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1. Elementary Statistics
Chapter 1:
Introduction to
Statistics
1.3 Collecting Sample
Data
1

2. Chapter 1:
Introduction to Statistics
1.1 Statistical and Critical Thinking
1.2 Types of Data
1.3 Collecting Sample Data
2
Objectives:
1. Demonstrate knowledge of statistical terms.
2. Differentiate between the two branches of statistics.
3. Identify types of data.
4. Identify the measurement level for each variable.
5. Identify the four basic sampling techniques.
6. Explain the difference between an observational and an experimental study.
7. Explain how statistics can be used and misused.

3. 1. Sampling Methods:
Random
Systematic
Stratified
Cluster
Convenience
1. Distinguish between an observational study and an experiment
2. Explain the various types of observational studies
3
Section Objectives

4. Key Concept
The method used to collect sample data influences the quality of the statistical
analysis.
If sample data are not collected in an appropriate way, the data may be useless.
Of particular importance is the simple random sample.
1.3 Collecting Sample Data
The Gold Standard:
Randomization with placebo/treatment groups is sometimes called the “gold
standard” because it is a highly effective method. (A placebo such as a sugar pill
has no medicinal effect.)
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Statistical methods are driven by the data that we collect. We typically
obtain data from two distinct sources: observational studies and
experiments.

5. Basics of Collecting Data
1.3 Collecting Sample Data
Experiment:
Apply some treatment and then proceed to observe its effects on the individuals. (The
individuals in experiments are called experimental units, and they are often called
subjects when they are people.) In other words, an experiment is a controlled study that
aims to determine the effect of one or more explanatory variables or factors on a
response variable. Any combination of the values of the factors is called a treatment.
The researcher manipulates the independent (explanatory) variable and tries to
determine how the manipulation influences the dependent (outcome) (response)
variable in an experimental study.
5
Observational study:
Observing and measuring specific characteristics without attempting to modify
(influence) the individuals being studied, in an observational study, the researcher
merely observes and tries to draw conclusions based on the observations.
Observational studies do not lead to a claim for
causation, they can lead to only association.

6. 6
Example 1
It’s an
experiment,
because
subjects were
given
treatments
a. Back pain Treatment: In a study to test the effectiveness of a drug
for back pain, 1643 patients were randomly assigned to:
Group 1 (Placebo: Pills with no medication): 547 subjects
Group 2 ( Pain Medication taken at regular intervals: 550 subjects
Group 3 ( Pain Medication taken as needed for pain: 546 subjects
Observational study or experiment? Any problem?
Experiment: Sample consists of male physicians only. It would be better to
include female physicians as well as males and females that re not physicians.
b. A physicians’ health study involved 22,701 male physicians. They randomly split
them in half; half of the physicians were treated with Aspirin and the other half were
given placebos.
Observational study, the sample is too small.
c. Blood pressure A researcher selected 4 males and 4 females to test for a difference in
systolic blood pressure levels between males and females who are 12 years of age .

7. An experiment is a controlled study that aims to determine the effect of one or more explanatory variables
or factors on a response variable. Any combination of the values of the factors is called a treatment.
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The experimental unit (or subject) is a person or object which a treatment is applied.
A control group serves as a reference point treatment that can be used to compare to other treatments.
A placebo is a harmless medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication with no
medicinal effect.
A Lurking (extraneous) variable is a variable that has an important effect on the relationship among the variables in the study,
but is not one of the explanatory variables studied. (It is one that is not considered in a study).
A confounding variable: Two variables are confounded when their effects on a response variable cannot be distinguished from
each other. A confounding variable influences the dependent variable but cannot be separated from the independent variable.
Replication is the repetition of an experiment on more than one individual. We can see effects of treatments through usage of large
sample sizes..
Randomization is used when subjects are assigned to different (treatment) groups through a process of random selection. Use
chance to create groups that are similar, and minimize the effects of variables whose level cannot be controlled. Therefore,
randomization is to “averages out” the effect of uncontrolled predictor variables.
Blinding is a technique in which the subject doesn’t know whether he or she is receiving a treatment or a placebo. Blinding is a way
to get around the placebo effect, which occurs when an untreated subject reports an improvement in symptoms.
Double-Blind: Blinding occurs at two levels:
1. The subject doesn’t know whether he or she is receiving the treatment or a placebo.
2. The experimenter does not know whether he or she is administering the treatment or placebo.
Features of an Experiment: A research scientist studies
the effect of diet and
exercise on a person's blood
pressure. Lurking
variables that also affect
blood pressure are whether a
person smokes and stress
levels.

8. Example 2
8
A Math Department is planning to offer an online version of the statistics
course. They randomly split a section of the course and half of the
students are placed in the traditional course and the other half in an online
version. At the end of the semester, both groups will be given a test to
determine which performed better.
a. Who are the experimental units?
b. What is the population for which this study applies?
c. What are the treatments?
d. What is the response variable?
e. Why can’t this experiment be conducted with blinding?
a. The students in the class
b. All students who
enroll in the
statistics course
c. Traditional vs. online instruction
d. dependent (outcome) (response) variable:
Test score
e. Both the students and instructor know which treatment they are receiving

9. Simple Random Sample (SRS)
1.3 Collecting Sample Data
SRS: A sample of n subjects is selected in such a way that every possible sample of the
same size n has the same chance of being chosen.
Random sampling is the process of using chance to select individuals from a population
to be included in the sample. A simple random sample is often called a random sample, but
strictly speaking, a random sample has the weaker requirement that all members of the
population have the same chance of being selected.
Some Sampling Techniques
Random – random number generator
Systematic – every kth subject
Stratified – divide population into homogeneous subgroups & pick from each group
Cluster – divide population into non-homogeneous subgroups & use all in those
groups
Convenient – mall surveys (the individuals are easily obtained)
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10. Systematic Sampling: Select some starting point
and then select every kth element in the population.
1.3 Collecting Sample Data
Stratified Sampling: Divide the population into
homogeneous (the subjects within the same subgroup
must be similar and share the same characteristics),
subgroups called strata, and then obtaining a simple
random sample from each subgroup (stratum).
Cluster Sampling: Divide the population into sections (or clusters)
non-homogeneous subgroups , then randomly select some of those
clusters, and choose all the members from those selected clusters.
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Convenience Sampling: Use data that are very easy to get.
Multistage Sampling: Collect data by using some combination of the
basic sampling methods. In a multistage sample design, pollsters
select a sample in different stages, and each stage might use different
methods of sampling. It is more practical for large-scale surveys to
obtain samples using a combination of the techniques discussed.

11. 11
Example 3: Given the following
a. What type of sampling is used? Does it affect the result?
b. Is this an Observational study or experiment?
c. What is the response rate (%)? Is it low? In general
what is the problem with a very low response rate?
Observational study because there was no treatment given to subjects .
717/5000 = 0.1434
717 or 14% is quite low; it can create a biased sample that consists of
those with a special interest in the topic.
Convenience Sampling: Although, the sample may not be representative of the
population, indication of which ear is used for cell phone calls and which hand is
the dominant should not be distorted much by a sample bias
A survey was emailed to 5000 people asking for which ear is used for
cell phone calls, and which hand is the dominant; and 717 were returned.

12. 12
What Sampling Technique is used?
Random, Systematic, Stratified, Cluster, Convenience
Convenience
Random
Cluster
Stratified
Systematic
Example 4

13. Observational Studies Observe and measure, but do not modify.
1.3 Collecting Sample Data
Types of Observational Studies
Cross-sectional study: Data are observed, measured, and collected at one point
in time, not over a period of time.
Retrospective (or Case-control) study: Data are collected from a past time
period by going back in time (through examination of records, interviews, and so
on). In case-control studies, individuals who have certain characteristics are matched
with those that do not.
Prospective (or longitudinal or cohort) study: Data are collected in the future
from groups sharing common factors (called cohorts).
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14. 14
Types of Observational Studies:
Cross-sectional study (at one point in time)
Retrospective (or case control) study (past time period )
Prospective (or longitudinal or cohort) study (future cohorts)
Retrospective (or case control) study
Cross-sectional study
Prospective (or longitudinal or cohort) study
Example 5

15. 1.3 Collecting Sample Data, Controlling Effects of Variables
Matched Pairs Design: Compare two treatment groups by using subjects matched in pairs
that are somehow related or have similar characteristics. (the same person before and after
a treatment, twins, husband and wife, same geographical location, and so on).
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Matched Pairs
Design
Example 6
Randomized Block Design
A Randomized Block Design is used when the experimental units (subjects) are divided into
homogeneous (similar) groups called blocks. Within each block, the subjects are randomly assigned
to treatments. Normally, blocks differ in ways that might affect the outcome of the experiment
Completely Randomized Experimental Design: Assign subjects to different
treatment groups through a process of random selection
Rigorously Controlled Design: Carefully assign subjects to different treatment groups, so that those given
each treatment are similar in ways that are important to the experiment. (difficult to implement)
Completely Randomized
Experimental Design

16. 16
Design of Experiment

17. Sampling Errors
No matter how well you plan and execute the sample collection process,
there is likely to be some error in the results.
Sampling error (or random sampling error) occurs when the sample has been
selected with a random method, but there is a discrepancy between a sample result and
the true population result; such an error results from chance sample fluctuations. ( it
results from using a sample to estimate information about a population and is due to
the fact that a sample gives incomplete information about a population.)
Non-sampling error is the result of human error, including such factors as wrong
data entries, computing errors, questions with biased wording, false data provided by
respondents, forming biased conclusions, or applying statistical methods that are not
appropriate for the circumstances.
Nonrandom sampling error is the result of using a sampling method that is not
random, such as using a convenience sample or a voluntary response sample.
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1.3 Collecting Sample Data

18. Example 7 (Time)
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Medication X is believed to be effective in preventing cavities. A sample of 75 kids
were given milk with and without medication X and were asked to evaluate the taste of
each. The researchers measured the children’s ratings of the two types of milk.
a. What is the response (dependent) variable?
Matched Pairs Design
a. Rating
b. Age and gender of the children; Milk
with and without med-X is the factor that
was manipulated
c. Milk with med-X and milk without med-X; 2
d. Matched-pairs design
e. 75 kids
f. Remove any effect due to
order in which milk is drunk.
g. Yes!
b. Think of some of the factors in the study. Which are
controlled? Which factor is manipulated?
c. What are the treatments? How many are there?
d. What type of experimental design is this?
e. Identify the experimental units.
f. Why would it be a good idea to randomly assign whether
the child drinks the milk with med-X first or second?
g. Would it be a good idea to double-blind this experiment?

19. Example 8
19
Step 1: The response variable is miles per gallon.
Step 2: Factors that affect miles per gallon:
Engine size, outside temperature, driving style, driving conditions, characteristics of car
Step 3: Use 12 cars all of the same model and year.
Step 4: We list the variables and their level.
• Octane level: 3 levels. Treatment A: 87, Treatment B: 89, Treatment C: 92 octane
• Engine size - fixed
• Temperature - uncontrolled, but will be the same for all 12 cars.
• Driving style/conditions - all 12 cars will be driven under the same conditions on a
closed track - fixed.
• Other characteristics of car - all 12 cars will be the same model year, however, there
is probably variation from car to car. To account for this, we randomly assign the
cars to the octane level.
Step 5: Randomly assign 4 cars to the 87 octane, 4 cars to the 89 octane, and 4 cars to the 92
octane. Give each car 3 gallons of gasoline. Drive the cars until they run out of gas. Compute
the miles per gallon.
Step 6: Determine whether any differences exist in miles per gallon.
The octane of fuel is a measure of its resistance to detonation with a higher
number indicating higher resistance. An engineer wants to know whether
the level of octane in gasoline affects the gas mileage of an automobile.
Completely Randomized Design

20. Example 9
20
A Randomized Block Design
This is a randomized block design where gender forms the block. This way, gender
will not play a role in the value of the response variable, test score. We do not compare
test results across gender.
Recall: A Math Department is
planning to offer an online version of
the statistics course. There is a belief
that there may be a difference in the
performance of the men and women
in these courses. Therefore, the
department randomly assigns half the
60 men to each of the two courses
and they do the same for the 70
women.

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• Suspect Samples
 Is the sample large enough?
 How was the sample selected?
 Is the sample representative of the population?
• Ambiguous Averages
 What particular measure of average was used and why?
• Changing the Subject
 Are different values used to represent the same data?
• Detached Statistics
 One third fewer calories…….than what?
• Implied Connections
 Studies suggest that some people may understand what this statement means.
• Misleading Graphs
 Are the scales for the x-axis and y-axis appropriate for the data?
• Faulty Survey Questions
 Do you feel that statistics teachers should be paid higher salaries?
 Do you favor increasing tuition so that colleges can pay statistics teachers higher salaries?
Uses and Misuses of Statistics (Time)
Computers and
Calculators
• Microsoft Excel
• Microsoft Excel with MegaStat
• TI-83/84
• Minitab
• SAS
• SPSS

22. Example 10
Observational Study: Observe past data to conclude that ice cream causes
drownings (based on data showing that increases in ice cream sales are associated with
increases in drownings).
Experiment: Conduct an experiment with one group treated with ice cream while
another group gets no ice cream.
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The mistake is to miss the lurking (extraneous: An extraneous variable is one that is
not considered in a study , and is not one of the explanatory variables in the study, but
is thought to affect the response variable.)variable of temperature and the failure to
see that as the temperature increases, ice cream sales increase and drownings increase
because more people swim.
We would see that the rate of drowning victims is about the same in both groups, so
ice cream consumption has no effect on drownings.
Here, the experiment is clearly better than the observational study.
Observational studies do not lead to a claim for
causation, they can lead to only association.

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Example 11 Observational study or experiment?
Do Flu shots Benefit Seniors?
The researchers looked at records of over 36,000 seniors (65 years and older) for 10 years.
The seniors were divided into two groups. Group 1 were seniors who chose to get a flu
vaccination shot, and group 2 were seniors who chose not to get a flu vaccination shot.
After observing the seniors for 10 years, it was determined that seniors who get flu shots
are 27% less likely to be hospitalized for pneumonia or influenza and 48% less likely to
die from pneumonia or influenza. Based on the results of this study, would you recommend that all
seniors go out and get a flu shot?
The study may have flaws! Namely, confounding.
Some lurking variables in this study: age, health status, or mobility of the senior
Even after accounting for potential lurking variables, the authors of the study
concluded that getting an influenza shot is associated with a lower risk of being
hospitalized or dying from influenza.

24. 24
Example 12 Illustrating Simple Random Sampling & Process
Suppose a study group of consists of 5 students:
Bob, Patricia, Mike, Jan, and Maria
2 of the students must go to the board to demonstrate a homework problem.
List all possible samples of size 2 (without replacement).
• Bob, Patricia
• Bob, Mike
• Bob, Jan
• Bob, Maria
• Patricia, Mike
• Patricia, Jan
• Patricia, Maria
• Mike, Jan
• Mike, Maria
• Jan, Maria
1) Obtain a frame that lists all
the individuals in the
population of interest.
Number the individuals in
the frame 1 – N.
2) Use a random number table,
graphing calculator, or
statistical software to
randomly generate n
numbers where n is the
desired sample size.

25. 25
Example 13 Obtaining a Simple Random Sample
The 112th Congress of the United States had 435 members in the House of
Representatives. Explain how to conduct a simple random sample of 5
members to attend a Presidential luncheon. Then obtain the sample.
Step 1 Put the members in alphabetical order. Number the members from
1 - 435.
Step 2 Randomly select five numbers using a random number generator.
First, set the seed. The seed is an initial point for the generator to start
creating random numbers—like selecting the initial point in the table of
random numbers. The seed can be any nonzero number. Then generate the
random numbers.
Step 3 Match the generated random numbers to the
corresponding Representatives.

26. 26
Example 14 Observational study & type, or experiment?
a. Researchers wanted to assess the long-term psychological effects on children evacuated during
World War II. They obtained a sample of 169 former evacuees and a control group of 43 people who
were children during the war but were not evacuated. The subjects’ mental states were evaluated
using questionnaires. It was determined that the psychological well being of the individuals was
adversely affected by evacuation. a. Observational study; Case-control
b. Xylitol has proven effective in preventing dental caries (cavities) when included in food or gum. A total
of 75 Peruvian children were given milk with and without xylitol and were asked to evaluate the taste of
each. Overall, the children preferred the milk flavored with xylitol. b. Designed experiment
c. A total of 974 homeless women in the Los Angeles area were surveyed to determine their level of
satisfaction with the healthcare provided by shelter clinics versus the healthcare provided by government
clinics. The women reported greater quality satisfaction with the shelter and outreach clinics compared
to the government clinics. c. Observational study; Cross-sectional
d. The Cancer Prevention Study II (CPS-II) is funded and conducted by the American Cancer Society. Its goal is to
examine the relationship among environmental and lifestyle factors on cancer cases by tracking approximately 1.2
million men and women. Study participants completed an initial study questionnaire in 1982 providing
information on a range of lifestyle factors such as diet, alcohol and tobacco use, occupation, medical history, and
family cancer history. These data have been examined extensively in relation to cancer mortality. Vital status of
study participants is updated biennially. Cause of death has been documented for over 98% of all deaths that have
occurred. Mortality follow-up of the CPS-II participants is complete through 2002 and is expected to continue for
many years. d. Observational study; cohort

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Sampling

28. 28
Example 15
EXAMPLE Multistage Sampling: In practice, most large-scale surveys obtain samples
using a combination of the techniques just presented.
As an example of multistage sampling, consider Nielsen Media Research. Nielsen randomly
selects households and monitors the television programs these households are watching
through a People Meter. The meter is an electronic box placed on each TV within the
household. The People Meter measures what program is being watched and who is watching it.
Nielsen selects the households with the use of a two-stage sampling process.
Stage 1 Using U.S. Census data, Nielsen divides the country into geographic areas (strata).
The strata are typically city blocks in urban areas and geographic regions in rural
areas. About 6000 strata are randomly selected.
Stage 2 Nielsen sends representatives to the selected strata and lists the households within the
strata. The households are then randomly selected through a simple random sample.
Nielsen sells the information obtained to television stations and companies. These results are
used to help determine prices for commercials.