1

3.- Effect size

! ηp2 = 54 / (54+4) = 54/58 = 0.93

4.- Multiple comparisons

HSD = q √(MSerror / n) n: sample size in each group q: ‘Studentized Range Statistic’ (Table G: α, k, dferror)

For the case of the previous numerical example with (α=.05, k=3, dferror=4): HSD = 5.04 √(1 / 3) = 2.87

Multiple comparisons For the case of the previous numerical example with (α=.05, k=3, dferror=4): HSD = 5.04 √(1 / 3) = 2.87

!  Factorial Designs ! Analysis of Variance (Two way)

!  Main effects !  Interaction effect

! Example

II. Inferential Statistics (12)

ANOVA !  F distribution

!  Squared version of z !  or t (with infinite df)

! No directional Hypotheses

1.- Factorial Designs ! Two or more independent variables are

manipulated systematically !  Provide the means of determining how those

independent variables jointly influence the dependent variable

! Main effects and Interaction effect

2

Factorial Designs ! Advantages

!  Efficiency !  Control over additional variables !  The study of interaction among independent

variables

2.- Two-way ANOVA !  A two-way ANOVA tests whether differences exist

among population means categorized by two factors or independent variables

!  Main effect !  The effect of a single factor when any other factor is

ignored !  Simple effect

!  The effect of one factor at a single level of another factor !  Interaction effect

!  The product of inconsistent simple effects

Two-way ANOVA !  Interaction

!  It occurs whenever the effects of one factor are not consistent for all values (or levels) of the second factor

Two-way ANOVA !  Statistical Hypotheses

!  H0 : µ.1 = µ.2 = µ.3 … = µ.K (no main effect due to columns)

!  H0 : µ1. = µ2. = µ3. … = µJ. (no main effect due to rows)

!  H0: all (µjk - µj. - µ.k + µ) = 0 (no effect due to interaction)

!  H1: H0 is not true (for each case)

Two-way ANOVA ! Three F ratios

!  In a Two-way ANOVA, three different null hypotheses are tested, one at a time

!  Therefore we now have three F ratios: •  Fcolumn

•  Frow

•  Finteraction

3

Two-way ANOVA Two-way ANOVA ! Example

Two-way ANOVA ! Data