Chapter 1
Introduction to Statistics
Chapter Outline
• 1.1 An Overview of Statistics
• 1.2 Data Classification
• 1.3 Experimental Design
Section 1.1
An Overview of Statistics
Section 1.1 Objectives
•
•
•
•
Define statistics
Distinguish between a population and a sample
Distinguish between a parameter and a statistic
Distinguish between descriptive statistics and
inferential statistics
What is Statistics?
Statistics
The science of collecting,
organizing, analyzing, and
interpreting data in order to
make decisions.
What is Data?
Data
Consist of information coming from observations,
counts, measurements, or responses.
• “Drinking just one glass of wine a day can
INCREASE risk of cancer by 168%, say the French!
(Source: INCA)
• “Drinking 1 glass of wine a day may lower the risk
for Barrett's esophagus by 56%” (Source:
Gastroenterology)
Data Sets
Population
The collection of all outcomes,
responses, measurements, or
counts that are of interest.
Sample
A subset of the population.
Example: Identifying Data Sets
In a recent survey of adults in the US,
10,200 participants were asked to
answer ʺyesʺ or ʺnoʺ to the question
ʺAre you in favor of the death penalty?ʺ
Six thousand five hundred responded
ʺyesʺ. Identify the population and the
sample. Describe the data set. (Adapted
from: Pew Research Center)
Solution: Identifying Data Sets
• The population consists of the
responses of all adults in the
U.S.
• The sample consists of the
responses of the 10,200 adults in
the U.S. in the survey.
• The sample is a subset of the
responses of all adults in the
U.S.
• The data set consists of 6500
yes’s and 3700 no’s.
Responses of adults in
the U.S. (population)
Responses of adults
in survey (sample)
Parameter and Statistic
Parameter: A number that describes a
population characteristic.
Average age of all people in
the Washington state
Statistic
A number that describes a sample
characteristic.
Average age of people from a sample of
three counties
Example: Distinguish Parameter and Statistic
Decide whether the numerical value describes a
population parameter or a sample statistic.
A recent survey of a sample of
top executives reported that the
average salary for top executive
is $12,000,000.
Solution:
Sample statistic (the executive 12,000,000 is based on
a subset of the population)
Example: Distinguish Parameter and Statistic
Decide whether the numerical value describes a
population parameter or a sample statistic.
2. According to the US census, the number
of Television sets in the United States in
1948 was 35,000.
Solution:
Population parameter, the US census is all of the
US population.
Branches of Statistics
Descriptive Statistics
Involves organizing,
summarizing, and
displaying data.
e.g. Tables, charts,
averages
Inferential Statistics
Involves using sample
data to draw
conclusions about a
population.
Example: Descriptive and Inferential
Statistics
Decide which part of the study represents the
descriptive branch of statistics. What conclusions might
be drawn from the study using inferential statistics?
A large sample of adults over the
age of 65, were studied for 18
years. It was shown that adults
having at least one pet decreases
the heart attack mortality rate by
about 3 percent. (Source: The
Journal of Pets)
Solution: Descriptive and Inferential
Statistics
Descriptive statistics involves statements such as “...
adults having at least one pet decreases the heart attack
mortality rate by about 3 percent.”
A possible inference drawn from
the study is that having a pet is
associated with a longer life.
Section 1.1 Summary
•
•
•
•
Defined statistics
Distinguished between a population and a sample
Distinguished between a parameter and a statistic
Distinguished between descriptive statistics and
inferential statistics
Larson/Farber 4th ed.
Section 1.2
Data Classification
Section 1.2 Objectives
• Distinguish between qualitative data and quantitative
data
• Classify data with respect to the four levels of
measurement
Types of Data
Qualitative Data
Consists of attributes, labels, or nonnumerical entries.
Major
Larson/Farber 4th ed.
Place of birth
Eye color
Types of Data
Quantitative data
Numerical measurements or counts.
Age
Weight of a letter
Temperature
Example: Classifying Data by Type
Which data are
qualitative data
and which are
quantitative
data?
Maker
Levi’s 545 (Skinny Legs)
AG Adriano Goldschmied (Stilt Roll
Cost
39.99
188.00
Up in 5 years)
Joe’s Jeans (Cigarette in Kennedy)
158.00
True Religion (Lizzy Capri in Lonestar)
172.00
Hudson (Collin Signature Skinny in
189.00
Blackburn)
7 For all Mankind (The Skinny Crop
178.00
and ...)
Rock Revival (Celine SK18 Skinny)
178.00
G-Star (Fender skinny Pant)
190.00
Levels of Measurement
Nominal level of measurement
• Qualitative data only
• Categorized using names, labels, or qualities
• No mathematical computations can be made
Ordinal level of measurement
• Qualitative or quantitative data
• Data can be arranged in order
• Differences between data entries is not meaningful
Larson/Farber 4th ed.
Example: Classifying Data by Level
Two data sets are shown. Which data set consists of
data at the nominal level? Which data set consists of
data at the ordinal level? (Source: Nielsen Media Research)
Grades for Math 109:
A - Excellent
B - Good
C - Okay
D - Needs improvement
F - Failed
Political Parties:
Democrat
Republican
Green
Independent
Other
Solution: Classifying Data by Level
Course Grades: A college Political Parties:
professor assigns grades Democratic, Republican,
of A, B, C, D, or F.
Independent, Green or
Other.
Nominal level (lists the
Ordinal level (lists the
parties - names, labels or
grades you might get.
categories)
Data can be ordered.
Difference between grades
is not meaningful.)
Levels of Measurement
Interval level of measurement
• Quantitative data
• Data can ordered
• Differences between data entries is meaningful
• Zero represents a position on a scale (not an inherent
zero – zero does not imply “none”)
Larson/Farber 4th ed.
Levels of Measurement
Ratio level of measurement
• Similar to interval level
• Zero entry is an inherent zero (implies “none”)
• A ratio of two data values can be formed
• One data value can be expressed as a multiple of
another
Larson/Farber 4th ed.
Example: Classifying Data by Level
Two data sets are shown. Which data set consists of
data at the interval level? Which data set consists of
data at the ratio level? (Source: Major League Baseball)
Larson/Farber 4th ed.
Solution: Classifying Data by Level
Interval level
(Quantitative data. Can
find a difference between
two dates, but a ratio does
not make sense.)
Larson/Farber 4th ed.
Ratio level (Can find
differences and write ratios.)
Summary of Four Levels of Measurement
Put data in
categories
Arrange
data in
order
Subtract
data
values
Determine if one
data value is a
multiple of another
Nominal
Yes
No
No
No
Ordinal
Yes
Yes
No
No
Interval
Yes
Yes
Yes
No
Ratio
Yes
Yes
Yes
Yes
Level of
Measurement
Larson/Farber 4th ed.
Section 1.2 Summary
• Distinguished between qualitative data and
quantitative data
• Classified data with respect to the four levels of
measurement
Larson/Farber 4th ed.
Section 1.3
Experimental Design
Larson/Farber 4th ed.
Section 1.3 Objectives
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•
•
•
Discuss how to design a statistical study
Discuss data collection techniques
Discuss how to design an experiment
Discuss sampling techniques
Larson/Farber 4th ed.
Designing a Statistical Study
1. Identify the variable(s)
of interest (the focus)
and the population of the
study.
2. Develop a detailed plan
for collecting data. If
you use a sample, make
sure the sample is
representative of the
population.
Larson/Farber 4th ed.
3. Collect the data.
4. Describe the data using
descriptive statistics
techniques.
5. Interpret the data and
make decisions about
the population using
inferential statistics.
6. Identify any possible
errors.
Data Collection
Observational study
• A researcher observes and measures characteristics of
interest of part of a population.
• Researchers observed and recorded the chewing
behavior of carpenter ants in cedar.
Larson/Farber 4th ed.
Data Collection
Experiment
• A treatment is applied to part of a population and
responses are observed.
• An experiment was performed in which athletes took
high doses of protein daily while a control group took
normal doses. After 5 years, the athletes who had the
increased dosage of protein show no noticeable
advantage over those who took normal dosages of
protein (ScienceDaily).
Data Collection
Simulation
• Uses a mathematical or physical model to reproduce
the conditions of a situation or process.
• Often involves the use of computers.
• Hydroelectric engineers use computer simulations to
determine the effects of earth movement on damn
structural integrity.
Data Collection
Survey
• An investigation of one or more characteristics of a
population.
• Commonly done by interview, mail, or telephone.
• A survey is conducted on a sample of female athletes
to determine whether the reason for picking certain
sport jackets is for the iPod pocket.
Example: Methods of Data Collection
Consider the following statistical studies. Which
method of data collection would you use to collect data
for each study?
1. A study of the effect of changing steering wheel
position on the effects of road safety.
Solution:
Simulation (It is impractical to
create this situation)
Example: Methods of Data Collection
2. A study of the effect of drinking water on lowering
your chances of cancer.
Solution:
Experiment (Measure the effect
of a treatment – drinking water)
Example: Methods of Data Collection
3. A study of how puppies learn to fetch.
Solution:
Observational study (observe
and measure certain
characteristics of part of a
population)
Example: Methods of Data Collection
4. A study of how european citizen’ feel about US
Foreign policy.
Solution:
Survey
Larson/Farber 4th ed.
Key Elements of Experimental Design
• Control
• Randomization
• Replication
Larson/Farber 4th ed.
Key Elements of Experimental Design:
Control
• Control for effects other than the one being measured.
• Confounding variables
 Occurs when an experimenter cannot tell the
difference between the effects of different factors on a
variable.
 A coffee shop owner remodels her shop at the same
time a nearby mall has its grand opening. If business
at the coffee shop increases, it cannot be determined
whether it is because of the remodeling or the new
mall.
Larson/Farber 4th ed.
Key Elements of Experimental Design:
Control
• Placebo effect
 A subject reacts favorably to a placebo when in
fact he or she has been given no medical treatment
at all.
• Blinding is a technique where the subject does not
know whether he or she is receiving a treatment or a
placebo.
• Double-blind experiment neither the subject nor the
experimenter knows if the subject is receiving a
treatment or a placebo.
Larson/Farber 4th ed.
Key Elements of Experimental Design:
Randomization
• Randomization is a process of randomly assigning
subjects to different treatment groups.
• Completely randomized design
 Subjects are assigned to different treatment groups
through random selection.
• Randomized block design
 Divide subjects with similar characteristics into
blocks, and then within each block, randomly
assign subjects to treatment groups.
Larson/Farber 4th ed.
Key Elements of Experimental Design:
Randomization
Randomized block design
• An experimenter testing the effects of a new weight
loss drink may first divide the subjects into gender
categories. Then within each gender group, randomly
assign subjects to either the treatment group or
control group.
Larson/Farber 4th ed.
Key Elements of Experimental Design:
Randomization
• Matched Pairs Design
 Subjects are paired up according to a similarity.
One subject in the pair is randomly selected to
receive one treatment while the other subject
receives a different treatment.
 Two subjects are paired up because of their
mathematical abilities.
Larson/Farber 4th ed.
Key Elements of Experimental Design:
Replication
• Replication is the repetition of an experiment using a
large group of subjects.
• To test a new enhanced headphone set for the iPhone,
9,000 people are given the new headphones and
another 9,000 people are given the old set that looks
exactly like the new set. Because of the sample size,
the effectiveness of the vaccine would most likely be
observed.
Larson/Farber 4th ed.
Example: Experimental Design
A company wants to test the effectiveness of a new gum
developed to help people quit smoking. Identify a
potential problem with the given experimental design
and suggest a way to improve it.
The company identifies one thousand adults who are
heavy smokers. The subjects are divided into blocks
according to gender. After two months, the female
group has a significant number of subjects who have
quit smoking.
Larson/Farber 4th ed.
Solution: Experimental Design
Problem:
The groups are not similar. The new gum may have a
greater effect on women than men, or vice versa.
Correction:
The subjects can be divided into blocks according to
gender, but then within each block, they must be
randomly assigned to be in the treatment group or the
control group.
Larson/Farber 4th ed.
Sampling Techniques
Simple Random Sample
Every possible sample of the same size has the same
chance of being selected.
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Larson/Farber 4th ed.
Simple Random Sample
• Random numbers can be generated by a random
number table, a software program or a calculator.
• Assign a number to each member of the population.
• Members of the population that correspond to these
numbers become members of the sample.
Larson/Farber 4th ed.
Example: Simple Random Sample
There are 73 students currently enrolled in statistics.
You wish to form a sample of eight students to answer
some survey questions. Select the students who will
belong to the simple random sample.
• Assign numbers 1 to 73 to each student taking
statistics.
• On the table of random numbers, choose a
starting place at random (suppose you start in the
third row, second column.)
Larson/Farber 4th ed.
Solution: Simple Random Sample
• Read the digits in groups of three
• Ignore numbers greater than 73
Larson/Farber 4th ed.
Other Sampling Techniques
Stratified Sample
• Divide a population into groups (strata) and select a
random sample from each group.
• To collect a stratified sample of the number of
people who live in West Ridge County
households, you could divide the households into
socioeconomic levels and then randomly select
households from each level.
Larson/Farber 4th ed.
Other Sampling Techniques
Cluster Sample
• Divide the population into groups (clusters) and
select all of the members in one or more, but not
all, of the clusters.
• In the West Ridge County example
you could divide the households
into clusters according to zip
codes, then select all the
households in one or more, but not
all, zip codes.
Larson/Farber 4th ed.
Other Sampling Techniques
Systematic Sample
• Choose a starting value at random. Then choose
every kth member of the population.
• In the West Ridge County example you could
assign a different number to each household,
randomly choose a starting number, then select
every 100th household.
Larson/Farber 4th ed.
Example: Identifying Sampling Techniques
You are doing a study to determine the opinion of
students at your school regarding stem cell research.
Identify the sampling technique used.
1. You divide the student population with respect
to majors and randomly select and question
some students in each major.
Solution:
Stratified sampling (the students are divided into
strata (majors) and a sample is selected from each
major)
Larson/Farber 4th ed.
Example: Identifying Sampling Techniques
2. You assign each student a number and generate
random numbers. You then question each student
whose number is randomly selected.
Solution:
Simple random sample (each sample of the same
size has an equal chance of being selected and each
student has an equal chance of being selected.)
Larson/Farber 4th ed.
60
Section 1.3 Summary
•
•
•
•
Discussed how to design a statistical study
Discussed data collection techniques
Discussed how to design an experiment
Discussed sampling techniques
Larson/Farber 4th ed.