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TRANSCRIPT
Introduction to Statistics
Chapter 1
Overview
Lesson 1-1
What is Statistics?
Statistics is the science of:
Collecting information
Surveys are used to collect data from a small part of
a larger group so we can learn something about the
larger group
Organizing and summarizing the information
collected
Analyzing the information collected in order to
draw conclusions.
Two Types of Statistics
Descriptive Statistics
Organizing and summarizing the information
collected.
Inferential Statistics
Drawing conclusions from the information
collected.
Individuals and Variables
Data are observations (such as measurement,
gender, or survey responses) that have been
collected.
Individuals are the objects described by a set of
data.
Individuals may be people, animals or things.
A variable is any characteristic of an individual.
A variable can take different values for different
individuals.
Populations and Samples
A population is the entire group of individuals
about which we want information about.
A sample is part of the population from which we
actually collect information, which is then used to
draw conclusions about the whole.
A census is a sample survey that attempts to
include the entire population in the sample
Example – Page 11, #18
Identify the (a) sample and (b) population. Also determine
whether the sample is likely to be representative of the
population.
Nielsen Media Research surveys 5000 randomly selected
households and finds that among TV sets in use 19% are
tuned to 60 Minutes.
Sample: _______________________
Population:________________________
5000 selected households
All households
Sample is representative of the population
Example – Page 11, #20
Identify the (a) sample and (b) population. Also determine
whether the sample is likely to be representative of the
population.
A graduate student at the University of Newport conducts a
research project about how adult Americans communicate.
She begins with a survey mailed to 500 adults that she knows.
She asks them to mail back a response to this question: “Do you
prefer to use e-mail or the U.S. Postal service?” She gets back
65 responses, with 42 of them indicating a preference for postal
mail.
Example – Page 11, #20A graduate student at the University of Newport conducts
a research project about how adult Americans communicate.
She begins with a survey mailed to 500 adults that she knows.
She asks them to mail back a response to this question: “Do
you prefer to use e-mail or the U.S. Postal service?” She gets
back 65 responses, with 42 of them indicating a preference
for postal mail.
Sample: _______________________
Population:________________________
65 respondents
All adult Americans
Sample is not representative of the population
Types of Data
Lesson 1-2
Parameters and Statistics
A parameter is a number that describes the
population
A parameter is a fixed number, but in practice
we don’t know its value
A statistics is a number that describes a sample.
The value of a statistic is known when we have
taken a sample, but it can change from sample
to sample
We often use a statistic to estimate an
unknown parameter.
Example – Page 9, #2
Determine whether the given value is a statistic or
a parameter.
A sample of students is selected and the average (mean)
number of textbooks purchased this semester is 4.2
Statistic
Example – Page 9, #4
Determine whether the given value is a statistic or
a parameter.
The study of all 2223 passengers aboard the Titanic, it was
found that 706 survived when it sank.
Parameter
Types of data
Categorical Data
The individuals being studied are grouped into
categories based on some qualitative trait.
The resulting data are merely labels or
categories
Measurement Data
The individuals being studied are “measured”
based on some quantitative trait.
The resulting data are sets of numbers.
Measurement data is classified as
Discrete
Results when the number of possible value is either
finite number or “countable” number. (That is, the
number of possible values is 0 or 1 or 2 and so on.)
Continuous
Results from infinitely many possible values that
correspond to some continuous scale that covers a
range of values without gaps, interruptions, or
jumps.
Example – Page 10, #6
Determine whether the given values are from discrete
or continuous data set.
A statistic student obtains sample data and finds that
the mean weight of cars in the sample is 3126 lb.
Continuous
Example – Page 10, #8
Determine whether the given values are from discrete
or continuous data set.
Discrete
When 19,218 gas masks from branches of the U.S.
military
Review – Types of Data
Categorical or Qualitative Data
Measurement or Quantitative Data
Discrete Data – Counting
Continuous Data - Measuring
Four Levels of Measurement
Nominal
The data cannot be arranged in an ordering
scheme ( such as low to high)
Ordinal
The categories are ordered, but differences
can’t be found or are meaningless.
Four Levels of MeasurementInterval
the categories are ordered, the differences are
meaningful, there is no natural starting point and
ratio are meaningless
Ratio
The categories are ordered, the differences are
meaningful, there is a natural zero starting point
and the ratios are meaningful.
Example – Page 10, #10
Determine which of the four levels of measurement
(nominal, ordinal, interval, ratio) is most appropriate.
Ratings of fantastic, good, average, poor, or unacceptable
for blind dates.
Ordinal
Example – Page 10, #12
Determine which of the four levels of measurement
(nominal, ordinal, interval, ratio) is most appropriate.
Numbers on the jerseys of women basketball players
in the WNBA.
Nominal
Example – Page 10, #14
Determine which of the four levels of measurement
(nominal, ordinal, interval, ratio) is most appropriate.
Social security numbers.
Nominal
Critical Thinking
Lesson 1-3
Misuses of Statistics
Bad Samples
Small Samples
Misleading Graphs
Pictographs
Distorted Percentages
Loaded Questions
Order of Questions
Refusals
Correlation and Causality
Self-Interest Study
Precise Numbers
Partial Pictures
Deliberate Distortions
Bad Samples
Voluntary responses samples is one in which the
respondents themselves decide whether to be
included.
Examples
Polls conducted through the Internet
Mail-in polls
Telephone call-in polls
Bad Samples
Loaded Questions
Misleading Graphs
Suppose that you’re looking
into a summer job and you
see advertisement for a
company that says that the
current salaries are
significantly higher than they
were two years ago.
What impression do you get
about the improvement in
salaries at this company from
this graph?
12
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Partial Pictures
Example – Page 17, #2
Use critical thinking to develop an alternative conclusion.
A study showed that homeowners tend to live longer than
those who do not live in their own homes. Conclusion:
Owning a home creates inner peace and harmony that
causes people to be in better health and live longer.
Homeowners tend to be more wealthier and they can better
afford health care, which leads to better health.
A better conclusion is that being a homeowner is associated
with living longer.
Example – Page 17, #6
Use critical thinking to address the key issue.
After a national census was conducted, the Poughkeepsie
Journal ran this front page headline: “281,421,906 in
America.” What is wrong with this headline?
The headline suggests that the census count was
determine with great precision, but the figure is likely
to be in error by millions of people.
Design of Experiments
Lesson 1-4
Observational Study
An observational study
observes individuals and
measures variables of
interest but does not
attempt to influence the
responses. The purpose of
an observational study is
to describe some group
or situation.
Experiment
An experiment deliberately imposes some treatment on
individuals in order to observe their responses. The purpose
of the experiment is to study whether the treatment causes a
change in the response.
Example – Page 27, #2
Much controversy arose over a study of patients with
syphilis who were not given a treatment that could
have cured them. Their health was followed for years
after they were found to have syphilis.
Determine where the given description corresponds
to an observational study or an experiment.
Observational Study
Example – Page 27, #4
Cruise ship passengers are given magnetic bracelets,
which they agree to wear in an attempt to eliminate
or diminish the effects of motion sickness.
Determine where the given description corresponds
to an observational study or an experiment.
Experiment
Different Types of
Observation Studies
Cross Sectional Study
Data are observed, measured and collected at
one point in time.
Retrospective (or Case Control) Study
Data are collected from the past by going back
in time.
Prospective (of Longitudinal or Cohort) Study
Data are collected in the future from groups
(called cohorts) sharing common factors.
Example – Page 27, #6
Identify the type of observation study (cross-sectional,
retrospective, or prospective).
A researcher from Mt. Sinai Hospital in New York City
plans to obtain data by following (to the year 2010) siblings
of victims who perished in the World Trade Center
terrorist attacked of September 11, 2001.
Prospective
Example – Page 27, #8
Identify the type of observation study (cross-sectional,
retrospective, or prospective).
An economist collects data by interviewing people who
won the lottery between the years of 1995 and 2000.
Retrospective
Confounding in Experiments
Confounding occurs in an experiment when
the experiment is not able to distinguish
between the effect of different factors.
Try to plan the experiment so the
confounding does not occur.
Controlling Effects of Variables
Blinding
Subjects doesn’t know whether their receiving a
treatment or a placebo.
Blocks
Groups subjects with similar characteristics
Completely Randomized Experimental Design
Subjects are put into different blocks through a process of
random selection.
Rigorously Controlled Design
Subjects are very carefully chosen.
Data Collection
If sample data are not collected in an
appropriate way, the data is completely
useless.
Randomness typically plays a crucial role in
determining which data is collected
Random Samples
In a random sample members from a
population are selected in such a way that
each individual member has equal chance of
being selected.
A simple random sample (SRS) of size n
subjects is selected in such a way that every
possible sample of the same size n has the same
chance of being chosen.
The Draft Lottery
Example – Page 29, #22
Does this sampling plan result in a random sample?
Simple random sample? Explain
A classroom consists of 30 students seated in five different
rows, with six students in each row. The instructor rolls
a die and the outcome is used to select a sample of the
students in a particular row.
Random Sample:
Simple Random Sample:
yes
No
Example – Page 29, #24
Does this sampling plan result in a random sample?
Simple random sample? Explain
A quality control engineer selects every 100th computer
power supply unit that passes on a conveyor belt. .
Random Sample:
Simple Random Sample:
No
No
Example – Page 29, #26
Does this sampling plan result in a random sample?
Simple random sample? Explain
A market researcher randomly selects 10 blocks in the
Village of Newport, then asks all adult residents of the
selected blocks whether they own a DVD player.
Random Sample:
Simple Random Sample:
Yes
No
Sampling Techniques
Random Sampling
Simple Random Sampling
Systematic Sampling
Convenience Sampling
Stratified Sampling
Cluster Sampling
Random Sampling Each member of the population has an equal chance of being
selected.
Systematic SamplingSelect some starting point and then select every kth (such as
every 3rd ) element in the population
Convenience Sampling
Use results that are easy to get
Stratified Sampling
Subdivide the population into at least two different subgroups
(or strata) that share the same characteristics (such as gender or
age bracket), then draw a sample from each subgroup.
Cluster Sampling
Divide the population into sections (or clusters); then
randomly select some of those clusters; choose all
members from the selected clusters
Example – Page 28, #10
Identify which of these types of sampling is used: random,
systematic, convenience, stratified, or cluster.
The Dutchess County Commissioner of Jurors obtains
a list of 42,763 car owners and constructs a pool of jurors
by selecting every 100th name on the list.
Systematic
Example – Page 28, #12
Identify which of these types of sampling is used: random,
systematic, convenience, stratified, or cluster.
A General Motors researcher has partitioned all registered
cars into categories of sub-compact, compact, mid-size,
intermediate and full-size. She is surveying 200 cars owners
from each category.
Stratified
Example – Page 28, #14
Identify which of these types of sampling is used: random,
systematic, convenience, stratified, or cluster.
A marketing executive for General Motors finds that its
public relations department has just printed envelopes with
the names and addresses of all Corvette owners. She wants
to do a pilot test of a new marketing strategy, so she
thoroughly mixed all of the envelopes in a bin, then obtains
a small sample group by pulling 50 of those envelopes.
Random
Sampling Error
Are errors by the act of taking a sample. It is
difference between a sample result and the true
population result; such an error results from
chance sample fluctuations
Nonsampling Error
Sample data that are incorrectly collected,
recorded, or analyzed (such as by selecting a
biased sample, using a defective instrument, or
copying the data incorrectly)
Errors in Sampling