Class 6- Sampling

8/7/2019 Class 6- Sampling

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Announcements

Tests returned at the end of class. Wewill discuss them next class period.

Theory and Hypotheses.

Due March 24

Assignment #2 (Chptr. 7 Sampling). Due March 31

Class cancelled on March 22. Tuesday after spring break


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Population v. Sample: Key Terms

Population: any well-defined set of units of analysis about

which we wish to generalize our theories.

Can be people, countries, corporations,

continents, etc.

Population Parameter:

Characteristics about a population that canbe quantified as a number.

(e.g. proportion, mean/average, etc.)


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Population v. Sample: Key Terms

Sample Any subset of units collected in some manner

from the population; the data we use to testour theories.

Estimator Numerically estimates the value of a

population characteristic, or populationparameter.

Sample Statistic An estimator of a population parameter

derived from a population sample.


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Types of Samples

Probability sample each element ofthe population has a known probabilityof being included in the sample

Nonprobability sample - each

element of the population has an

unknown probability of being includedin the sample


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Types of Nonprobability Samples

Convenience sample elements areincluded because they are convenientor easy for the researcher to select

Researcher may haphazardly selectindividuals

Problem may not be representativeof the population to which we want togeneralize


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Types of Nonprobability Samples

Quota samples elements arechosen based on selectedcharacteristics and the representation

of these characteristics in thepopulation

Ensures accurate representation of

selected characteristics Elements with selected characteristics

chosen in convenience fashion


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Problems with Non-ProbabilitySampling: Examples Remember the Dewey v. Truman

election? What happened?

Polls conducted during the Landen-Roosevelt and Dewey-Truman

elections were inaccurate.

Improper use of convenience samples Improper use of quota samples


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Problems with Non-ProbabilitySampling: Examples

Before 1936 Upper class and Working Class similar

partisan distribution


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Problems with Non-ProbabilitySampling: Examples

Before 1936 Upper class and Working Class similar

partisan distribution

1936 and beyond Upper class disproportionately

Republican

Working class disproportionatelyDemocrat


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1948 quota sampling incorrectly predicts Dewey to defeat Truman


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Types of Probability Samples

Simple random sample eachelement of the population has anequal chance of being selected

Systematic sample elementsselected from a list at predetermined

intervals


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Stratified sample elements inpopulation are grouped into strata,and each strata is randomly sampled


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Cluster sample elements aregrouped into clusters, and samplingproceeds in two stages:

A random sample of clusters is chosen Elements within selected clusters are then

randomly selected and aggregated to form finalsample

This is the sampling method used in manynational surveys (e.g. clusters=metropolitanareas, zip codes, area codes)


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Sampling and Statistical Inference:

Key Terms

Frequency distributions

Mean and Standard deviation

Proportions

Sampling distribution

Standard error

Sampling error

Confidence interval


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Frequency Distributions

For any variable X, a tabular orgraphical display of the number ofobservations per value/category of

that variable


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Mean and Standard Deviation

For any collection of observationsmeasured at the interval or ratio level:

Mean = the simple average/expectedvalue

Standard deviation = the averagedistance of each observation from themean (intuitive definition)


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Mean and Standard Deviation

Weekly Income Mean Deviation100 100 200 =100150 150 200 = -50

200 200 200 = 0300 300 200 =100250 250 200 = 50

Mean = 200 Standard Deviation = 79.06


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Proportion

The ratio of the number ofobservations taking a specific value, tothe total number of observations

P = # / N

Example: 4/10=.40


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Sampling Distribution(of sample proportions)

Population

Draw Random Sample of Size N

Calculate sample proportion

Repeat until all possible random samples of size Nare exhausted

The resulting collecting of sample proportions is the samplingdistribution of sample proportions


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Sampling Distribution(of Sample Proportions)

Def: A frequency distribution of allpossible sample proportions for a

given sample size (N)

The mean of the samplingdistribution will be equal to the

population proportion.


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Sampling Distribution(of Sample Proportions)

The shape of the sampling distributionwill be a normal distribution


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Example of a Sampling Distribution


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Example of a Sampling Distribution


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Standard Error

How the sample proportions vary fromsample to sample (i.e. within thesampling distribution) is expressedstatistically by the value of thestandard deviation of the samplingdistribution (the standard error).


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Standard Error, cont.

The standard error for a sampleproportion is equal to the square

root of: P(1-P) / N

(where P=population proportion)


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The Standard Error and the Margin

of Error in Surveys

The standard error is a measure ofsampling variability for a samplestatistic

If we know the standard error, we cancalculate a margin of error for our

sample proportion


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Calculating the Margin of Error

First, we must choose a level ofcertainty (confidence level); usually95%

The margin of error (with a 95%confidence level) is equal to 1.96*SE


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Example: Presidential Approval

Newsweek Poll conducted byPrinceton Survey ResearchAssociates International. Sept. 29-30,

2005. N=1,004 adults nationwide.MoE 3..

"Do you approve or disapprove of

the way George W. Bush ishandling his job as president?(40% approve)


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Calculating the margin of error for a

40% approval rating The standard error for a sample proportion

is equal to the square root of: P(1-P) / N

The margin of error (with a 95% confidence

level) is equal to 1.96*SE .40*.60/1004=.000239

.000239 = .01546

1.96*.01546=.03 (and thus, MOE = +/- .03)


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Sample Size and Sampling Error


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Polling Accuracy

Presidential Election 2008 Actual outcome: Obama 52.9%, McCain 45.7%

Pollster.com: http://www.pollster.com/polls/us/08-us-pres-ge-mvo.php

Are todays samples truly representative? Cell phone-only households and sampling bias

http://www.pollster.com/blogs/cell_phone_only_househol

ds_by.php http://pewresearch.org/pubs/964/cell-phones-and-the-

2008-vote-an-update

http://www.pollster.com/blogs/plotting_pollster_accuracy.php
http://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/blogs/cell_phone_only_households_by.phphttp://www.pollster.com/blogs/cell_phone_only_households_by.phphttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://www.pollster.com/blogs/plotting_pollster_accuracy.phphttp://www.pollster.com/blogs/plotting_pollster_accuracy.phphttp://www.pollster.com/blogs/plotting_pollster_accuracy.phphttp://www.pollster.com/blogs/plotting_pollster_accuracy.phphttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://pewresearch.org/pubs/964/cell-phones-and-the-2008-vote-an-updatehttp://www.pollster.com/blogs/cell_phone_only_households_by.phphttp://www.pollster.com/blogs/cell_phone_only_households_by.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.phphttp://www.pollster.com/polls/us/08-us-pres-ge-mvo.php

Class 6- Sampling

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