Chapter 1 Introduction to Statistics

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Chapter 1Introduction to Statistics

• 1-1 Overview
• 1-2 Types of Data
• 1-3 Critical Thinking
• 1-4 Design of Experiments

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Section 1-1Overview
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Overview

• A common goal of studies and surveys and other
  data collecting tools is to collect data from a
  small part of a larger group so we can learn
  something about the larger group.
• In this section we will look at some of the ways
  to describe data.

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Definitions
population

• Data observations (such as measurements,
  genders, survey responses) that have been
  collected
• Statisticsa collection of methods for planning
  studies and experiments, obtaining data, and then
  organizing, summarizing, presenting, analyzing,
  interpreting, and drawing conclusions based on
  the data

parameter
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• Population the complete collection of all
  elements (scores, people, measurements, and so
  on) to be studied the collection is complete in
  the sense that it includes all subjects to be
  studied
• Census Collection of data from every member
  of a population
• Sample Sub collection of members selected
  from a population

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Chapter Key Concepts

• Sample data must be collected in an
  appropriate way, such as through a process of
  random selection.
• If sample data are not collected in an
  appropriate way, the data may be so completely
  useless that no amount of statistical torturing
  can salvage them.

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Section 1-2 Types of Data
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Key Concept

• The subject of statistics is largely about using
  sample data to make inferences (or
  generalizations) about an entire population. It
  is essential to know and understand the
  definitions that follow.

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• Parametera numerical measurement describing some
  characteristic of a population.
• Statistica numerical measurement describing some
  characteristic of a sample.
• Quantitative data numbers representing counts or
  measurements.
• Qualitative (or categorical or attribute)
  datacan be separated into different categories
  that are distinguished by some nonnumeric
  characteristic.

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Working with Quantitative Data

• Quantitative data can further be described by
  distinguishing between discrete and continuous
  types.

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• Discrete data result when the number of possible
  values is either a finite number or a countable
  number (i.e. the number of possible values is 0,
  1, 2, 3, . .)
• Continuous (numerical) data
• result from infinitely many possible values
  that correspond to some continuous scale that
  covers a range of values without gaps,
  interruptions, or jumps

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4 Levels of Measurement another way to classify
data

• Nominal level of measurement characterized by
  data that consist of names, labels, or categories
  only, and the data cannot be arranged in an
  ordering scheme (such as low to high)
• Ordinal level of measurement involves data that
  can be arranged in some order, but differences
  between data values either cannot be determined
  or are meaningless
• Interval level of measurement like the ordinal
  level, with the additional property that the
  difference between any two data values is
  meaningful, however, there is no natural zero
  starting point (where none of the quantity is
  present)
• Ratio level of measurement the interval level
  with the additional property that there is also a
  natural zero starting point (where zero indicates
  that none of the quantity is present) for
  values at this level, differences and ratios are
  meaningful

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Summary - Levels of Measurement

• Nominal - categories only
• Ordinal - categories with some order
• Interval - differences but no natural starting
  point
• Ratio - differences and a natural starting point

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Extra Example

• The following are the finishing positions of a
  sample of drivers in a NASCAR race 3, 8, 12, 15,
  27 (3rd place, 8th place, etc.)
• What is the level of measurement of these data?
• Are these data discrete or continuous?
• Are the data qualitative or quantitative?

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Class Survey

• Please complete the survey and submit. Do not
  sign your name.
• ___Female ___Male
• Randomly select four digits and enter them
  here__ __ __ __
• Your eye color
• Your height in inches
• Total value of the coins now in your possession
• Number of keys in your possession right now
• Number of credit cards in your possession right
  now
• Enter the last four digits of your social
  security number ___ ___ ___ ___
• Record your pulse rate by counting the number of
  heartbeats for one minute.
• Do you exercise vigorously for at least 20
  minutes twice a week (running, swimming, cycling,
  tennis, basketball, etc.)? YES/NO
• How many classes are you taking this semester?
• Are you currently employed? YES/NO
• If yes, how many hours do you work each week?
• 13) During the past 12 months, have you been the
  driver of a car that was involved in a crash?
  YES/NO
• 14) Do you smoke? YES/NO
• 15) Are you Left-handed Right-handed Ambidextrou
  s

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• Section 1-3
• Critical Thinking

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Key Concepts

• Success in the introductory statistics course
  typically requires more common sense than
  mathematical expertise.
• This section is designed to illustrate how common
  sense is used when we think critically about
  data and statistics.

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Misuses of Statistics

• Voluntary response sample (or self-selected
  sample)
• One in which the respondents themselves decide
  whether to be included.
• In this case, valid conclusions can be made only
  about the specific group of people who agree to
  participate.
• 2) Small sample
• Conclusions should not be based on samples that
  are far too small.

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Misuse 3- Graphs
To correctly interpret a graph, you must analyze
the numerical information given in the graph, so
as not to be misled by the graphs shape.
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Misuse 4- Pictographs
Part (b) is designed to exaggerate the difference
by increasing each dimension in proportion to the
actual amounts of oil consumption.
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Misuse 5- Percentages

• Misleading or unclear percentages are sometimes
  used. For example, if you take 100 of a
  quantity, you take it all. 110 of an effort
  does not make sense.

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Other Misuses of Statistics

• Loaded Questions
• Order of Questions
• Refusals
• Correlation Causality
• Self Interest Study
• Precise Numbers
• Partial Pictures
• Deliberate Distortions

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• During a broadcast of a show on MTV, the host
  asks viewers to call in and vote for or against a
  new song, with the result that 74 of 12, 335
  viewers favor it. Given that the sample is so
  large and the percentage is so far above 50, is
  it valid to conclude that the majority of
  Americans favor the song? Why or why not?