Descriptive & Inferential Statistics

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					Descriptive & Inferential
       Statistics
Merryellen Towey Schulz, Ph.D.
     College of Saint Mary
           EDU 496
The Meaning of Statistics
Several Meanings
   Collections of             Last year’s
    numerical data              enrollment figures
   Summary measures           Average enrollment
    calculated from a           per month last year
    collection of data
   Activity of using and      Evaluators made a
    interpreting a              projection of next
    collection of               year’s enrollments
    numerical data
Descriptive Statistics
 Use of numerical information to
  summarize, simplify, and present data.
 Organized and summarized for clear
  presentation
 For ease of communications
 Data may come from studies of
  populations or samples
Descriptive Statistics Associated
with Methods and Designs
Design                       Descriptive Statistics
Survey Studies               Percentages, measures of
                             central tendency and variation
Meta-analysis                Effect sizes
Causal comparative studies   Measures of central tendency &
                             variation, percentages, standard
                             scores
Experimental                 Measures of central tendency &
                             variation, percentages, standard
                             scores, effect sizes
Descriptive Stats Vocabulary
 Central tendency
 Mode
 Median
 Mean
 Variation
 Range
 Standard deviation
 Normal distribution
Descriptive Stats Vocabulary
cont’d
 Standard score
 Effect size
 Correlation
 Regression
Inferential Statistics

 To generalize or predict how a large
  group will behave based upon
  information taken from a part of the
  group is called and INFERENCE
 Techniques which tell us how much
  confidence we can have when we
  GENERALIZE from a sample to a
  population
Inferential Stats Vocabulary
 Hypothesis
 Null hypothesis
 Alternative hypothesis
 ANOVA
 Level of significance
 Type I error
 Type II error
Examples of Descriptive and
Inferential Statistics
    Descriptive Statistics             Inferential Statistics
   Graphical                         Confidence interval
     –   Arrange data in tables       Margin of error
     –   Bar graphs and pie
                                      Compare means of two
         charts
                                       samples
   Numerical                          –   Pre/post scores
     –   Percentages
                                       –   t Test
     –   Averages
                                      Compare means from
     –   Range
                                       three samples
   Relationships                      –   Pre/post and follow-up
     –   Correlation coefficient
                                       –   ANOVA = analysis of
     –   Regression analysis               variance
Problems With Samples
   Sampling Error
    –   Inherent variation between sample and population
    –   Source is “chance or luck”
    –   Results in bias
   Sample statistic -- a number or figure
    –   Single measure -- how sure accurate
    –   Comparing measures --see differences
          How much due to chance?
          How much due to intervention?
What Is Meant By A Meaningful
Statistic (Significant)?
   Statistics, descriptive or inferential are NOT a
    substitute for good judgment
    –   Decide what level or value of a statistic is
        meaningful
    –   State judgment before gathering and analyzing
        data
   Examples:
    –   Score on performance test of 80% is passing
    –   Pre/post rules instruction reduces incidents by
        50%
Interpretation of Meaning
   Population Measure (statistic)
    –   There is no sampling error
    –   The number you have is “real”
    –   Judge against pre-set standard
   Inferential Measure (statistic)
    –   Tells you how sure (confident) you can be
        the number you have is real
    –   Judge against pre-set standard and state
        how certain the measure is

				
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posted:3/14/2012
language:English
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