Kin 304 Tests of Differences between Means: ANOVA Analysis of Variance

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Kin 304Tests of Differences between MeansANOVA
Analysis of Variance

• N-way ANOVA
• Analysis of Covariance
• Factorial Design
• Repeated Measures ANOVA

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ANOVA Factorial design Multiple factors

• Test of differences between means with two or
  more grouping factors, such that each factor is
  adjusted for the effect of the other
• Can evaluate significance of factor effects and
  interactions between them
• 2 way ANOVA Two factors considered
  simultaneously

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• Example 2 way ANOVA
• Dependent - VO2max
• Grouping Factors
• AGE (17, 18, 19)
• SEX (1, 2)
• Significant difference in VO2max (plt0.05) by
  SEXMain effect
• Significant difference in VO2max (plt0.05) by
  AGEMain effect
• No Significant Interaction (plt0.05) AGE SEX

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Analysis of Covariance (ANCOVA)

• Taking into account a relationship of the
  dependent with another continuous variable
  (covariate) in testing the difference between
  means of one or more factor
• Tests significance of difference between
  regression lines

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• Scatterplot showing correlations between
  skinfold-adjusted Forearm girth and maximum grip
  strength for men and women

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Use of T tests for difference between means?

• Men are significantly (plt0.05) bigger than women
  in skinfold-adjusted forearm girth and grip
  strength

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ANCOVADependent Maximum Grip Strength
(GRIPR)Grouping Factor Sex Covariate
Skinfold-adjusted Forearm Girth (SAFAGR)

• SAFAGR is a significant Covariate
• No significant difference between sexes in Grip
  Strength when adjusted for Covariate
  (representing muscle size)
• Therefore one regression line (not two, for each
  sex) fit the relationship

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3-way ANOVA

• For 3-way ANOVA, there will be
• - three 2-way interactions (AxB, AxC) (BxC)
• - one 3-way interaction (AxBxC)
• If for each interaction (p gt 0.05) then use main
  effects results
• Typically ANOVA is used only for 3 or less
  grouping factors

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Repeated Measures ANOVA

• Repeated measures design the same variable is
  measured several times over a period of time for
  each subject
• Pre- and post-test scores are the simplest design
  use paired t-test
• Advantage - using fewer experimental units
  (subjects) and providing a control for
  differences (effect of variability due to
  differences between subjects can be eliminated)