The Role of Statistics and the Data Analysis Process

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Chapter 1

• The Role of Statistics and the Data Analysis
  Process

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1.1 Three Reasons to Study Statistics

• Reason 1. Being Informed.
• You should be able to
• Extract information from tables, charts, and
  graphs
• Follow numerical arguments
• Understand the basics of how data should be
  gathered, summarized, and analyzed.

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1.1 Three Reasons to Study Statistics

• Examples of Being Informed
• An analysis of data from University of Utah
  concluded that drivers engaged in cell phone
  conversations missed twice as many simulated
  signals as drivers who were not talking over the
  phone.
• An article on the Journal of the American Medical
  Association concluded that surgery patients at
  hospitals with a severe shortage of nurses had a
  31 greater risk of dying while in the hospital.
• Based on interviews with 24,000 women in 10
  different country, WHO found that the percentage
  of women who have been abused by a partner varied
  widely-from 15 in Japan to 71 in Ethiopia.

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1.1 Three Reasons to Study Statistics

• Reason 2. Making Informed Judgments
• To make informed decisions, you must be able to
  take the following steps
• Decide whether existing information is adequate
  or whether additional information is required.
• If necessary, collect more information in a
  reasonable and thoughtful way.
• Summarize the available data in a useful and
  informative manner.
• Analyze the available data.
• Draw conclusions, make decisions, and assess the
  risk of an incorrect decision.

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1.1 Three Reasons to Study Statistics

• Examples of Making Informed Decisions
• Almost all industries, as well as government and
  nonprofit organizations, use market research
  tools, such as consumer surveys, that are
  designed to provide information about who uses
  their products or services.
• Modern science and its applied fields rely on
  statistical methods for analyzing data and
  deciding whether various conjectures are
  supported by observed data.
• In law, class-action lawsuit can depend on a
  statistical analysis of whether one kind of
  injury or illness is more common in a particular
  group than in general public.
• We also use the five steps to make everyday
  decision Should we go out for a sport that
  involves the risk of injury. If we choose a
  particular major, what are our chance of finding
  a job when you graduate?

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1.1 Three Reasons to Study Statistics

• Reason 3. Evaluating Decisions That Affect Your
  Life Other people use statistical methods to
  make decisions that affect you. An understanding
  of statistical techniques will allow you to
  question and evaluate decisions that affect your
  well-being.
• Insurance company use statistical techniques to
  set auto insurance rates.
• University financial aid offices collect data on
  family incomes and savings, and use the data to
  set criteria for deciding who receives financial
  aid.
• Medical researchers use statistical methods to
  make recommendations regarding the choice between
  surgical and nonsurgical treatment of such
  diseases as coronary heart disease and cancer.

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1.2 The Nature and Role of Variability

• Variability is almost universal.
• Imagine an unrealistic situation In a
  university, every student takes the same courses,
  spends exactly the same amount of money on
  textbooks, and has the same GPA.
• Populations with no variability almost do not
  exist.
• We need to understand variability to be able to
  collect, analyze, and draw conclusions from data
  in a sensible way.

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1.3 Statistics and Data Analysis

• Statistics is the science of collecting,
  analyzing, and drawing conclusions from data.
• The Population the entire collection of
  individuals or objects about which information is
  desired.
• A Sample A subset of the population, selected
  for study in some prescribed manner.
• Descriptive statistics includes methods for
  organizing and summarizing data
• Inferential statistics involves generalizing from
  a sample to the population from which it was
  selected, and assessing the reliability of such
  generalization.

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The Data Analysis Process

• Understand the nature of the problem.
• Decide what to measure and how to measure it.
• Collect data with a carefully developed plan.
• Summarize the data and start preliminary
  analysis.
• Apply the appropriate inferential statistical
  method for formal data analysis.
• Interpret the results.

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1.3 Statistics and Data Analysis

• Example A consumer group conducts crash tests of
  new model cars. To determine the severity of
  damage to 2003 Mazda 626s resulting from a 10-mph
  crash into a concrete wall, the research group
  tests six cars of this type and assesses the
  amount of damage. Describe the population and
  sample for this problem.

Population All 2003 Mazda 626s Sample The six
Mazda 626 being tested.
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1.3 Statistics and Data Analysis

• Example The supervisors of a rural county are
  interested in the proportion of property owners
  who support the construction of a sewer system.
  Because it is too costly to contact all 7000
  property owners, a survey of 500 owners (selected
  at random) is undertaken. Describe the population
  and sample for this problem

Population All 7000 property owners in the
county Sample The 500 property owners being
surveyed
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Example A Proposed New Treatment for Alzheimers
Disease

• Doctors at Stanford Medical Center were
  interested in determining if a new surgical
  approach to treating Alzheimers disease results
  in improved memory functioning. (The surgical
  procedure involves implanting a thin tube, called
  a shunt.)
• 11 patients have shunts implanted and were
  followed for a year, receiving quarterly tests
  for memory function.
• Another sample of Alzheimers patients received
  standard care, and was used as a comparison
  group.
• After analyzing the data from this study, the
  researchers concluded that the treated patients
  essentially held their own in the cognitive test
  while the patients in the comparison group
  steadily declined.

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1.3 Statistics and Data Analysis

• In the example A proposed new treatment for
  Alzheimers disease, what is the population and
  sample?
• Do you think the sample is good enough to produce
  conclusive statistical evidence?
• The limitations of the study the result is from
  a small sample. They need a larger, more
  sophisticated study, and a new data analysis
  cycle begins.
• A much larger 18-month study was planned. The
  study was to include 256 patients at 25 medical
  centers around the country.

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1.4 Types of Data and Some Simple Graphical
Displays

• Definitions
• A variable is an characteristic whose value may
  change from one individual or object to another
  in a population. e.g. The population is the set
  of all students in our stats class. The brand of
  calculator owned by each student is a variable,
  and the distance to UHD from each students home
  is also a variable.
• A data set consisting of observations on a single
  variable (attribute) is a univariate data set.
• A univariate data set is categorical (or
  qualitative) if the individual observations are
  categorical responses. (e.g. the brand of
  calculator)
• A univariate data set is numerical (or
  quantitative) if each observation is a number.
  (e.g. the distance to UHD)

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1.4 Types of Data and Some Simple Graphical
Displays

• Discrete and Continuous Data
• Numerical data are discrete if the possible
  values are isolated points on the number line.
• Numerical data are continuous if the set of
  possible values forms an entire interval on the
  number line.

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1.4 Types of Data and Some Simple Graphical
Displays

• 1. Example Airline Safety Violations
• The FAA monitors airlines and can take
  administrative actions for safety violations
  Security (S), Maintenance (M), Flight Operations
  (F), Hazardous Materials (H), or Other (O).
• Data for 20 administrative actions are given
  below.
• S S M H M O S M S S
• F S O M S M S M S
  M
• Classify the attribute as categorical or
  numerical.

Answer categorical
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An Example of Numerical Data

• 2. Example Revisiting Airline Safety Violation
• The following data present the number of
  violations and the average fine per violation for
  the period 1985-1998 for 10 major airlines
• Airline No. of Violation Average Fine per
  Violation ()
• Alaska 258 5038.760
• American West 257 3112.840
• American 1745 2693.410
• Continental 973 5755.390
• Delta 1280 3828.125
• Northwest 1097 2643.573
• Southwest 535 3925.234
• TWA 642 2803.738
• United 1110 2612.613
• US Airways 891 3479.237

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1.4 Types of Data and Some Simple Graphical
Displays Frequency Distributions

• Frequency Distributions for Categorical Data is a
  table that displays the possible categories along
  with the associated frequencies and/or relative
  frequencies.
• The frequency for a particular category is the
  number of times the category appears in the data
  set.
• The relative frequency for a particular category
  is the fraction or proportion of the observations
  resulting in the category
• If the table includes relative frequency, it is
  sometimes referred to as a relative frequency
  distribution.

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Frequency Distributions

• Example To ensure safety, the motorcycle helmet
  should reach the bottom of the motorcyclists
  ears, according to the standards set by US
  Department of Transportation. Data was collected
  by observing 1700 motorcyclists nationwide at
  selected roadway locations. There were 731 riders
  who wore no helmet, 153 who wore a noncompliant
  helmet, and 816 who wore a compliant helmet.
  Determine the frequency distribution and relative
  frequency distribution. Use the code
• N no helmet, NH noncompliant helmet, and
• CH compliant helmet
• Frequency distribution for helmet use

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Some Simple Graphical Displays Bar Charts

• When to use a bar chart Categorical data
• How to Construct
• Draw a horizontal line, and write the category
  names or labels below the line at regularly
  spaced intervals.
• Draw a vertical line, and label the scale using
  either frequency or relative frequency.
• Place a rectangular bar above each category
  label. The height is determined by the categorys
  frequency or relative frequency, and all bars
  should have the same width. With the same width,
  both the height and the area of the bar are
  proportional to frequency and relative frequency.
• Construct a bar chart for the helmet data.

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Create a Bar Chart Using Excel
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Excel generates the bar chart. You can choose
from Chart Layout to add title, give
explanations and do other modifications.
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1.4 Types of Data and Some Simple Graphical
Displays Dotplots for Numerical Data

• When to use a dotplot Small numerical data sets
• How to construct a dotplot
• Draw a horizontal line and mark it with an
  appropriate measurement scale
• Locate each value in the data set along the
  measurement scale, and represent it by a dot. If
  there are two or more observations with the same
  value, stack the dots vertically.
• What to Look For
• A representative or typical value in the data
  set.
• The extent to which the data values spread out.
• The nature of the distribution of values along
  the number line.
• The presence of unusual values in the data set.

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1.4 Types of Data and Some Simple Graphical
Displays Dotplots for Numerical Data

• Example The Chronicle of Higher Education
  reported graduation rate for NCAA Division I
  schools.. The rates reported are the percentage
  of full-time freshmen in fall 1993 who had earned
  a bachelors degree by August 1999. Data from 20
  schools in California and 19 schools from Texas
  are as follows
• California
• Texas
• Construct (1) a dotplot of graduation rates
• (2) a dotplot of graduation rate for
  California and Texas

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Dotplot of graduation rates (California and Texas
together)
Separate dotplots of graduation rates for Texas
and California