Sample DesignSample DesignSection 4.1Section 4.1

TerminologyTerminology

• Observational Study – observes Observational Study – observes individuals and measures variables individuals and measures variables of interest but does not impose of interest but does not impose treatment on the individuals.treatment on the individuals.

• Experiment – deliberately imposes Experiment – deliberately imposes treatment on individuals and treatment on individuals and measures the responsesmeasures the responses

Observational vs. Observational vs. ExperimentExperiment

• Observational studies often have Observational studies often have confounding variables.confounding variables.

• Well-designed experiments, on the Well-designed experiments, on the other hand, try to reduce other hand, try to reduce confounding variables. confounding variables.

More terminologyMore terminology

• Population – the entire group of Population – the entire group of individuals that we want information individuals that we want information aboutabout

• Sample – a part of the population Sample – a part of the population that we actually examine in order to that we actually examine in order to gather informationgather information

• Census – attempts to contact every Census – attempts to contact every individual in the entire populationindividual in the entire population

Sample DesignSample Design

• Sample design is the method used to Sample design is the method used to select the sample from the select the sample from the population.population.

• Some poor examples of sample Some poor examples of sample design are as follows:design are as follows:

Voluntary Response SampleVoluntary Response Sample

• What it is: people who choose What it is: people who choose themselves by responding to a general themselves by responding to a general appeal.appeal.

• Why it’s bad: people with strong Why it’s bad: people with strong opinions, especially negative opinions, opinions, especially negative opinions, are more likely to respond. Therefore, are more likely to respond. Therefore, the sample is not likely to be the sample is not likely to be representative of the whole population.representative of the whole population.

Convenience SamplingConvenience Sampling

• What it is: a sample chosen because the What it is: a sample chosen because the individuals are the easiest to reachindividuals are the easiest to reach

• Why it’s bad: It’s not likely to be Why it’s bad: It’s not likely to be representative of the entire population.representative of the entire population.– Example: Mall surveys… People at the mall Example: Mall surveys… People at the mall

tend to be wealthier. Also, those people who tend to be wealthier. Also, those people who are attracted by mall surveys tend to be are attracted by mall surveys tend to be teens or the elderly.teens or the elderly.

Common ThreadCommon Thread

• Sample designs are bad when they Sample designs are bad when they are not representative of the whole are not representative of the whole population.population.

– Sample designs are called BIASED if Sample designs are called BIASED if they systematically favor certain they systematically favor certain outcomes.outcomes.

Some Other Problems:Some Other Problems:• Undercoverage: Undercoverage: Who did we leave out?Who did we leave out?• Non-response: Non-response: Can’t be contacted; Can’t be contacted;

refuses to participate.refuses to participate.

Good Sample DesignsGood Sample Designs

• Probability Sample (any sample Probability Sample (any sample chosen by chance). We must know chosen by chance). We must know what samples are possible and what what samples are possible and what probability each sample has of being probability each sample has of being chosen.chosen.– Choosing a sample by chance allows Choosing a sample by chance allows

neither favoritism by the sampler nor neither favoritism by the sampler nor self-selection by respondents.self-selection by respondents.

Examples of Probability Examples of Probability SamplesSamples

• SRS (Simple Random Sample)SRS (Simple Random Sample)– The simplest way to use chance to The simplest way to use chance to

select a sampleselect a sample– Analogous to putting names in a hat Analogous to putting names in a hat

(the population) and drawing out a (the population) and drawing out a handful (the sample).handful (the sample).

– Each individual has an equal chance of Each individual has an equal chance of being chosen and each sample is being chosen and each sample is equally likely.equally likely.

How to Choose an SRSHow to Choose an SRS

1.1. LabelLabel Assign a number to each individual in the Assign a number to each individual in the

population. They must all have the same population. They must all have the same number of digits.number of digits.

2.2. Decide if you will throw out repeats.Decide if you will throw out repeats.

3.3. Random Selection:Random Selection:• TableTable

Use Table B to select numbers at random.Use Table B to select numbers at random.

• OR CalculatorOR Calculator Use calculator to find random digitsUse calculator to find random digits

Random Digits from Table BRandom Digits from Table B

• Each digit 0-9 is equally as likely.Each digit 0-9 is equally as likely.• If you need to have 1-10 individuals, look If you need to have 1-10 individuals, look

at numbers 0-9 (one digit). Have 1-100 at numbers 0-9 (one digit). Have 1-100 individuals use numbers 00-99 (two individuals use numbers 00-99 (two digits). Have 1-1000 individuals, digits). Have 1-1000 individuals, numbers 000-999 (three digits) and so numbers 000-999 (three digits) and so forth.forth.

• Choose a row in your table to start with Choose a row in your table to start with (if you use this method on the AP exam (if you use this method on the AP exam you should state which row you start you should state which row you start with).with).

• Follow the row and choose individuals.Follow the row and choose individuals.

Let’s perform our own SRSLet’s perform our own SRS

• We will choose 5 students from the We will choose 5 students from the class at random. First, lets use Table class at random. First, lets use Table B. How will we label? B. How will we label?

Microsoft Excel Worksheet

Random Digits in CalculatorRandom Digits in Calculator

• Go to MathGo to Math

• PRBPRB

• RandInt(1RandInt(1stst #, last #, how many #, last #, how many numbers)numbers)

Let’s perform our own SRSLet’s perform our own SRS

• We will choose 5 students from the We will choose 5 students from the class at random. Now let’s try using class at random. Now let’s try using our calculator. our calculator.

Microsoft Excel Worksheet

Another Probability SampleAnother Probability Sample

• Stratified Random SampleStratified Random Sample– Divide the population into groups of Divide the population into groups of

similar individuals, called strata. Then similar individuals, called strata. Then choose a separate SRS from each choose a separate SRS from each stratum and combine the SRSs to form a stratum and combine the SRSs to form a full sample.full sample.•Example: Choose an SRS from each class – Example: Choose an SRS from each class –

freshmen, sophomores, juniors, and seniors.freshmen, sophomores, juniors, and seniors.

And AnotherAnd Another

• Cluster Random SampleCluster Random Sample– When you have items (or people) When you have items (or people)

grouped into clusters and you choose a grouped into clusters and you choose a random sample of the clusters and random sample of the clusters and examine all in the cluster.examine all in the cluster.•Ex. You choose an SRS of 2Ex. You choose an SRS of 2ndnd period classes period classes

(clusters) at NCHS and sample everyone in (clusters) at NCHS and sample everyone in those classesthose classes

Final Probability SampleFinal Probability Sample

• Multi-stage SampleMulti-stage Sample– Chooses the sample in stages.Chooses the sample in stages.

•Example: Take a random sample of the Example: Take a random sample of the counties in NC. Then, divide the counties counties in NC. Then, divide the counties into sectors. Take a random sample of the into sectors. Take a random sample of the sectors. Then divide each sector into blocks. sectors. Then divide each sector into blocks. Take a random sample of blocks. On each Take a random sample of blocks. On each block, take a random sample of households.block, take a random sample of households.

CAUTIONS:CAUTIONS:

• Response Bias:Response Bias:People Lie! Especially with People Lie! Especially with embarrassing or incriminating topics.embarrassing or incriminating topics.

• Wording of questions can be misleading:Wording of questions can be misleading:Choose one:Choose one:

Yes, I would like my taxes to stay the Yes, I would like my taxes to stay the same and not support the schools.same and not support the schools.

No, I approve of passing the bond to No, I approve of passing the bond to fund new schools.fund new schools.

• Larger random samples give more Larger random samples give more accurate results than smaller samples.accurate results than smaller samples.

Homework Homework

Chapter 4Chapter 4

# 2, 3, 8, 9, 10 # 2, 3, 8, 9, 10

Night 2: # 11, 12, 17, 21, 30Night 2: # 11, 12, 17, 21, 30