AP StatisticsMonday, 28 September 2015

• OBJECTIVE TSW explore sampling design.

• TESTS are graded.

• AGENDA: 09/28/15 – 10/02/15– MONDAY Read Ch. 11 (pp. 280-299)

Sampling Design NotesTest Addendum

– TUESDAY WS Sampling Design (due on Friday, 10/02/15)

Test Addendum due– WED Read Ch. 12 (pp. 305-325)

Experimental Design Notes

– FRIDAY ASSESSMENT: 1st Six Weeks (partners, I choose)

Chapter 2Sampling Design

How do we gather data?• Surveys • Opinion polls• Interviews• Experiments • Studies

– Observational– Retrospective (past)– Prospective (future)

Population•the entire group of individuals that we want information about

Census•a complete count of the population

Why would we not use a census all

the time?1) Not accurate2) Very expensive3) Perhaps impossible4) *If using destructive sampling, you

would destroy population • Breaking strength of soda bottles• Lifetime of flashlight batteries• Safety ratings for cars

Look at the U.S. census – it has a huge amount of error in it; plus it takes a long time to compile the

data making the data obsolete by the time we

get it!

Suppose you wanted to know the average weight

of the white-tail deer population in Texas –

would it be feasible to do a census?

Since taking a census of any population takes time, censuses are VERY costly

to do!

Sample• A part of the population that we actually examine in order to gather information

• Use sample to generalize to population

Sampling design•refers to the

method used to choose the sample from the population

Sampling frame•a list of every

individual in the population

How good is a census?

Do frog fairy tale . . .

The answer is 83!

AP StatisticsTuesday, 29 September 2015

• OBJECTIVE TSW explore sampling design.

• Hand forward TEST Addendum.

• AGENDA: 09/28/15 – 10/02/15– MONDAY Read Ch. 11 (pp. 280-299)

Sampling Design NotesTest Addendum

– TUESDAY WS Sampling Design (due on Friday, 10/02/15)

Test Addendum due– WED Read Ch. 12 (pp. 305-325)

Experimental Design Notes

– FRIDAY ASSESSMENT: 1st Six Weeks (partners, I choose)

• consists of n individuals from the population chosen in such a way that–every individual has an equal chance of being selected

–every set of n individuals has an equal chance of being selected

Simple Random Sample (SRS)Suppose we were to take an SRS

of 100 JVHS students – put each students’ name in a hat. Then

randomly select 100 names from the hat. Each student has the same chance to be selected!

Not only does each student have the same chance to be selected – but every possible group of 100 students has the same chance to be selected! Therefore, it has to

be possible for all 100 students to be seniors in order for it to be an

SRS!

Stratified random sample•population is

divided into homogeneous groups called strata

•SRS’s are pulled from each strata

Homogeneous groups are groups that are alike based upon some characteristic of the group members.

Suppose we were to take a stratified random sample of 100 JVHS

students. Since students are already divided by grade level,

grade level can be our strata. Then randomly select 50 seniors and

randomly select 50 juniors.

Systematic random sample•select sample by

following a systematic approach

• randomly select where to begin

Suppose we want to do a systematic random sample of JVHS students -

number a list of students(Suppose there are approximately 2000 students – if we want a sample of 100,

2000/100 = 20)Select a number between 1 and 20 at random. That student will be the first

student chosen, then choose every 20th student from there.

Cluster Sample•based upon

location•randomly pick a location & sample all there

Suppose we want to do a cluster sample of JVHS students. One way to do this would be to randomly select

10 classrooms during 2nd period. Sample all students in those rooms!

Multistage sample

• select successively smaller groups within the population in stages

• SRS used at each stage

To use a multistage approach to sampling JVHS students, we could

first divide 2nd period classes by level (AP, Honors, Regular, etc.) and

randomly select 4 second period classes from each group. Then we could randomly select 5 students from each of those classes. The

selection process is done in stages!

SRS• Advantages

–Unbiased–Easy

• Disadvantages–Large variance

–May not be representative

–Must have sampling frame (list of population)

Stratified• Advantages

–Gives a more precise unbiased estimator than SRS

–Less variability

–Cost reduced if strata already exist

• Disadvantages–Difficult to do if

you must divide stratum

–Formulas for SD & confidence intervals are more complicated

–Need sampling frame

Systematic Random Sample

• Advantages–Unbiased–Ensures that the sample is

distributed across population–More efficient, cheaper, etc.

• Disadvantages–Large variance–Can be

confounded by a trend or a cycle

–Formulas are complicated

Cluster Samples

• Advantages–Unbiased –Cost is reduced–Sampling frame may not be available (not needed)

• Disadvantages–Clusters may not be representative of population

–Formulas are complicated

Identify the sampling design

1)The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, etc.) Then they randomly selected 3 colleges from each group.

Stratified random sample

2) A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks.

Identify the sampling design

Cluster sampling

3) A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer, and to every 10th customer after them, to fill it out before they leave.

Identify the sampling design

Systematic random sampling

Random digit table

•each entry is equally likely to be any of the 10 digits

•digits are independent of each other

The following is part of the random digit table found on page 847 of your textbook:

Row

1 4 5 1 8 5 0 3 3 7 1

2 4 2 5 5 8 0 4 5 7 0

3 8 9 9 3 4 3 5 0 6 3

Numbers can be read across.

Numbers can be read vertically.

Numbers can be read diagonally.

Suppose your population consisted of these 20 people:

1) Aidan6) Fred 11) Kathy 16) Paul2) Bob 7) Gloria 12) Lori 17) Shawnie3) Chico 8) Hannah 13) Matthew 18) Tracy4) Doug 9) Israel 14) Nan 19) Uncle Sam5) Edward 10) Jung 15) Opus 20) Vernon

Use the following random digits to select a sample of five from these people.

We will need to use double digit random

numbers, ignoring any number greater than 20.

Start with Row 1 and read across.

Row1 4 5 1 8 0 5 1 3 7 12 0 1 5 5 8 0 1 5 7 03 8 9 9 3 4 3 5 0 6 3

Ignore.

18) Tracy

5) Edward

13) Matthew

1) Aidan

15) Opus

Ignore.Ignore.Ignore.

Stop when five people are selected. So my sample would

consist of :

Aidan, Edward, Matthew, Opus, and Tracy

AP StatisticsWednesday, 30 September 2015

• OBJECTIVE TSW (1) finish exploring sampling design, and (2) investigate experimental design.

• ASSIGNMENT DUE FRIDAY– WS Sampling Design given today

• LOOKING AHEAD– Friday, 02 Oct 2015: ASSESSMENT Units 1 & 2

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70366 04570

4518503371…87

Bias•ERROR•favors certain outcomes

Anything that causes the data to be wrong! It might be attributed

to the researchers, the respondent, or to the sampling method!

Response bias• occurs when the behavior of respondent or interviewer causes bias in the sample

• wrong answers

Suppose we wanted to survey high school students on drug

abuse and we used a uniformed police officer to

interview each student in our sample – would we get honest

answers?

Response bias occurs when for some reason (interviewer’s or

respondent’s fault) you get incorrect answers.

Wording of the Questions

• wording can influence the answers that are given

• connotation of words• use of “big” words or technical words

Questions must be worded as neutral as possible to avoid influencing the response.

The level of vocabulary should be appropriate for the population you are surveying

– if surveying Podunk, TX, then you should

avoid complex vocabulary.

– if surveying doctors, then use more

complex, technical wording.

Sources of Bias

• things that can cause bias in your sample

•cannot do anything with bad data

Voluntary response

•People chose to respond

•Usually only people with very strong opinions respond

An example would be the surveys in magazines that ask readers to

mail in the survey. Other examples are call-in shows,

American Idol, etc.

Remember, the respondents select themselves to participate

in the survey!

Remember – the way to determine

voluntary response is:

Self-selection!!

Convenience sampling

•Ask people who are easy to ask

•Produces bias results

An example would be stopping friendly-looking people in the

mall to survey. Another example is the surveys left on

tables at restaurants - a convenient method!

The data obtained by a convenience sample will be

biased – however this method is often used for surveys & results

reported in newspapers and magazines!

Undercoverage•some groups of

population are left out of the sampling process

Suppose you take a sample by

randomly selecting names from the phone

book – some groups will not

have the opportunity of being selected!

People with unlisted phone numbers – usually high-income families

People without phone numbers –usually low-income families

People with ONLY cell phones – usually young adults

Nonresponse• occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate

• telephone surveys 70% nonresponse

People are chosen by the researchers, BUT refuse to

participate.

NOT self-selected!

This is often confused with voluntary response!

Because of huge telemarketing efforts in the past few years,

telephone surveys have a MAJOR problem with nonresponse! One way to help with the

problem of nonresponse is to make follow up contact with the people who are not home when you first contact them.

Source of Bias?1) Before the presidential election of 1936, FDR against Republican Alf Landon, the magazine Literary Digest predicted Landon winning the election in a 3-to-2 victory. It was a survey of 10 million people. George Gallup surveyed only 50,000 people and predicted that Roosevelt would win. The Digest’s survey came from magazine subscribers, car owners, telephone directories, etc.

Undercoverage – since the Digest’s survey comes from car owners, etc., the people selected were mostly from high-income families and thus mostly Republican! (other answers are possible)

2) Suppose that you want to estimate the total amount of money spent by students on textbooks each semester at Texas Tech. You collect register receipts for students as they leave the bookstore during lunch one day.

Convenience sampling – easy way to collect data

orUndercoverage – students who

buy books from on-line bookstores are not included.

3) To find the average value of a home in Jersey Village, one averages the price of homes that are listed for sale with a realtor.

Undercoverage – leaves out homes that are not for sale or

homes that are listed with different realtors.

(other answers are possible)

Assignment• WS Sample Design

– Due on Friday, 02 October 2015.

• LOOKING AHEAD– Friday, 02 October 2015: ASSESSMENT Units 1 & 2

(partners I choose)

– Tuesday, 06 October 2015: QUIZ: Sampling Design

• I will start Experimental Design at 12:20 PM.