Section 13'1: Sampling Techniques

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Section 13.1 Sampling Techniques

• Dr. Fred Butler
• Math 121 Fall 2004

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Definition of Statistics

• Statistics is the science of gathering,
  analyzing, and making predictions from numerical
  information obtained in an experiment.
• Descriptive statistics is concerned with the
  collection, organization, and analysis of data.
• Inferential statistics is concerned with making
  predictions based on data.

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More Statistics Definitions

• The entire group you are studying using
  statistics is called the population.
• The subset selected for statistical study is
  called the sample.
• For example in a telephone poll about who people
  are going to vote for in an election, the entire
  electorate is the population, while the people
  who are called and polled are the sample.

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An Example

• Suppose you were given a box with 100 marbles in
  it 90 blue marbles and 10 red marbles as
  pictured below.
• Let us consider different ways to draw
  conclusions about the population in this example,
  the entire contents of 100 marbles in the box.

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Probability vs. Statistics

• In probability, we would count the marbles and
  see that there are 100 total, 10 red and 90 blue,
  so the probability of picking a red marble is
  10/1001/10.
• In statistics, we would select a sample of
  marbles from the box and try to predict what the
  probability of selecting a red marble is based on
  this sample.

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Probability vs. Statistics contd.

• There is always the possibility that predictions
  based on a sample will be incorrect.
• For example, we could randomly select 5 marbles,
  get all blue marbles, and incorrectly predict
  that there are only blue marbles in the box.
• If we selected a larger sample (say 15 marbles)
  we would likely choose some red marbles, and in
  this case we could probably make a more accurate
  prediction based on the sample selected.

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Why Sample?

• It is often impossible to obtain data on an
  entire population.
• Sampling is less expensive and takes less time
  and effort.

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Unbiased Samples

• An unbiased sample is one that is a small replica
  of the entire population with regard to income,
  education, gender, race, political affiliation,
  age, etc.
• Statisticians use sophisticated techniques to
  obtain an unbiased sample.
• Unbiased samples allow accurate predications
  based on relatively small samples of the entire
  population.

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Random Sampling

• If a sample is drawn in such a way that each item
  in the population has an equal chance of being
  selected, the sample is said to be a random
  sample.
• This technique is used when all items in the
  population are similar with regard to the
  specific characteristics we are interested in
  studying.

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Systematic Sampling

• When a sample is obtained by drawing every nth
  item on a list or production line, the sample is
  a systematic sample.
• It is important that every item from the
  population is included on the list used.
• Also be careful of a constantly recurring
  characteristic problem (Robot X example).

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Cluster Sampling

• Cluster sampling is a sampling technique in which
  we divide a geographic area into sections or
  clusters, and then randomly select sections or
  clusters.
• Either all members of each selected cluster are
  included in the sample, or a random sample of the
  members of each cluster is used.

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Stratified Sampling

• Stratified sampling involves dividing the
  population into strata by characteristics called
  stratifying factors (such as gender, race,
  religion, or income), and taking random samples
  from each stratum or class.
• The use of stratified sampling requires some
  knowledge about the population.

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Convenience Sampling

• A convenience sample uses data that are easily or
  readily obtained.
• One must be very careful with this sampling
  technique, because convenience sampling can be
  extremely biased.

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Determining Sampling Methods

• On the next several slides we will consider
  specific sampling scenarios, and we will try to
  determine what sampling method is being used in
  each of these scenarios.

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Class Question 5.11

• I look at the Math 121 class list and select
  every tenth student on the list to take a survey
  about the course.
• 1. random 2. systematic 3. cluster
• 4. stratified 5. convenience

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Answer to Class Question 5.11

• This is an example of systematic sampling,
  because it involves choosing every nth item (in
  our case n10).

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Class Question 5.12

• Students at WVU are classified by their major,
  and a random sample of 25 students from each
  major is selected.
• 1. random 2. systematic 3. cluster
• 4. stratified 5. convenience

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Answer to Class Question 5.12

• This is an example of stratified sampling.
• Students in this example are divided into strata
  based on their majors, and a random sample from
  each of the strata is chosen.

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Class Question 5.13

• I ask the students sitting in the front row what
  they think of this course.
• 1. random 2. systematic 3. cluster
• 4. stratified 5. convenience

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Answer to Class Question 5.13

• This is an example of a convenience sample,
  because I am picking people that are easily
  obtained.
• One possible bias that could be built into the
  survey is that students sitting in the front row
  might pay closer attention, and might think more
  highly of the course than other students.

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Class Question 5.14

• I write each Math 121 students name on a
  separate slip of paper, put the slips into a box,
  and draw ten student names to complete a survey
  about the course.
• 1. random 2. systematic 3. cluster
• 4. stratified 5. convenience

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Answer to Class Question 5.14

• This is an example of a random sample.
• Each student has an equal chance of being chosen
  from the box of names.

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Class Question 5.15

• Students at WVU are divided according to which
  dorm they live in, a random sample of dorms is
  chosen, and all students living in the chosen
  dorms are polled.
• 1. random 2. systematic 3. cluster
• 4. stratified 5. convenience

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Answer to Class Question 5.15

• This is an example of a cluster sample.
• The students are divided into geographic areas
  of the dorm they live in, and a random sample of
  these geographic areas are chosen.

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Section 13.2 The Misuses of Statistics

• Dr. Fred Butler
• Math 121 Fall 2004

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Questions to Ask When Examining Statistical
Statements

• Was the sample used to gather the statistical
  data unbiased?
• Was the sample used to gather the statistical
  data of sufficient size?
• Is the statistical statement ambiguous in any way?

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An Example

• Consider the statement, Four out of five
  dentists recommend sugarless gum for their
  patients who chew gum.
• Is the sample unbiased? (Maybe they sampled only
  dentists who own stock in the gum company
  conducting the survey.)
• How large is the sample? (Did they only survey
  five total dentists?)
• Is the statement ambiguous? (Maybe only 1 out of
  100 dentists recommend gum at all.)

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Ambiguous Words Average

• There are at least four different averages in
  statistics
• mean (traditional average)
• median (value in the middle)
• mode (most frequently occurring piece of data)
• midrange (half way between highest and lowest
  value in data set)

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Misusing the Word Average

• For example in a union contract negotiating, the
  company could state that the average salary of
  its employees is 35,000, while the union states
  that the average employee salary is 30,000.
• It is possible for both parties to be telling the
  truth, but to be using different meanings of the
  word average.

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Misusing the Word Largest

• Another word that can be used vaguely in
  statistical statements is largest.
• If company ABC claims it is the largest
  department store in the US, this could mean they
  have the largest
• 1. profit 4. staff
• 2. total sales 5. acreage
• 3. building 6. number of outlets.

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Drawing Irrelevant Conclusions

• Another deceptive technique (commonly used in
  advertising) is to state a claim from which the
  public may draw irrelevant conclusions.
• For example a paper towel company may claim that
  its paper towels are heavier than the
  competition, from which you are expected to
  conclude that they are more absorbent.
• Heaviness doesnt have anything to do with
  absorbency a rock is heavier than a sponge, but
  a sponge is more absorbent.

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Drawing Irrelevant Conclusions contd.

• A foreign car companys ad claims that 9 out of
  10 of one of the popular model cars it sold in
  the U.S. in the past 10 years are still on the
  road, from which you conclude that the car is
  well manufactured and will last a long time.
• The ad could neglect to mention that this model
  has only been sold in the U.S. for 5 years.
• They could have just as easily claimed that 9 out
  of 10 of this model car sold in the U.S. in the
  past 100 years are still on the road.

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Misleading Graphics

• It is also easy to be misled by graphical
  representations of statistical data.
• Some examples of this are discussed in the lab.

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Class Question 5.16

• According to the graphs below, which stock
  performed better between January and May?
• 1. Stock A 2. Stock B 3. Same

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Answer to Class Question 5.16
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Lecture Summary

• Sampling techniques include random sampling,
  systematic sampling, cluster sampling, stratified
  sampling, and convenience sampling.
• One must be careful when analyzing claims based
  on statistical data.

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Homework

• Do problems from Sections 13.1 and 13.2 of
  textbook.
• I will be giving lab help in the IML computer lab
  today (December 02) 330-430 and tomorrow
  (December 03) 1030-1130.
• Lab 5 is due Monday December 06 by 1100 PM