Transcript PowerPoint (1.1 to 1.4)

Chapter 1
Statistics may be defined as "a body of methods
for making wise decisions in the face of
uncertainty." ~W.A. Wallis
LEARNING GOAL
Understand the two meanings of the term statistics and
the basic ideas behind any statistical study, including
the relationships among the study’s population, sample,
sample statistics, and population parameters.
Two Definitions of Statistics
•Statistics is the science of
collecting, organizing, and
interpreting data.
•Statistics are the data (numbers
or other pieces of information)
that describe or summarize
something.
Definitions
The population in a statistical
study is the complete set of
people or things being studied.
Population parameters are specific
characteristics of the population.
What are some specific
characteristics of a population?
For each of the following situations, describe the
population being studied and identify some of the
population parameters that would be of interest.
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A political campaign worker wishes to conduct a
poll to determine how her candidate is likely to
fair in the upcoming state senate election.
A researcher wants to determine the average
number of text messages sent per month by
college students who have cell phones.
A college admissions counselor is interested in
studying the relationship between high school
GPA and composite score on the ACT.
Definitions
A sample is a subset of the population
from which data are actually obtained.
The raw data is the actual measurements
or observations.
Sample statistics are characteristics of the
sample found by consolidating or
summarizing the raw data.
Remember:
 Parameters
are characteristics
of the population.
 Statistics are characteristics of
a sample.
5000 Americans are polled and the
average (mean) amount of time watching
television is 4.6 hours per day.
 As shown in the Crime Watch article of the
local newspaper, 37% of the crimes in the
county in the month of September were
crimes against property.
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•Sample statistics are used to estimate
population parameters.
•A confidence interval is a range of values likely
to contain the population parameter.
• The confidence interval is:
from (sample statistic – margin of error)
to (sample statistic + margin of error)
•The margin of error is usually defined to give a
95% confidence interval, meaning that 95% of
samples of the size used in the study would
contain the actual population parameter (and 5%
would not).
January 13, 2012
In U.S., Slightly More Want Obama to Set Course Than GOP
Obama has maintained slight edge since early 2011
by Jeffrey M. Jones
PRINCETON, NJ -- Americans say they want Barack Obama (46%)
rather than the Republicans in Congress (42%) to have more
influence over the direction the nation takes in the next year. U.S.
preferences have been closely divided on this question since early
2011, after Republicans won a majority in the House of
Representatives, but Obama has consistently had a slim advantage,
suggesting a real lead for him. Prior to 2011, Americans favored
congressional Republicans.
http://www.gallup.com/poll/152027/Slightly-Obama-Set-CourseGOP.aspx
Implications
Given a choice, Americans are fairly evenly divided in their
preferences for whether President Obama or the Republicans in
Congress should have more influence over the course of the
nation during the next year, with Obama having a slight edge.
Obama's slightly better positioning is consistent with the
president's usual advantage on this question, with Americans
generally preferring the opposition party in Congress only when
the president is highly unpopular. Obama is certainly not popular
at the moment, but on a relative basis he is more popular than
the Republicans in Congress.
Survey MethodsResults for this Gallup poll are based on telephone interviews
conducted Jan. 5-8, 2012, with a random sample of 1,011 adults, aged 18 and older,
living in all 50 U.S. states and the District of Columbia.
For results based on the total sample of national adults, one can say with 95%
confidence that the maximum margin of sampling error is ±4 percentage points.
Interviews are conducted with respondents on landline telephones and cellular phones,
with interviews conducted in Spanish for respondents who are primarily Spanishspeaking. Each sample includes a minimum quota of 400 cell phone respondents and
600 landline respondents per 1,000 national adults, with additional minimum quotas
among landline respondents by region. Landline telephone numbers are chosen at
random among listed telephone numbers. Cell phone numbers are selected using
random-digit-dial methods. Landline respondents are chosen at random within each
household on the basis of which member had the most recent birthday.
Samples are weighted by gender, age, race, Hispanic ethnicity, education, region, adults
in the household, and phone status (cell phone only/landline only/both, cell phone mostly,
and having an unlisted landline number). Demographic weighting targets are based on
the March 2011 Current Population Survey figures for the aged 18 and older noninstitutionalized population living in U.S. telephone households. All reported margins of
sampling error include the computed design effects for weighting and sample design.
In addition to sampling error, question wording and practical difficulties in conducting
surveys can introduce error or bias into the findings of public opinion polls.
View methodology, full question results, and trend data.
Gallup Daily: Obama Job Approval
Each result is based on a three-day
rolling average
January 13, 2011
•On January 16, 2012, President Obama’s approval rating was 46%.
•Gallup tracks daily the percentage of Americans who approve or disapprove
of the job Barack Obama is doing as president. Results are based on
telephone interviews with approximately 1,500 national adults; Margin of
error is ±3 percentage points.
•Find the 95% confidence interval.
•Is it possible that the majority of Americans approve of the job President
Obama is doing?
An internet supplier of refilled ink cartridges for
ink jet printers sold cartridges to 30,000
customers over the past two months. A random
sample of 1000 of those customers revealed
that 18% were not happy with their purchase.
The margin of error was 2%.
•Identify the population.
•Identify the sample.
•Is 18% a parameter or a statistic?
•What range is likely to contain the population
parameter?
Definitions
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Descriptive Statistics—describes raw data in the
form of graphics and sample statistics
Inferential Statistics—infers or estimates
population parameters from sample data
We will use descriptive statistics from sample data
to make inferences about population
parameters.
Basic Steps in a Statistical Study
1.
2.
3.
4.
5.
State the goal of your study precisely. Identify
the population and what you want to determine.
Choose a sample from the population using an
appropriate sampling technique.
Collect raw data from the sample. Summarize
by finding sample statistics of interest.
Use the sample statistics to make inference
about the population parameter.
Draw conclusions. Determine what you have
learned and if the goal was achieved.
Copyright © 2009 Pearson Education, Inc.
A researcher wanted to study the relationship between coffee
drinking and heart problems. She interviewed all patients at
several area hospitals and found that patients in the hospital
for treatment of heart problems drank an average of 2.7 cups
of coffee per day (margin of error is 1.4 cups) while those
patients being treated for other problems averaged only 1.4
cups of coffee per day (margin of error is 0.8 cups). What
conclusion can you draw about coffee as a cause of heart
problems from this information?
a. Coffee is bad for you.
b. Coffee is good for you.
c. Heart patients drink more coffee than other patients.
d. None, because only patients in hospitals were
interviewed.
End of 1.1
1.2 Sampling
Not everything that can be counted counts,
and not everything that counts can be
counted.
Albert Einstein
Learning Goal—Understand the importance
of choosing a representative sampling and
become familiar with several common
methods of sampling.
Definitions
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Census—collection of data from every member of a
population.
Sample—collecting data from part of a population.
Representative sample—a sample in which the relevant
characteristics of the sample members are generally the
same as the characteristics of the population.
What are advantages and disadvantages of collecting
data using a census?
What are advantages and disadvantages of collecting
data using a representative sample?
How will you know if the sample represents the
population?
What is the census?
Countdown to Census Day: April 1, 2010
•The census is a count of everyone living in the United States every 10
years.
•The census is mandated by the U.S. Constitution.
•2010 is a census year.
•Your participation in the census is required by law.
•It takes less than 10 minutes to complete.
•Federal law protects the personal information you share during the
census.
•Census data are used to distribute Congressional seats to states, to
make decisions about what community services to provide, and to
distribute $300 billion in federal funds to local, state and tribal
governments each year.
http://2010.census.gov/2010census/
Bias
A statistical study suffers from bias if its design or
conduct tends to favor certain results.
When can bias occur?
 When members of the sample differ in some specific
way from members of the population. Example—Use
members of SEMO’s football team to predict the average
weight of all college males.
 When a researcher has a personal stake in the outcome.
The researcher may intentionally or unintentionally
distort the true meaning of the data.
 Even if the study is done well, it may be reported in a
biased fashion.
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Sampling Methods
Simple Random Samples
 Systematic Sampling
 Convenience Samples
 Cluster Samples
 Stratified Samples
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Simple Random Samples (SRS)
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A random sample is one in which every
member of the population has an equal chance
of being selected to be part of the sample.
With simple random sampling every possible
sample of a particular size has an equal chance
of being selected.
Use a random number generator to find samples
of size 5 from this class. Go to
http://www.randomizer.org/
Systematic sampling
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randomly select a member of the sampling
frame for the sample
using a set procedure or rule, select the rest of
the individuals for the sample
 for
example, randomly select an individual from the
sampling frame, and then select every 25th member of
the sampling frame to be in the sample
 Each individual has an equal likelihood of being
chosen, but not every group has an equal likelihood
of being chosen.
Convenience Samples
• The sample is chosen for convenience
rather than by a more sophisticated
procedure.
• Self-selected sample—when people
choose whether or not to be part of the
sample.
Cluster Samples
Cluster sampling involves the selection of all members in
randomly selected groups, or clusters.
 Divide the population into clusters.
 Randomly choose clusters.
 All subjects in the chosen clusters make up the sample.
 For example—The clusters could be the ER in each
hospital in a city. Randomly choose 5 hospitals and
survey all the ER triage nurses in the 5 hospitals about
certain practices.
Stratified Sampling
Stratified sampling involves randomly selecting members
from each stratum.
 first divide the population into groups of similar
individuals, called strata
 second, choose a separate simple random sample in
each stratum
 third, combine these simple random samples to form the
full sample
 For example—choose a simple random sample of 50
freshmen, 50 sophomores, 50 juniors and 50 seniors.
Together, these students make up the full sample of size
200.
Summary of Sampling Methods
Keep in mind the following three key
ideas:
• A study can be successful only if the sample is
representative of the population.
• A biased sample is unlikely to be a
representative sample.
• Even a well-chosen sample may still turn out to
be unrepresentative just because of bad
luck in the actual drawing of the sample.
Summary of Sampling
Methods
Simple Random Sampling (SRS):
Every sample of the same size has an equal chance of being
selected. Computers are often used to generate random numbers.
Copyright © 2009 Pearson Education, Inc.
Systematic Sampling:
Select every kth member.
Copyright © 2009 Pearson Education, Inc.
Convenience Sampling:
Use results that are readily available.
Copyright © 2009 Pearson Education, Inc.
Cluster Sampling:
Divide the population into clusters, randomly select some of those
clusters, then choose all members of the selected clusters.
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Stratified Sampling:
Partition the population into at least two strata, then draw a
sample from each.
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Identify each sample as SRS, systematic sample, convenience sample,
stratified sample, or cluster sample. In each case, state whether you think the
sampling method is likely to yield a representative sample or a biased sample,
and explain why.
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A quality improvement technician samples every 500th bag of potato chips
coming off the assembly line to test the chips for fat content. Identify the
type of sampling.
A political science student randomly selects 100 names from the voter list of
registered Democrats and 100 from the list of registered Republicans.
Identify the type of sampling.
The Gallup Organization plans to conduct a poll of New York City residents
with the “212” area code. Computers are used to randomly generate
telephone numbers that are automatically called.
Southeast conducts a study of student drinking by randomly selecting 10
different classes and surveys all of the students in each of those classes.
A student surveys all students on his floor about residence life issues.
End of 1.2
1.3 Types of Statistical Studies
You can observe a lot by just watching.
Yogi Berra
LEARNING GOAL
Understand the differences between observational studies and
experiments; recognize key issues in experiments, including the
selection of treatment and control groups, the placebo effect, and
blinding.
Definition
The subjects of a study are the people, animals (or
other living things), or objects chosen for the sample;
if the subjects are people, they may also be called the
participants in the study.
Copyright © 2009 Pearson Education, Inc.
Two Basic Types of
Statistical Studies
In an observational study, researchers
observe or measure characteristics of the
subjects but do not attempt to influence or
modify these characteristics
 In an experiment, researchers apply
some treatment and observe its effects on
the subjects of the experiment.

Identify the study as an observational study or an experiment.
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Researchers at a medical school want to compare two
methods of treating blocked arteries. Fifty patients in
similar condition are randomly assigned to two groups.
One group is treated surgically and the other group is
treated with drugs.
Researchers at a medical school want to compare the
rates of birth defects in babies born to mothers whose
diets are classified as low fat with those born to mothers
whose diets are high in fat. For one year, they collect
data on all babies and their mothers in area hospitals,
using information obtained from the mothers to
determine whether they fall in low fat or high fat diet
category.
Definitions
A variable is any item or quantity that can
vary or take on different values.
 The variables of interest in a statistical
study are the items or quantities that the
study seeks to measure.
 The explanatory variable may explain or
cause the effect.
 The response variable responds to
changes in the explanatory variable.

State the type of study, observational or experiment, that
would best answer the question. Identify the variables of
interest. State the explanatory variable and response
variable.
Do people who take a vitamin supplement
have lower rates of colon cancer than
those who do not take the supplement?
 Does texting while driving cause
accidents?

Observational Studies
In most observational studies the data is
collected all at once (or as close to that as
possible.
Other types of observational studies:
•Retrospective (or case-control) study—
uses data from the past, such as official
records or past interviews
•Prospective (or longitudinal) study—set up
to collect data in the future from groups that
share common factors.
What type of study should be used?
You want to know how meth abuse during
pregnancy effects the learning ability of a
child?
 You want to know whether ACT scores as
a senior in high school predicts college
GPA.

Experiments
Most of the time, a treatment and a control
group is used to fairly reach conclusions in
an experiment.
 Treatment group—group of subjects who
receive the treatment
 Control group—group of subjects who do
not receive the treatment
 Important—Both groups should be
randomly selected. Why?
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An educator wants to compare the effectiveness of
using songs to teach number and counting skills
with that of a a standard curriculum. He tests the
number and counting skills of each student in a
class of kindergartners, then divides them into two
groups. One group uses songs to learn, while the
other studies a standard curriculum. At the end of
the year, he retests all the students and compares
the increase in the skills of the two groups.
Is this an experiment? Why or why not?
Identify the treatment.
Identify the treatment and control groups? How
should the students be put into these groups?
Confounding
A study suffers from confounding if the
effects of different variables are mixed so
we cannot determine the specific effects of
the variables of interest.
 The variables that lead to the confusion
are called confounding variables.
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Confounding
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An article in a women’s magazine says that
women who nurse their babies feel warmer and
more receptive toward the infants than mothers
who bottle-fee. The author concludes that
nursing has desirable effects on the mother’s
attitude toward the child. But women choose
whether to nurse or bottle-feed. What are some
confounding variables that may make you
skeptical of this conclusion.
Most colleges determine scholarships using a
student’s high school GPA and ACT score. The
assumption is that a student with a high GPA
and ACT score will be successful in college.
What are some confounding variables that may
effect this premise?
Strategies for Selecting
Treatment and Control Groups
1. Select groups at random. Each subject
should have an equal chance of being
assigned to either the treatment or control
2. Use sufficiently large groups. Make sure
that the treatment and control groups are both
sufficiently large that they are unlikely to differ
in a significant way (aside from the fact that
one group gets the treatment and the other
does not).
Placebos
A placebo lacks the active ingredients of a
treatment being tested in a study, but
looks or feels like the treatment so that
participants cannot distinguish whether
they are receiving the placebo or the real
treatment.
 The placebo effect—patients improve
simply because they believe they are
receiving a useful treatment.
 Are placebos ethical?

A nutritionist wants to conduct a study to
determine the efficacy of an herb as an aid in
weight loss. She randomly assigns half of a
group of overweight persons to a treatment
group who are given herbs with instructions for
its use and a planned diet for six weeks.
•The other half of the group is to be the control
group. What will they be given and told to do?
•Identify confounding variables.
A mathematics teacher wanted to determine whether
assigning homework had a beneficial effect on student
learning in first year algebra. His class met a 8:00 in the
morning and he obtained the cooperation of another teacher
of the same class that met at 2:00 in the afternoon. He gave
his class no homework while the other teacher continued to
assign homework as he usually did. Both teachers gave the
same tests so that they could compare the results.
•What is the treatment?
•What is the explanatory variable?
•What is the response variable?
•Name some confounding variables?
•Is this good experimental design? Why or why not?
Definition
An experimenter effect occurs when a
researcher or experimenter somehow influences
subjects through such factors as facial
expression, tone of voice, or attitude.
Blinding in Experiments
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Single-blind experiment--participants do not
know whether they are members of the
treatment or control group, but the
experimenters do know
Double-blind experiment--neither the
participants or the experimenters know who
belongs to the treatment or control group
Why is single-blind important? Double-blind?
How is a double-blind experiment feasible?
.
Design an experiment to test the
effectiveness of Sleepeze, a new drug that
allegedly cures insomnia. There are 90
subjects suffering from insomnia that have
agreed to participate.
•Specify how the groups will be chosen and
the treatment given to each group.
•Should the experiment be single-blind,
double-blind or neither?
Meta-Analysis
Definition
In a meta-analysis, researchers review many past
studies. The meta-analysis considers these studies as a
combined group, with the aim of finding trends that were
not evident in the individual studies.
Copyright © 2009 Pearson Education, Inc.
End of 1.3
1.4 Should You Believe a Statistical Study?
If I have ever made any valuable
discoveries, it has been owing more to
patient attention, than to any other talent.
Isaac Newton
LEARNING GOAL
Be able to evaluate statistical studies that you hear about
in the media, so that you can decide whether the results
are meaningful.
Eight Guidelines for Critically Evaluating a
Statistical Study
1. Identify the goal of the study, the population
considered, and the type of study.
2. Consider the source, particularly with regard to
whether the researcher may be biased.
3. Examine the sampling method to decide whether it is
likely to produce a representative sample.
4. Look for problems in defining or measuring the
variables of interest, which can make it difficult to
interpret any reported results.
Copyright © 2009 Pearson Education, Inc.
Eight Guidelines for Critically Evaluating a
Statistical Study
5. Watch out for confounding variables that can invalidate
the conclusions of a study.
6. Consider the setting and wording in surveys or polls,
looking for anything that might tend to produce
inaccurate or dishonest responses.
7. Check that results are fairly represented in graphics
and concluding statements, because both researchers
and media often create misleading graphics or jump to
conclusions that the results do not support.
8. Stand back and consider the conclusions. Did the
study achieve its goals? Do the conclusions make
sense? Do the results have any practical significance?
Copyright © 2009 Pearson Education, Inc.
Guideline 1: Identify the Goal,
Population and Type of Study
Based on what you hear or read about a study, try to
answer these basic questions:
• What was the study designed to determine?
• What was the population under study? Was the
population clearly and appropriately defined?
• Was the study an observational study, an
experiment, or a meta-analysis?
Copyright © 2009 Pearson Education, Inc.
Guideline 2: Consider the Source
Statistical studies are supposed to be objective, but the
people who carry them out and fund them may be
biased.
It is therefore important to consider the source of a
study and evaluate the potential for biases that might
invalidate the study’s conclusions.
Definition
Peer review is a process in which several experts in a field
evaluate a research report before the report is published.
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Guideline 3: Examine the
Sampling Method
A statistical study cannot be valid unless the sample
is representative of the population under study.
Definitions
Selection bias (or a selection effect) occurs whenever
researchers select their sample in a biased way.
Participation bias occurs any time participation in a
study is voluntary.
A self-selected survey (or voluntary response
survey) is one in which people decide for themselves
whether to be included in the survey.
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Guideline 4: Look for Problems in
Defining or Measuring the
Variable of Interest
Results of a statistical study may be difficult to
interpret if the variables under study are difficult to
define or measure.
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Guideline 5: Watch Out for
Confounding Variables
Often, variables that are not intended to be part of the
study can make it difficult to interpret results
properly.
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Guideline 6: Consider the Setting
and Wording in Surveys
Even when a survey is conducted with proper
sampling and with clearly defined terms and
questions, you should watch for problems in the
setting or wording that might produce inaccurate or
dishonest responses.
Dishonest responses are particularly likely when the
survey concerns sensitive subjects.
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Guideline 7: Check That Results
Are Fairly Represented in Graphics
or Concluding Statements
Even when a statistical survey is done well, it may be
misrepresented in graphics or concluding statements.
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Guideline 8: Stand Back and
Consider the Conclusions
Ask yourself questions such as these:
• Did the study achieve its goals?
• Do the conclusions make sense?
• Can you rule out alternative explanations for the
results?
• If the conclusions make sense, do they have any
practical significance?
Copyright © 2009 Pearson Education, Inc.
End of Chapter 1