Factorial ANOVA - PowerPoint by vymIR8ke

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									Factorial ANOVA



  Chapter 12
                   Research Designs
   Between – Between (2 between subjects factors)
   Mixed Design (1 between, 1 within subjects factor)
   Within – Within (2 within subjects factors)
   The purpose of this experiment was to determine
    the effects of testing mode (treadmill, bike) and
    gender (male, female) on maximum VO2.
        Testingmode is a within subjects factor with 2 levels
        Gender is a between subjects factor with 2 levels
        Maximum VO2 is the dependent variable.
                A 3 x 2 Design
   The designs are sometimes identified by the
    number of factors and the levels of each factor.
   The purpose of this experiment was to determine
    the effects of intensity (low, med, high) and
    gender (male, female) on strength development.
    All subjects experience all three intensities.
   A 3 x 2 factorial ANOVA was used to determine
    the effects of intensity (low, med, high) and
    gender (male, female) on strength development.
   Gender is a between subjects factor, intensity is a
    within subjects factor.
                    Interaction?

   Interaction is the combined effects of the factors
    on the dependent variable.
   Two factors interact when the differences
    between the means on one factor depend upon
    the level of the other factor.
   If training programs affect men and women
    differently then training programs interact with
    gender.
   If training programs affect men and women the
    same they do not interact.
No Interactions (Parallel   Slopes)


                                 The red lines
                                 represent
                                 the average
                                 scores for
                                 BOTH A1 &
                                 A2 at each
                                 level of B.
                                 The red lines
                                 are graphing
                                 B Main
                                 Effects.
No Interaction

                 Red line is the
                 Average A1
                 mean
                 (averaged
                 across all
                 levels of B).
                 Blue line is the
                 average A2
                 mean.
                 Main effect for
                 A compares
                 the red and
                 blue mean
                 values.
Significant Interaction


                          Groups A1
                          and A2 are
                          NOT
                          EQUALLY
                          affected by
                          the levels of
                          B.
Strong Interaction
                     Groups A1 and A2
                     are NOT EQUALLY
                     affected by the
                     levels of B.
                     A1 goes DOWN
                     A2 goes UP
                     Draw in the means
                     for A1 and A2?
                     Draw in means for
                     B1, B2, B3.
Significant Interaction
                          Groups A1 and A2
                          are NOT
                          EQUALLY
                          affected by the
                          levels of B.

                          Draw in the
                          means for A1 and
                          A2.

                          Draw in means for
                          B1, B2, B3.
         Factorial ANOVA Assumptions
   Between-Between designs have the same assumptions as
    One-way ANOVA.
      Dependent Variable is interval or ratio.
      The variables are normally distributed
      The groups have equal variances (for between-subjects
       factors)
      The groups are randomly assigned.
   Between-Within are similar to Repeated measures
    ANOVA, but now sphericity must be applied to the
    pooled data (across groups) & the individual group, this is
    referred to as multisample sphericity or circularity.
   Sphericity :requires equal differences between within
    subjects means. In other words the changes between each
    time point must be equal.
    A Between-Between Factorial ANOVA
   The purpose of this experiment was to determine
    the effects of practice (1, 3, 5 days/wk) and
    experience (athlete, non-athlete) on throwing
    accuracy.
   9 athletes & 9 non-athletes were randomly
    assigned to the practice groups (1, 3, 5 days/wk).
   A 3 x 2 Factorial ANOVA with two between
    subjects factors practice (1, 3, 5 days/wk) and
    experience (athlete, non-athlete) was used to test
    the effects of practice and experience on throwing
    accuracy.
               ANOVA Terminology
   The purpose of this experiment was to compare
    the effects of Gender (M,F) and the dose of
    Gatorade (none, 2 pints, 4 pints) on VO2. Subjects
    were randomly assigned to Gatorade groups.
   The independent variables Gatorade and Gender
    are FACTORS.
   The Gatorade has 3 LEVELS (none, 2 pints, 4
    pints) , Gender has 2 LEVELS
   The dependent variable in this experiment is VO2
   This a 2 x 3 ANOVA with two between subjects
    factors.
The Effects of Gender & Gatorade on VO2




                  Create a categorical variable for all
                  Between-Subjects Factors.

                  Gender (0 – Male, 1 – Female)
                  Gatorade (1 – None, 2 – 2 pints, 3 –
                  4 pints.
Enter Dependent Variable and Factors
                 Options Button




Check homogeneity of variance if      Choose the Sidak post hoc
you have a between subjects factor.   test.
           Plots




1. Enter Gatorade on horizontal
   axis, Gender for Separate Lines.
2. Click Add Button, then Continue
   Buttton.
                                               Method 1 for Simple
 UNIANOVA VO2 BY Gender Gatorade                    Effects
  /METHOD=SSTYPE(3)
  /INTERCEPT=INCLUDE
  /PLOT=PROFILE(Gatorade*Gender)
  /EMMEANS=TABLES(OVERALL)
  /EMMEANS=TABLES(Gender) COMPARE ADJ(SIDAK)
  /EMMEANS=TABLES(Gatorade) COMPARE ADJ(SIDAK)
  /EMMEANS=TABLES(Gender*Gatorade) COMPARE(Gender) ADJ(SIDAK)
  /EMMEANS=TABLES(Gatorade*Gender) COMPARE(Gatorade) ADJ(SIDAK)
  /PRINT=OPOWER ETASQ HOMOGENEITY DESCRIPTIVE
  /CRITERIA=ALPHA(.05)
  /DESIGN=Gender Gatorade Gender*Gatorade.


 Enter the first interaction term in the Compare ( ).
 Then switch the order.



Click Paste, then Window to view Syntax
Window
              Method 2 for Simple Effects


MANOVA
VO2 BY Gender(0 1) Gatorade(1 3)
/Design = Gender within Gatorade(1) Gender WITHIN Gatorade(2) Gender
Within Gatorade(3)
/Design = Gatorade Within Gender(1) Gatorade Within Gender(2)
/print CELLINFO SIGNIF( Univ MULTIV AVERF HF GG).
Output: Descriptives
           See page 405 of Field for an additional
           test to check for homogeneity of
           variance.

           Check homogeneity of variance if
           you have a between subjects factor.
           The null hypothesis is that the
           groups have equal variance. In this
           case you retain the null. You don’t
           want this to be significant, if it is
           significant you are violating an
           assumption of ANVOA: homogeneity
           of variance.


         The groups have equal variance, Levine’s
         test F(5,42) = 1.53, p = .20
                  ANOVA Results




No main effect for Gender F(1,42) = 2.032, p = .161.
Sig. main effect for Gatorade F(2,42) = 20.065, p = .000
Sig. interaction between Gender and Gatorade dose F(2,42)
= 11.911, p = .000
Gender * Gatorade F(2,42) = 11.91, p = .000

                         Male             Female       Gatorade Mean
 None                66.88 ± 10.33      60.62 ± 4.96      63.75 ± 8.47
 2 pints             66.87 ± 12.52      62.50 ± 6.55      64.69 ± 9.91
 4 pints             35.63 ± 10.84      57.50 ± 7.07     46.56 ± 14.34
 Gender Mean         56.46 ± 18.50      60.21 ± 6.34     58.33 ± 13.81


   Gender F(1,42) = 2.032, p = .161              Gatorade F(2,42) = 20.065, p=.000


   This slide indicates which means are being compared by each F ratio.
 Post hoc for Gender Main Effect




Gender F(1,42) = 2.032, p = .161
Post hoc for Gatorade Main Effects

                  4 pints was significantly different from
                  none and 2 pints.
                  Simple Effects Testing 2 Steps
Compare gender at each level of
gatorade.
Are males diff from females for                    Male          Female
none?                                None      66.88 ± 10.33   60.62 ± 4.96
                                     2 pints   66.87 ± 12.52   62.50 ± 6.55
Are males diff from females for 2
pints?                               4 pints   35.63 ± 10.84   57.50 ± 7.07

Are males diff from females for 4
pints?


Compare the dose of gatorade for
each level of gender. For males is
there a difference between none, 2                Male           Female
pints, 4 pints?
                                     None      66.88 ± 10.33   60.62 ± 4.96
For females is there a difference    2 pints   66.87 ± 12.52   62.50 ± 6.55
between none, 2 pints, 4 pints?      4 pints   35.63 ± 10.84   57.50 ± 7.07
Difference in Gender at each Gatorade Level




                            Males are significantly
                            different from females for 4
                            pints of Gatorade.
Difference in Gatorade at
    each Gender Level




  For males, 4 pints is significantly
  different from none and 2 pints.
                      Homework
Analyze the Task 1 the book, see page 455.

Do a Sidak post hoc test instead of the planned contrast
suggested in the book.

Use simple effects testing for a significant interaction.




Use the Sample Methods and Results section as a guide to
write a methods and results section for your homework.

								
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