordingPoor Question Wording One-sided, leadingOne-sided, leading

Parts of an ExperimentParts of an Experiment

Experimental Units: Individuals on which the Experimental Units: Individuals on which the experiment is being performed, (called subjects or experiment is being performed, (called subjects or participants when human)participants when human)

Treatment: An experimental condition applied to the Treatment: An experimental condition applied to the units.units.

Factors: The explanatory variables in an experiment.Factors: The explanatory variables in an experiment. Level: A specific value of a factorLevel: A specific value of a factor

Examples: Dosage, temperatureExamples: Dosage, temperature Combination of levels and factors form the treatment.Combination of levels and factors form the treatment.

Example: 200mg given orally, 400mg administered intravenously Example: 200mg given orally, 400mg administered intravenously

Principles of Experimental DesignPrinciples of Experimental Design

1. Control1. Control Minimize the effects of lurking variables by comparing several Minimize the effects of lurking variables by comparing several

treatments in the same environment. (utilize placebos and control treatments in the same environment. (utilize placebos and control groups)groups)

Placebo Effect: response to a dummy treatmentPlacebo Effect: response to a dummy treatment 2. Replication2. Replication

Use many experimental units to reduce chance variation in the Use many experimental units to reduce chance variation in the resultsresults

3. Randomization3. Randomization Use impersonal chance to assign experimental units to Use impersonal chance to assign experimental units to

treatments.treatments. Goal: Find Goal: Find statistical significancestatistical significance…the observed effect is so …the observed effect is so

large that it is unlikely to have occurred by chance.large that it is unlikely to have occurred by chance.

Types of Experimental DesignsTypes of Experimental Designs

Completely Randomized DesignCompletely Randomized Design aka a basic comparative experimentaka a basic comparative experiment All experimental units are allocated at random All experimental units are allocated at random

among all the treatmentsamong all the treatments

Comparative ExperimentComparative Experiment

Types of Experimental DesignsTypes of Experimental Designs

Block DesignBlock Design An experiment is conducted separately for An experiment is conducted separately for

different groups (blocks) of experimental units.different groups (blocks) of experimental units. Use blocks if you expect certain groups of Use blocks if you expect certain groups of

units/subjects to systematically affect the response units/subjects to systematically affect the response to the treatments.to the treatments.

It is similar to stratified random sampling.It is similar to stratified random sampling.

Block DesignBlock Design

Types of Experimental DesignsTypes of Experimental Designs

Matched Pairs Design (type of block design)Matched Pairs Design (type of block design) Compares two treatments by comparing the Compares two treatments by comparing the

response of two matched experimental units.response of two matched experimental units. Units are matched one of two ways….Units are matched one of two ways….

(a) Two different units/subjects matched based on (a) Two different units/subjects matched based on similar characteristics (e.g. identical twins)similar characteristics (e.g. identical twins)

(b) One subject/unit receives both treatments (i.e. A (b) One subject/unit receives both treatments (i.e. A person is paired with him/herself. Each subject serves person is paired with him/herself. Each subject serves as his/her own control.)as his/her own control.)

Randomization is still used to determine who gets Randomization is still used to determine who gets which treatment, or which treatment is given first.which treatment, or which treatment is given first.

Example: Fertilizing a FieldExample: Fertilizing a Field

Other Considerations with Other Considerations with ExperimentsExperiments

It is sometimes better if the experiment is It is sometimes better if the experiment is conducted in a conducted in a double-blinddouble-blind manner. manner. Neither the subjects nor the people administering Neither the subjects nor the people administering

the experiment know which treatment the subjects the experiment know which treatment the subjects received.received.

Sometimes a Sometimes a lack of realismlack of realism is a problem for is a problem for experiments.experiments. A laboratory setting is not always the same as real A laboratory setting is not always the same as real

life, which makes it difficult to generalize your life, which makes it difficult to generalize your findings.findings.

Other Considerations Cont…Other Considerations Cont…

Don’t forget to describe your randomization process Don’t forget to describe your randomization process in detail when writing an open-ended response.in detail when writing an open-ended response.

Random sampleRandom sample Allows you to generalize your results to the populationAllows you to generalize your results to the population

Random allocation to treatment groupsRandom allocation to treatment groups Allows you to state that the difference between the Allows you to state that the difference between the

responses in the treatment groups was due to the effects of responses in the treatment groups was due to the effects of the explanatory variable, not the personal characteristics of the explanatory variable, not the personal characteristics of the subjects.the subjects.