Chapter 10 OneWay Analysis of Variance ANOVA

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Chapter 10 One-Way Analysis of Variance (ANOVA)

• Cynthia Vira
• Guillermo Pro

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ANOVA

• ANOVA is a statistical analysis for evaluating
  the equality of means (mean differences, or
  differences of means) on a single, at least
  intervally-scaled outcome variable across two or
  more groups.
• When testing the equality of means with more than
  two groups, ANOVA has several advantages, only
  one of which involves control of the
  experimentwise Type I error rate.

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Experimentwise Type 1 Error

• Definition rejecting Ho when in reality the
  null hypothesis is true in the population.
• Experimentwise error rate refers to the
  probability of having made one or more Type I
  errors anywhere within the study.

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Heuristic Explanation

• Coin example If you begin flipping a coin.
• If you flip it once, lets say you equate the
  result with Type I error, then the probability of
  heads is 50. If you toss it three times instead
  of once, what is the probability of heads? It is
  still 50 because the coins flipping is
  uncorrelated to previous results.

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Controlling Experimentwise Error Rates

• Always means
• experimentwise Type I error rates.
• Omnibus hypothesis is a test of differences in
  means across groups that simultaneously considers
  all group means.
• Example Ho Mmales Mfemales. Here we
  consider the only categories constituting gender
  with the omnibus hypothesis.
• If we test
• HoMfreshman MsophomoresMjuniorsMseniorsMgrad
  uate students

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ANOVA terminology

• Way or factor is an independent or grouping
  variable.
• One-way studies are ANOVA studies involving a
  single grouping variable such as gender.
• Multiway studies involve more than one way. Each
  group added is called a level.
• Example If a researcher is exploring the
  effects of two teaching methods on posttest
  reading achievement scores, the one way has two
  levels.
• Example I did a 5x3x2 ANOVA. The numbers
  specify levels such as (5)fresh, soph, junior,
  senior, graduate (3)left or right handed or
  ambidextrous, and finally, (2)gender.

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The Logic of Analysis of Variance

• ANOVA can be implemented to estimate the effect
  sizes associated with group mean differences, or
  to test the statistical significance of
  differences in group means, or for both purposes.
• Analysis of variance can test whether group
  dependent variable means are equal, given that
  location and dispersion are two separate
  characterization of data.

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Practical and Statistical Significance

• The sum of squares partitions can be employed to
  estimate the effect size associated with group
  differences, in a metric like that of r2. This
  estimate is called n2, or the correlation ratio.
• N2 SOS between/ SOS total

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Post Hoc tests

• Are analyses conducted following the rejection of
  an omnibus null involving three or more levels to
  investigate more specifically which group means
  differ.