ANOVA

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ANOVA
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Conceptual Basics

• One variable (Interval / Ratio level DV) one
  group (No IV) surveyed once
• One variable (Interval / Ratio level DV) two
  groups (One categorical level IV with two groups
  (also called factors)) each group surveyed
  once
• One variable (Interval / Ratio level DV only)
  one group (No IV) surveyed twice
• One variable (Interval / Ratio level DV) more
  than two groups (One categorical level IV with
  more than two groups (also called factors))
  surveyed once

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Conceptual Basics One Way ANOVA

• Each group (factor) in the sample may feel
  differently about the dependent variable being
  measured (recall stratified sampling???)
• Within each group (factor), the members amongst
  themselves may also feel somewhat differently
  about the variable being measured
• Objective of the ANOVA

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Conceptual Basics One Way ANOVA

• Differences between groups sums of squares
  between factors
• D.f. are number of factors 1
• Ratio gives you Mean sums of squares for
  numerator (MSS n)
• Differences within groups sums of squares
  within factors
• D.f. are sample size number of factors
• Ratio gives you Mean sums of squares for the
  denominator (MSS d)
• Ratio of MSS n and MSS d gives you the observed
  test statistic (the F ratio)

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Conceptual Basics One Way ANOVA

• The Observed test statistic (F ratio)

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Conceptual Basics One Way ANOVA

• The critical test statistic (critical F ratio)
• Becomes smaller as sample size increases but
  larger as number of groups/factors increase
• If observed F gt critical F, reject the Ho
• If observed F lt critical F, accept the Ho