Factorial anova

Factorial anova

1. more than 1 iv. looks at main effects and interactions

2. gives more infomation

   • generalisability
     • Can look at the effects of individual differences
     • can look at the effect of related factors
   • interactions
     • When the effects of one factor on the dependent variable are different at different levels of the other factor. usually the main source of interest in factorial design
       • multiple comparisons for interactions
         • simple effects analysis- issolates effects of 1 iv at diffrent levels of the other iv
           • compare means in the quadrant
           • T TEST and compare to t test
             • Can use linear contrasts (via the one-way ANOVA procedure)
     • The number of interactions are a function of the number of factors thus AXB = i interaction, AXBXC = 4 interactions
     • examining interactions
       • ordinal
         • 1 is consistently higher than the other
           • When the differences between different levels of one factor reverse at some level of the other factor
       • disordinal
         • lines cross
           • When the differences between different levels of one factor are reduced, at some level of the other factor
       • Asumptions
         • normaility - skewcurtosis, data screen, shipiro wilk
           • Effect size
             • ANOVA-partial eta squared and Cohen’s f
               • partial eta squared - Is the proportion of the ‘effect + error’ variance that is attributable to the effect
                 • The sums of the eta partial squared values are not additive – they do not sum to the amount of dependent variable variance accounted for by the independent variables- must be < than 1
                   • s=.01 m=.09 l= .25
             • Multiple comparison- Cohens D
         • Levenes test of Homongeinity
         • Independence of observations- one group and one group only - nobody is influenceing the score of other individuals
   • efficiency
     • Can look at the effects of several factors within one experiment
     • Not as many subjects are needed for the same amount of statistical power

3. every level of every factor is paired with every level of every other factor

   • Can include experimentally manipulated independent variables and differential independent variables
     • Main effects
       • Main effects are the effects of one factor on the dependent variable when the other factor is held constant
       • Same as looking at the effect of one factor after averaging across the effects of the other factor
       • report a main effect for every IV
       • need to report an interaction of αβ
       • structural model of Factorial anova
         • Xijk = μ + αi + βj + αβij + εijk
           • μ is the population mean αi is the main effect of factor Ai βj is the main effect of factor Bj αβij is the interaction between factor Ai and Bj εijk is the variability (error) associated with an individual observation
         • spss - Analysis - general linear model - univariant- iv's in fixed factors
           • Null hypothesis for each IV and interaction
             • FactorA- X1 =X2 or α = 0
             • Factor B - X1= X2 or β = 0
             • Factor AB = X11 = X12 = X21 = X22 or αβij = 0
           • in the results ignore corrected model, intercept and total
             • SPSS sometimes says MSwithin or MSerror
               • F= MSbetween / MS within
                 • MStotal = MSa +MSb + MSab +MSerror
                 • MS = SS/DF

4. 2x3 = 2way design with 2 levels on the 1st iv and 3 levels on the 2nd iv