One-Way and Factorial ANOVA

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One-Way and Factorial ANOVA

• SPSS Lab 3

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One-Way ANOVA

• Two ways to run a one-way ANOVA
• Analyze ? Compare Means ? One-Way ANOVA
• Use if you have multiple DVs, but only one IV
• Analyze ? General Linear Model ? Univariate
• Use if you have only one DV bc/ can provide
  effect size statistics
• More on this later (factorial ANOVA section)

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Method 1 Compare Means

• First we have to test if we meet the assumptions
  of ANOVA
• Independence of Observations
• Cannot be tested statistically, is determined by
  research methodology only
• Normally Distributed Data
• Shapiro-Wilks W statistic, if significant,
  indicates significant non-normality in data
• Analyze ? Descriptive Statistics ? Explore
• Click on Plots, make sure Normality Plots
  w/Tests is checked

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Testing Assumptions
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Testing Assumptions

• Homogeneity of Variances (Homoscedasticity)
• Tested at the same time you test ANOVA
• Analyze ? Compare Means ? One-Way ANOVA
• Click on Options and make sure Homogeneity of
  variance test is checked
• If violated, use Brown-Forsythe or Welch
  statistics, which do not assume homoscedasticity

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Method 1 Compare Means

• One-Way ANOVA
• Analyze ? Compare Means ? One-Way ANOVA
• Dependent List DVs Factor IV
• Options
• Descriptive
• Fixed and random effects
• Homogeneity of variance test
• Levenes Test Significant result ?
  Non-homogenous variances
• Brown-Forsythe
• Welch
• Means plot

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Method 1 Compare Means
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Method 1 Compare Means
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Method 1 Compare Means

• One-Way ANOVA
• Post-Hoc
• Can only be done if your IV has 3 levels
• Pointless if only 2 levels, just look _at_ the means
• Click the test you want, either with equal
  variances assumed or not assumed
• DONT just click all of them and see which one
  gives what you want (thats cheating), select the
  test you want priori

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Method 1 Compare Means

• Contrasts
• Click Polynomial, Leave Degree at default
  (Linear)
• Enter in your coefficients
• of coefficients should equal of levels of
  your IV
• Doesnt count missing cells, so if you have 3
  levels, but no one in one of the levels, you
  should have 2 coefficients
• Coefficients need to sum to 0

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Method 1 Compare Means

• Contrasts
• Enter in your coefficients
• IV Race 1Caucasian, 2African American,
  3Asian American, 4Hispanic, 5Native American,
  6Other, BUT there were no Native Americans in
  the sample
• If you want to compare Caucasians to Other,
  coefficients 1, 0, 0, 0, -1
• Caucasians vs. everyone else -1, .25, .25, .25,
  .25

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Method 1 Compare Means
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Method 2 Univariate

• Univariate works for both one-way (1 IV) and
  factorial ANOVAs (2 IVs)
• Allows for specification of both fixed and random
  factors (IVs)
• Assumptions
• Independence of Observations
• Normally Distributed Data
• Both same as one-way ANOVA

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Factorial ANOVA

• Assumptions
• Homoscedasticity
• Tested at the same time you test ANOVA
• Click on Analyze ? General Linear Model ?
  Univariate
• Click on Options and make sure Homogeneity
  tests is checked

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Factorial ANOVA

• Options
• Estimated Marginal Means
• Displays means, SDs, CIs for each level of
  each IV selected
• If Compare main effects is checked, works as
  one-way ANOVA on each IV selected
• Confidence interval adjustments allows you to
  correct for inflation of alpha using Bonferroni
  or Sidak method
• Descriptive statistics
• Estimates of effect size
• Observed power
• Pointless, adds nothing to interpretation of
  p-value and e.s.
• Homogeneity tests
• Levenes test

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Factorial ANOVA
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Factorial ANOVA

• Save
• Dont worry about this for now
• Post Hoc
• Select the IV for which you wish to compare all
  levels against all other levels (i.e. that you
  dont plan to do planned comparisons on)
• Click on the right arrow button so the IV is in
  the box labeled Post Hoc Tests for
• Check the post hoc tests you want done, either
  with equal variances assumed or not assumed
• Click Continue

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Factorial ANOVA

• Plots
• Horizontal Axis
• What IV is on the x-axis
• Separate Lines
• Separate Plots

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Factorial ANOVA

• The following graph has the IV Race on the
  horizontal axis and separate lines by the IV
  Gender

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Factorial ANOVA

• Model
• Allows you to
• Denote which main effects and interactions you
  are interested in testing (default is to test ALL
  of them)
• Specify which type of sum of squares to use
• Usually you wont be tinkering with this

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Factorial ANOVA

• Contrasts
• Tests all levels within one IV
• Concern yourself with Simple only for now
• Reference category What level all others are
  compared to (either first or last, with this
  referring to how they were numbered)
• Can test specific levels within one IV with
  specific levels in another IV, but requires
  knowledge of syntax

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Factorial ANOVA
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Factorial ANOVA

• Interpreting interactions
• See graphs