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

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Kin 304Tests of Differences between MeansANOVA
Analysis of Variance
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ANOVA Analysis of Variance

• Can cope with multiple groups, not just two
• Similar to independent t-test, in that the
  difference between means is evaluated based upon
  the variance about the means.
• F (ratio) statistic is calculated and is
  evaluated in comparison to the critical value of
  F (ratio) statistic (p0.05)

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One-way ANOVA

• One grouping factor
• Hypothesis
• Group means are different
• Two or more levels of grouping factor
• Sex 1 or 2
• Age Group 7, 8, 9 or 10

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F (ratio) Statistic

• The F ratio compares two sources of variability
  in the scores.
• The variability among the sample means, called
  Between Group Variance, is compared with the
  variability among individual scores within each
  of the samples, called Within Group Variance.

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CFS Kids 17 19 years (Boys)

• ANOVA
• Dependent - VO2max
• Grouping Factor - Age (17, 18, 19)
• No Significant difference between means for
  VO2max (plt0.05)

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CFS Kids 17 19 years (Girls)

• ANOVA
• Dependent - VO2max
• Grouping Factor - Age (17, 18, 19)
• Significant difference between means for VO2max
  (plt0.05)

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But which means are different?

• Post Hoc Tests
• Test for differences between multiple means shown
  to be different by ANOVA

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Scheffe Post Hoc Test
Boys
Girls

• Boys no significant differences, would not run
  post hoc tests
• Girls 19 significantly different than 17 and 18

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2-way ANOVA

• Test of differences between means with two
  grouping factors
• Can evaluate interactions between factors

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• 2 way ANOVA
• Dependent - VO2max
• Grouping Factors
• AGE (17, 18, 19)
• SEX (1, 2)
• Significant difference in VO2max (plt0.05) by SEX
• No Significant difference in VO2max (plt0.05) by
  AGE
• 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 sig. diff. Between regression lines

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• ANCOVA
• Dependent Max Grip Strength
• Grouping Factor Sex (plt0.05?)
• Covariate Skinfold-adjusted Forearm Girth
  (plt0.05)

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T test for difference between means by Sex

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

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ANCOVADependent Max Grip StrengthGrouping
Factor Sex (plt0.05?)Covariate
Skinfold-adjusted Forearm Girth (plt0.05)

• Skinfold-adjusted Forerarm Girth is a significant
  Covariate
• No significant difference between sexes in Grip
  Strength when adjusted for Covariate

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Paired Analysis

• ANOVA with Repeated Measures