Stat 1510 Statistical Thinking

1
Stat 1510Statistical Thinking Concepts

• Producing Data Sampling

2
Data

• Primary Data is the data collected by the
  investigator conducting the research / study with
  a specific purpose.
• Secondary Data - is data collected by someone
  other than the user for the same or different
  purpose.

3
Population

• Researchers often want to answer questions about
  some large group of individuals (this group is
  called the population)
• Population is a set of units. This population is
  potentially infinite or even hypothetical.
• If the time that unit are measured is important,
  then the population is often called process.
• So in analysis, it is important to be clear about
  what is the definition of population.

4
Population Sample

• We consider three type of units.
• The target population is the set of units to
  which the investigators set out to investigate in
  the definition of the problem
• The study population is the set of units that
  could have been in the sample
• The sample which is the set of units actually
  selected for the investigation. The total number
  of units in the sample is called sample size and
  the way that the samples are selected is called
  sampling protocol or sampling design.

5
Population Sample
6
Example

• Faculty of Science of Memorial University want
  to know the opinion of students on the university
  facilities. For this purpose, they conducted a
  survey by selecting a random sample of 200
  students survey registered for Winter 2013.
• Identify target population, study population
  sample sampling unit

7
Example

• Target Population Faculty of Science, MUN,
  Students
• Study Population All students registered for
  Winter 2013 in FoS of MUN
• Sample 200 students selected for this survey
• Sampling Unit Each selected student

8
Bad Sampling Designs

• Voluntary response sampling
• allowing individuals to choose to be in the
  sample
• Convenience sampling
• selecting individuals that are easiest to reach
• Both of these techniques are biased
• systematically favor certain outcomes

9
Voluntary Response

• To prepare for her book Women and Love, Shere
  Hite sent questionnaires to 100,000 women asking
  about love, sex, and relationships.
• 4.5 responded
• Hite used those responses to write her book
• Moore (Statistics Concepts and Controversies,
  1997) noted
• respondents were fed up with men and eager to
  fight them
• the anger became the theme of the book
• but angry women are more likely to respond

10
Convenience Sampling

• Sampling mice from a large cage to study how a
  drug affects physical activity
• lab assistant reaches into the cage to select the
  mice one at a time until 10 are chosen
• Which mice will likely be chosen?
• could this sample yield biased results?

11
Purposive Sampling

• Consider the selection of football team or soccer
  team.
• Consider selection of students for a math skill
  competition
• In the above sampling scheme, we select the
  sampling units with a well defined purpose and
  samples are not randomly picked.

12
Simple Random Sampling

• Each individual in the population has the same
  chance of being chosen for the sample
• Each group of individuals (in the population) of
  the required size (n) has the same chance of
  being the sample actually selected
• Random selection
• drawing names out of a hat
• table of random digits
• computer software

13
Table of Random Digits

• Table B on pg. 692 of text
• each entry is equally likely to be any of the 10
  digits 0 through 9
• entries are independent of each other (knowledge
  of one entry gives no information about any other
  entries)
• each pair of entries is equally likely to be any
  of the 100 pairs 00, 01,, 99
• each triple of entries is equally likely to be
  any of the 1000 values 000, 001, , 999

14
Choosing a Simple Random Sample (SRS)

• STEP 1 Label each individual in the population
• STEP 2 Use Table B to select labels at random

15
Simple Random Sample with and without
replacement

• Case 1 In without replacement, each selected
  sampling unit will not replaced back to the
  population.
• Case 2 In with replacement, each sampled unit
  will be replaced back to the population.

16
Probability Sample

• a sample chosen by chance
• must know what samples are possible and what
  chance, or probability, each possible sample has
  of being selected
• a SRS gives each member of the population an
  equal chance to be selected

17
Stratified Random Sample

• first divide the population into groups of
  similar individuals, called strata
• second, choose a separate SRS in each stratum
• third, combine these SRSs to form the full sample

18
Stratified Random SampleExample

• Suppose a university has the following student
  demographics
• Undergraduate Graduate First Professional
  Special
• 55 20
  5 20

A stratified random sample of 100 students could
be chosen as follows select a SRS of 55
undergraduates, a SRS of 20 graduates, a SRS of 5
first professional students, and a SRS of 20
special students combine these 100 students.
19
Stratified Random SampleExample

• We would like to take a sample to represent
  Canadian population
• We have different provinces and we wish
  represent the all provinces should be represented
  in the sample

A stratified random sample of 1000 people could
be chosen as follows From each province, we
select random samples. Since population in each
province differ heavily, samples from each
province should be proportional to its population.
20
Multistage Sample

• several stages of sampling are carried out
• useful for large-scale sample surveys
• samples at each stage may be SRSs, but are often
  stratified
• stages may involve other random sampling
  techniques as well (cluster, systematic, random
  digit dialing, )

21
Cautions about Sample Surveys

• Undercoverage
• some individuals or groups in the population are
  left out of the process of choosing the sample
• Nonresponse
• individuals chosen for the sample cannot be
  contacted or refuse to cooperate/respond
• Response bias
• behavior of respondent or interviewer may lead to
  inaccurate answers or measurements
• Wording of questions
• confusing or leading (biased) questions words
  with different meanings

22
Nonresponse

• To prepare for her book Women and Love, Shere
  Hite sent questionnaires to 100,000 women asking
  about love, sex, and relationships.
• 4.5 responded
• Hite used those responses to write her book
• angry women are more likely to respond

23
Response Bias

• A door-to-door survey is being conducted to
  determine drug use (past or present) of members
  of the community. Respondents may give socially
  acceptable answers (maybe not the truth!)
• For this survey on drug use, would it matter if a
  police officer is conducting the interview?
  (bias from interviewer)

24
Asking the UninformedWashington Post National
Weekly Edition (April 10-16, 1995, p. 36)
Response Bias

• A 1978 poll done in Cincinnati asked people
  whether they favored or opposed repealing the
  1975 Public Affairs Act.
• There was no such act!
• About one third of those asked expressed an
  opinion about it.

25
Wording of Questions
A newsletter distributed by a politician to his
constituents gave the results of a nationwide
survey on Americans attitudes about a variety of
educational issues. One of the questions asked
was, Should your legislature adopt a policy to
assist children in failing schools to opt out of
that school and attend an alternative
school--public, private, or parochial--of the
parents choosing? From the wording of this
question, can you speculate on what answer was
desired? Explain.
26
Wording Deliberate Bias

• If you found a wallet with 20 in it, would you
  return the money?
• If you found a wallet with 20 in it, would you
  do the right thing of returning the money?

27
Wording Unintentional Bias

• I have taught several students over the past few
  years.
• How many students do you think I have taught?
• How many years am I referring to?
• Over the past few days, how many servings of
  fruit have you eaten?
• How many days are you considering?
• What constitutes a serving?

28
Wording Unnecessary Complexity

• Do you sometimes find that you have arguments
  with your family members and co-workers?
• Arguments with family members
• Arguments with co-workers

29
Wording Ordering of Questions

• How often do you normally go out on a date?
  about ___ times a month.
• How happy are you with life in general?
• Strong association between these questions.
• If the ordering is reversed, then there would be
  no strong association between these questions

30
Inferences about the Population

• Values calculated from samples are used to make
  conclusions (inferences) about unknown values in
  the population
• Variability
• different samples from the same population may
  yield different results for a particular value of
  interest
• estimates from random samples will be closer to
  the true values in the population if the samples
  are larger
• how close the estimates will likely be to the
  true values can be calculated -- this is called
  the margin of error