sampling and experiments

Sampling and ExperimentsSection 6.1

Cathy Poliak, [email protected]

Office hours: T Th 2:30 - 5:15 pm 620 PGH

Department of MathematicsUniversity of Houston

March 22, 2016

Cathy Poliak, Ph.D. [email protected] Office hours: T Th 2:30 - 5:15 pm 620 PGH (Department of Mathematics University of Houston )Section 6.1 March 22, 2016 1 / 23

Outline

1 Beginning Questions

2 Sampling

3 An Example of an Infamous Sample

4 Simple Random Sample

5 Observational Studies vs. Experiments

Popper Set Up

Fill in all of the proper bubbles.

Use a #2 pencil.

This is popper number 13.

Popper #13 Questions

To conduct a pre-election opinion poll on a proposed city ordinance, arandom sample of telephone numbers from the city phone book werechosen and called. (Assume all who were called answered).

1. Identify the population.a) The city ordinanceb) All telephone numbers from the city phone book.c) The telephone numbers chosen and calledd) The people who answered

2. Identify the sample.a) The city ordinanceb) All telephone numbers from the city phone book.c) The telephone numbers chosen and calledd) The people who vote

Ways to obtain data

Previous information (Published Source)

Surveys

Designed Experiments

Observational Studies

Sampling: Examine part of the whole

We would like to draw conclusions about an entire population ofindividuals, but examining all of them may not be practical so wetake a sample.

The population in a statistical study is all members of a specifiedgroup, not necessary people, about which we want information.

A census is systematically getting information about the entirepopulation.

A sample is a part of the population from which we actually collectinformation, used to draw conclusion about the whole.

A sampling frame is a list of individual from which a sample isactually selected.

Why sample?

Obtaining information from the entire population maybe expensive.

It is impossible to examine every member of an infinitely largepopulation.

Business Statistics Communicating with Numbers, Jaggia and Kelly,2013, pg 6

Types of sampling

"A probability sample is a sample in which each member of thepopulation has a known, non-zero chance of being selected forthe sample." (Business Statistics, Donnelly, 2013, pg 294).

A Simple random sample (SRS)of size n consist of n individualsfrom the population chosen in such a way that every set of nindividuals has and equal chance to be the sample actuallyselected.

Stratified sampling - subdivide the population into at least twodifferent subgroups (strata) that share the same characteristics(as in gender or age bracket) then draw a simple random samplefrom each stratum.

In multistage sample design samples are taken from varioussubsets of the population until a manageable number of sample tointerview are arrived upon.

Types of sampling

Biased samples

The design of a study is biased if it systematically favors certainoutcomes. These sampling method favor some parts of thepopulation over others.

Voluntary Response Sample consists of people who choosethemselves by responding to a general appeal. This type ofsample is biased because people with strong opinions, especiallynegative opinions, are most likely to respond.

Convenience Sampling is a non-probability type of samplewhere the sample is chosen based on their convenientaccessibility and proximity.

Biased samples

Examples of Sampling

Identify the type of sampling design.A pollster wants to know who would likely get the highestPresidential vote in Houston. He randomly selects 1,000 people inHouston and ask who they would likely vote for in the nextPresidential election.

A pollster wants to know who would get the highest Presidentialvote in Houston but he thinks it may be different by age. So heseparates everyone by 18 - 25, 26 - 40, and 40 and older. Thentakes a simple random sample of 1,000 people in each group andask who they would likely vote for in the next Presidential election.

A local radio hosts wants to know who his listeners will likely votefor in the Presidential election. He asks his listeners to call in andsay who they will likely vote for in the next Presidential election.

An example of a survey

http://online.wsj.com/news/articles/SB115974322285279370?mod=tff_main_tff_top

In 1936 it was a presidential election year FDR vs. Landon.

The Literary Digest magazine predicted that Landon would winwith Roosevelt getting only 43% of the popular vote.

There were over 2 million replies to the survey.

However, Roosevelt won in 1936 62% to 38%.

What went wrong?

Undercoverage occurs when some groups in the population areleft out of the process of choosing the sample. The sample camefrom telephone listings, magazine subscriptions, car registrations,and club memberships.

Nonresponse occurs when an individual chosen for the samplecan’t be contacted or refuses to cooperate. Although there were2.3 million that responded, there were 10 million surveys sent out.Only a 23% response rate.

Cautions about surveys

Be careful of bias in an outcome. The design of a study is biasedif it systematically favors certain outcomes.

In human populations, even probability samples can suffer frombias due to:

I undercoverageI nonresponseI poorly worded questions

To conduct a pre-election opinion poll on a proposed city ordinance, arandom sample of telephone numbers from the city phone book werechosen and called. (Assume all who were called answered).

3. Identify the type of sampling design.a) Simple Random Sample (SRS)b) Stratified samplingc) Voluntary sampled) Multistage Sample design

How to take a Simple Random Sample (SRS)

We select an SRS by labeling all the individuals in the populationand using software or a table of random digits to select a sampleof the desired size.

In R: sample(1:N,n) where N = the number of individuals in thepopulation and n = the number of individuals in the sample.

A table of random digits is a long string of the digits 0 - 9 whereeach entry in the table is equally likely to be any of the 10 digitsand the entries are independent of each other.

Example of a Simple Random Sample

From The Practice of Business Statistics by Moore, et.al. 2011, p.157

A campus newspaper plans a major article on spring breakdestinations. The authors intend to call a few randomly chosenresorts at each detestation to asked about their attitudes towardgroups of students as guest.

In the next slide are the resorts listed in one city along withlabeling the members of this population.

01 Aloha Kai 10 Coconuts 19 Sea Castle02 Anchor Down 11 Diplomat 20 Sea Club03 Banana Bay 12 Holiday Inn 21 Sea Grape04 Banyan Tree 13 Lime Tree 22 Sea Shell05 Beach Castle 14 Outrigger 23 Silver Beach06 Best Western 15 Palm Tree 24 Sunset Beach07 Cabana 16 Radisson 25 Tradewinds08 Captiva 17 Ramada 26 Tropical Breeze09 Casa del Mar 18 Sandpiper 27 Tropical Shores

28 Veranda

The authors want to choose three of these resorts to call.To use the Random digits table read two-digit groups until youhave chosen three resorts. Ignore any two digits that are above28.To use R, sample(1:28,3)

Use the Random Digit Table start at line 120

> sample(1:28,3)[1] 10 13 4

The authors would call (10) Coconuts, (13) Lime Tree and (04) BanyanTree.

You have been hired by a company that is planning to build a newapartment complex for students in a college town. They want you tocollect information about preferences of potential customers for theircomplex. Most of the college student who live in an apartment live inone of the 10 complexes.

1 Ashley Oaks 2 Bay Pointe 3 Beau Jardin4 Brownstone 5 Cambridge 6 Chauncey Village7 Country View 8 Del-Lynn 9 Fairway Knolls10 Georgetown

4. Select a simple random sample of 2 of the following complexesstarting at line 137 using the Random Digits Table. Use 0 out ofthe digits for 10.

a) Beau Jardin & Fairway Knolls c) Ashely Oaks & Bay Pointeb) Beau Jardin & Beau Jardin d) Del-Lynn & Fairway Knolls

Another Example of Sampling

It is believed that 75% of all apartment dwellers in a large city deadbolttheir doors in addition to locking them as an added precaution againstburglary. Describe how you would select ans SRS of 20 apartmentdwellers to survey if there are 50 complexes in the city and eachcomplex has 250 residents.

Observation versus experiment

An observational study observes individuals and measuresvariables of interest but does not attempt to influence theresponses.

I Example: A pharmacy student would like to know if there is adifference in results from a specific brand of drug and its equivalentgeneric prescription. She randomly selects 50 people who take thedrug hand has them complete a questionnaire regarding theirsymptoms and improvements after taking the specific brand orgeneric equivalent.

An experiment deliberately imposes some treatment onindividuals in order to observe their responses.

I The editor of a magazine is wondering if the type of font used in thearticles affects the reading speed of the subscribers of themagazine. Hes asks 10 subscribers to read 4 articles each withdifferent fonts. If the reading speed increases with a particular font,hew will use it in the next publication.

Are each of these an a) experiment or b) observational study.5. Nordic mobiles from early-1980s may hike brain tumor risk.

Long-term users of some first generation cell phones primarilyused in Nordic countries face up to 80 percent greater risk ofdeveloping brain tumors than those who did not use the phones, anew Swedish study shows.

6. Work in mice paves way to new drugs. Studies of the ginsengberry may someday bear fruit for millions of Americans who sufferfrom obesity and its life-threatening complications. If new work inmice can be duplicated in people, researchers predict thedevelopment of novel drugs that deflate spare tires, while wardingoff diabetes.

sampling and experiments

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