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					  Introduction to
  Statistics
Quantitative Methods in HPELS
440:210
Agenda
n Roadmap
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Roadmap
  Descriptive Statistics                       Inferential Statistics
 •Central tendency                           •Parametric
 •Variability                                •Nonparametric




                Correlational Method   Experimental Method
Agenda
n Roadmap
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Basic Concepts
n Statistics: A set of mathematical
  procedures for organizing, summarizing
  and interpreting information
n Statistics generally serve two purposes:
    ¨ Organize     and summarize information
      n   Descriptive statistics
    ¨ Answer     questions (interpretation)
      n   Inferential statistics
Basic Concepts
n   Population: The set of all individuals or subjects
    of interest in a particular study
n   Sample: The set of individuals or subjects
    selected from a population intended to represent
    the population of interest
n   Parameter: A value that describes a population
n   Statistic or test statistic: A value that describes a
    sample
    Basic Concepts
n   Inferential statistics: Procedures that allow
    you to make generalizations about a
    population based on information about the
    sample
    ¨ Figure   1.1, p 6
    Basic Concepts
n   Sampling error: The discrepancy that exists
    between a sample statistic and the
    population parameter
    ¨ Figure   1.2, p 8
Agenda
n Roadmap
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Inferential Statistics
n Statistical Inference: Statistical process
  that uses probability and information about
  a sample to make inferences about a
  population
n Two Main Methods
                  Method
    ¨ Correlational
    ¨ Experimental Method
Correlational Method
n   Process:
    ¨ Observe  two variables naturally
    ¨ Quantify strength and direction of relationship

n Advantage: Simple and elegant
n Disadvantage: Does not assume “cause
  and effect”
    ¨ Shoe   size and IQ in elementary students?
Experimental Method
n   Process:
    ¨ Manipulate one variable
    ¨ Observe the effect on the second variable
n Advantage: A well controlled experiment
  can make a strong case for a “cause and
  effect” relationship
n Disadvantage: Difficult to control for all
  “confounding” variables
Experimental Method
n   Which variable is manipulated?
    ¨ Independent variable
    ¨ Treatment (not always a pill)

n   Which variable is observed?
    ¨ Dependent variable
    ¨ Measure or test

n   What is the effect of the IV on the DV?
Agenda
n Roadmap
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Scales of Measurement
n   The scales of measurement describe the
    nature/properties of data
n   The scale of measurement affects the selection
    of the test statistic
n   The are four scales of measurement:
    1. Nominal
    2. Ordinal
    3. Interval
    4. Ratio
Scales of Measurement: Nominal

n   Characteristics of Nominal Data:
n   Assigns names to variables based on a
    particular attribute
n   Divides data into discrete categories
n   No quantitative meaning
Scales of Measurement: Nominal
n   Example: Gender as a variable
n   Names assigned to variables based on
    particular attribute
      -Male or female
n   Divides data into discrete categories
      -Male or female (not both)
n   No quantitative meaning
      -Males cannot be quantified as “more or less” than
      girls
Scales of Measurement: Ordinal
n   Characteristics of Ordinal Data:
n   Has quantifiable meaning
n   Intervals between values not assumed to
    be equal
Scales of Measurement: Ordinal
n Example: Likert Scales
n UNI Teacher Evaluations:
n “Does the instructor show interest . . .”
    ¨ Never
    ¨ Seldom
    ¨ Frequently
    ¨ Always
 Scales of Measurement: Ordinal
 n      Example: Likert Scales
 n      Has quantifiable meaning
          -”Never” is less than “seldom”
          -Values can be rank ordered
 n      Intervals between values not assumed to
        be equal
            ?                                 ?




Never             Seldom         Frequently       Always
Scales of Measurement: Ordinal
n   Other examples:
    ¨ Small,medium, large sizes
    ¨ Low, medium, high performance
Scales of Measurement: Interval
n   Characteristics of Interval Data:
n   Has quantifiable meaning
n   Intervals between values are assumed to be
    equal
n   Zero point does not assume the absence of a
    value
n   Values do not originate from zero
n   Values cannot be expressed as multiples or
    fractions
Scales of Measurement: Interval
n   Example: Temperature (Fahrenheit or Celcius)
n   Has quantifiable meaning
      -10 C° is less than 20 C°
n   Intervals between values are assumed to be equal
      -The difference between 5 and 10 C° = difference between 15
      and 20 C°
n   Zero point does not assume the absence of a value
      -0 C° does not mean absence of temperature
n   Values do not originate from zero
      -0 C° is arbitrary based on freezing point
n   Values cannot be expressed as multiples or fractions
      -10 C° is not twice as cold as 5 C°
Scales of Measurement: Ratio
n   Characteristics:
n   Has quantifiable meaning
n   Intervals between values are assumed to be
    equal
n   Zero point assumes the absence of a value
n   Values originate from zero
n   Values can be expressed as multiples or
    fractions
Scales of Measurement: Ratio
n   Example: Length
n   Has quantifiable meaning
n   Intervals between values are assumed to be
    equal
n   Zero point assumes the absence of a value
n   Values originate from zero
n   Values can be expressed as multiples or
    fractions
Scales of Measurement
n How do the scales of measurement affect
  the selection of the test statistic?
n Bottom Line:
    ¨ Nominal   and ordinal data à Nonparametric
    ¨ Interval and ratio data à Parametric
Scales of Measurement
n   Parametric statistics:
    ¨ Definition:Statistical techniques designed for use
      when the data have certain specific characteristics in
      regards to:
       n   Scale of measurement: Interval or ratio
       n   Distribution: Normal
    ¨ More    powerful
n   Nonparametric statistics:
                Statistical techniques designed to be used
    ¨ Definition:
      when the data are:
       n   Scale of measurement: Nominal or ordinal or
       n   Distribution: Nonnormal
Agenda
n Roadmap
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Statistical Notation
n Textbook à progressive introduction of
  statistical notation
n Summation = S
Summation Example
n SX = 3+1+7=11     X   X2

n SX2 = 9+1+49=59   3   9
n S(X)2=11*11=121
                    1   1

                    7   7
Textbook Problem Assignment
n   Problems: 2, 8, 12a, 12c, 16, 20.

				
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posted:4/15/2014
language:English
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