Unit 3 Applied Prob /Stat

Unit 3 Applied Prob/Stat Sampling Design

How do we gather data? • Surveys • Opinion polls • Interviews • Studies • Observational • Retrospective (past) • Prospective (future) • Experiments

the entire group of individuals that we want information about Population

a complete count of the population Census

How good is a census?Do frog fairy tale . . . The answer is 83!

Not accurate Very expensive Perhaps impossible If using destructive sampling, you would destroy population Breaking strength of soda bottles Lifetime of flashlight batteries Safety ratings for cars Why would we not use a census all the time? Look at the U.S. census – it has a huge amount of error in it; plus it takes a long to compile the data making the data obsolete by the time we get it! Since taking a census of any population takes time, censuses are VERY costly to do! Suppose you wanted to know the average weight of the white-tail deer population in Texas – would it be feasible to do a census?

A part of the population that we actually examine in order to gather information Use sample to generalize to population Sample

refers to the method used to choose the sample from the population Sampling design

a list of every individual in the population Sampling frame

Jelly Blubber Activity • Select 5 Jelly blubbers that you think are representative of the population of blubbers in regards to length. • Find the mean length of your sample

consist 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 PWSH 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 has 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!

population is divided into homogeneous groups called strata SRS’s are pulled from each strata Stratified random sample 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 PWSH students. Since students are already divided by grade level, grade level can be our strata. Then randomly select 50 seniors and randomly select50 juniors.

select sample by following a systematic approach randomly select where to begin Suppose we want to do a systematic random sample of PSWH students - number a list of students (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. Systematic random sample

based upon location randomly pick a location & sample all there Suppose we want to do a cluster sample of PSWH students. One way to do this would be to randomly select 10 classrooms during 2nd period. Sample all students in those rooms! Cluster Sample

For the Jelly Blubber colony: m = 19.41

Advantages Unbiased Easy Disadvantages Large variance May not be representative Must have sampling frame (list of population) SRS

Advantages More precise unbiased estimator than SRS Less variability Cost reduced if strata already exists Disadvantages Difficult to do if you must divide stratum Formulas for SD & confidence intervals are more complicated Need sampling frame Stratified

Advantages Unbiased Don’t need sampling frame Ensure that the sample is spread across population More efficient, cheaper, etc. Disadvantages Large variance Can be confounded by trend or cycle Formulas are complicated Systematic Random Sample

Advantages Unbiased Cost is reduced Sampling frame may not be available (not needed) Disadvantages Clusters may not be representative of population Formulas are complicated Cluster Samples

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

Identify the sampling design 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. Cluster sampling

Identify the sampling design 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. Systematic random sampling

each entry is equally likely to be any of the 10 digits digits are independent of each other Numbers can be read across. Random digit table Numbers can be read vertically. The following is part of the random digit table found on page 597 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 diagonally.

Suppose your population consisted of these 20 people: 1) Aidan 6) Fred 11) Kathy 16) Paul 2) Bob 7) Gloria 12) Lori 17) Shawnie 3) Chico 8) Hannah 13) Matthew 18) Tracy 4) Doug 9) Israel 14) Nan 19) Uncle Sam 5) 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. 1) Aidan 13) Matthew 18) Tracy 15) Opus 5) Edward Ignore. Ignore. Ignore. Ignore. Stop when five people are selected. So my sample would consist of : Aidan, Edward, Matthew, Opus, and Tracy Row 1 4 5 1 8 0 5 1 3 7 1 2 0 1 5 5 8 0 1 5 7 0 3 8 9 9 3 4 3 5 0 6 3

A systematic error in measuring the estimate favors certain outcomes Bias Anything that causes the data to be wrong! It might be attributed to the researchers, the respondent, or to the sampling method!

things that can cause bias in your sample cannot do anything with bad data Sources of Bias

People chose to respond Usually only people with very strong opinions respond Voluntary response 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 respondent selects themselves to participate in the survey! Remember – the way to determine voluntary response is: Self-selection!!

Ask people who are easy to ask Produces bias results Convenience sampling The data obtained by a convenience sample will be biased – however this method is often used for surveys & results reported in newspapers and magazines! 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!

some groups of population are left out of the sampling process 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 Undercoverage Suppose you take a sample by randomly selecting names from the phone book – some groups will not have the opportunity of being selected!

occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate telephone surveys 70% nonresponse Nonresponse Because of huge telemarketing efforts in the past few years, telephone surveys have a MAJOR problem with nonresponse! People are chosen by the researchers, BUT refuse to participate. NOT self-selected! This is often confused with voluntary response! One way to help with the problem of nonresponse is to make follow contact with the people who are not home when you first contact them.

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 Response bias occurs when for some reason (interviewer’s or respondent’s fault) you get incorrect answers.

wording can influence the answers that are given connotation of words use of “big” words or technical words – if surveying Podunk, TX, then you should avoidcomplex vocabulary. – if surveying doctors, then use more complex, technical wording. Wording of the Questions The level of vocabulary should be appropriate for the population you are surveying Questions must be worded as neutral as possible to avoid influencing the response.

Source of Bias? 1) Before the presidential election of 1936, FDR against Republican ALF Landon, the magazine Literary Digest predicting Landon winning the election in a 3-to-2 victory. A survey of 2.8 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 SMU. You collect register receipts for students as they leave the bookstore during lunch one day. Convenience sampling – easy way to collect data or Undercoverage – students who buy books from on-line bookstores are included.

3) To find the average value of a home in Plano, 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)

Unit 3 Applied Prob /Stat