Descriptive & Inferential Statistics

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Descriptive Inferential Statistics

• Merryellen Towey Schulz, Ph.D.
• College of Saint Mary
• EDU 496

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The Meaning of Statistics Several Meanings

• Last years enrollment figures
• Average enrollment per month last year
• Evaluators made a projection of next years
  enrollments

• Collections of numerical data
• Summary measures calculated from a collection of
  data
• Activity of using and interpreting a collection
  of numerical data

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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

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Descriptive Statistics Associated with Methods
and Designs
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Descriptive Stats Vocabulary

• Central tendency
• Mode
• Median
• Mean
• Variation
• Range
• Standard deviation
• Normal distribution

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Descriptive Stats Vocabulary contd

• Standard score
• Effect size
• Correlation
• Regression

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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

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Inferential Stats Vocabulary

• Hypothesis
• Null hypothesis
• Alternative hypothesis
• ANOVA
• Level of significance
• Type I error
• Type II error

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Examples of Descriptive and Inferential Statistics

• Descriptive Statistics
• Graphical
• Arrange data in tables
• Bar graphs and pie charts
• Numerical
• Percentages
• Averages
• Range
• Relationships
• Correlation coefficient
• Regression analysis

• Inferential Statistics
• Confidence interval
• Margin of error
• Compare means of two samples
• Pre/post scores
• t Test
• Compare means from three samples
• Pre/post and follow-up
• ANOVA analysis of variance

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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?

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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

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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