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One-Way and Factorial ANOVAPowerPoint Presentation

One-Way and Factorial ANOVA

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### One-Way and Factorial ANOVA

SPSS Lab #3

One-Way ANOVA

- Two ways to run a one-way ANOVA
- Analyze Compare Means One-Way ANOVA
- Use if you have multiple DV’s, 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)

- Analyze Compare Means One-Way ANOVA

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-Wilk’s 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

- Independence of Observations

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

Method #1: Compare Means

- One-Way ANOVA
- Analyze Compare Means One-Way ANOVA
- “Dependent List” = DV’s; “Factor” = IV
- Options
- Descriptive
- Fixed and random effects
- Homogeneity of variance test
- Levene’s Test: Significant result Non-homogenous variances

- Brown-Forsythe
- Welch
- Means plot

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 @ the means

- Click the test you want, either with equal variances assumed or not assumed
- DON’T just click all of them and see which one gives what you want (that’s cheating), select the test you want priori

- Can only be done if your IV has 3+ levels

- Post-Hoc

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
- Doesn’t 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

- # of coefficients should equal # of levels of your IV

Method #1: Compare Means

- Contrasts
- Enter in your coefficients
- IV = Race – 1=Caucasian, 2=African American, 3=Asian American, 4=Hispanic, 5=Native American, 6=Other, 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

- Enter in your coefficients

Method #2: Univariate

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

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

- Homoscedasticity

Factorial ANOVA

- Options
- Estimated Marginal Means
- Displays means, SD’s, & CI’s 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

- Displays means, SD’s, & CI’s for each level of each IV selected
- Descriptive statistics
- Estimates of effect size
- Observed power
- Pointless, adds nothing to interpretation of p-value and e.s.

- Homogeneity tests
- Levene’s test

- Estimated Marginal Means

Factorial ANOVA

- Save
- Don’t 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 don’t 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”

Factorial ANOVA

- Plots
- Horizontal Axis
- What IV is on the x-axis

- Separate Lines
- Separate Plots

- Horizontal Axis

Factorial ANOVA

- The following graph has the IV “Race” on the horizontal axis and separate lines by the IV “Gender”

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 won’t be tinkering with this

- Allows you to:

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

Factorial ANOVA

- Interpreting interactions
- See graphs

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