Two-Way Mixed ANOVA
Psyc301- Spring 2014
Sezin Öner
• Two-way Between Subj. ANOVA  Two categorical IVs
• Two-way Mixed ANOVA 
One categorical IV + One within subjects IV
(At least)
Two-way Mixed ANOVA
One categorical IV (Groups)
One within subjects IV (Same tests A-B)
Group I
Group II
Test A
Test A
Test B
Test B
Why do we use mixed ANOVA?
MAIN EFFECTS and INTERACTION EFFECT
• Main effects are assessed at to levels, one effect for the
categorical IV one for the within-subj. IV.
• Interaction effect: If the effect of one IV depends on the other.
(Does the change across the same individuals depend on the
group/condition?)
Assumptions
• Independence of observations – observations must not influenced by any other
observation
• Random Sample
• Homogenity of difference scores
• Check Mauchly’s test of sphericity (Sign. greater than .05)
• Homogeneity of Variance – Similar variability of scores for each group
• Levene’s test for equality of variances(Sig. greater than .05)
• Homogeneity of intercorrelations – The pattern of intercorrelations among the levels
of the within-subjects variables should be the same for each of the levels of the
between-subjects variable.
• Check Box’s M statistic (Sign. greater than .001)
Hypotheses
Three hypotheses are tested simultaneously:
1) The effect of within-subjects IV on DV (main effect#1).
2) The effect of categorical IV on DV (main effect#2).
3) The combined (joint) effect of different types of Ivs on DV
(interaction effect).
Working Example
• Data: Longitidunal Data.sav
Calm
Anxious
TIME_1: 1 year
TIME_1: 1 year
Social Functions
Social Functions
TIME_2: 3 year
TIME_2: 3 year
Social Functions
Social Functions
Executive Function
Executive Function
TIME_3: 5 year
TIME_3: 5 year
Social Functions
Social Functions
Executive Function
Executive Function
TIME_4: 7 year
TIME_4: 7 year
Social Functions
Social Functions
Executive Function
Executive Function
School Adaptation
School Adaptation
Working Example
• Data: Longitidunal Data.sav
• Is there any difference between the “calm” and “anxious”
children in terms the developmental course of executive
functions? Compare EF_TIME_2, EF_TIME_3, EF_TIME_4
depending on the temperamental reactivity (TEMP) (CALM vs
ANXIOUS) of children
Questions:
 Is there a change in the executive function of children over
the time course? main effect#1
(Is the change across time similar between time periods?)
 Does the temperamental status of children have an effect on the
level of executive function?  main effect #2
 Is the change across time periods similar for calm and anxious
children?  (Interaction effect)
(Does the change in development of executive function depend on the
children’s temperamental status?)
Design
TEMP
IVs
TIME
TIME_1
TIME_2
TIME_3
TIME_4
Calm
.
.
.
.
Calm
.
.
.
.
Anxious
.
.
.
.
Calm
.
.
.
.
Anxious
.
.
.
.
• IV#1: Within-subj. IV = TIME
• IV#2: Categorical IV = TEMP
• Analyze-General Linear Model- Repeated Measures
• Name the withinsubjects variable (IV#1) and write the level (how
many conditions for IV#1)
• Move all levels of IV#1 to the Within subj. factors
(EF_TIME_2, EF_TIME_3, EF_TIME_4)
• Move IV#2 to Fixed factors
(TEMP)
• (Click on Post-hoc if categorical variable has more than two levels:
select only that variable for Post-hoc analysis, then select Tukey.
• Finally, click on Options…
• Display Means For: all IVs and the interaction
• Select the boxes for Descriptive statistics and homogeneity tests
• OK.
• Check homogenity of intercorrelations assumption!
not significant OK
Check homogenity of variance for the differences
NOT
SIGNIFICANT
• Check main effect#1 and interaction from this table!
Main effect#1
Check homogenity of variance of each level of DV
NOT
SIGNIFICANT
• Main effect#2 is not also significant! (F(1, 36) = .998; p = .324).
Interaction effect tested whether the effects are overlapped. Since it is
not significant, you do not need to report the means. But still you
should report the F and p value.
Interaction effect
How to report main effects?
• The main effect of time on children’s executive function was significant.,
(F(2, 72) = 106.051, p < .000), which indicated that children showed the
worst performance at TIME 2, at their youngest age (M =12.42 , SD = 1.89).
Although the performance at TIME 3 (M = 15.21 , SD = 1.72) did not differ
from the performance at TIME 4 (M = 15.55 , SD = 1.95), it was higher than
TIME 1.
• The main effect of temperamental reactivity on the execuitve function was
not significant, (F(1, 36) = .998; p = .324).
Lets move to a more complex analysis.
The question is:
Is there any difference between the “calm” and “anxious”
children in terms the developmental course of social functions.
Compare SF_TIME_1, SF_TIME_2, SF_TIME_3, SF_TIME_4
depending on the temperamental reactivity (TEMP) (CALM vs
ANXIOUS) of children!
Everything will be the same, except;
Change the level of within-subj factor since SF_TIME has four levels
• All effects are significant!
Report the main effects:
For IV#1: TIME
The main effect of time on children’s social functions was
significant., (F(2.602, 93.660) = 503.374, p < .000). Results
demonstrated that children performed the worst at TIME 1
(M = 4.51 , SD = 1.41) and the best at TIME 4 (M = 9.20 ,
SD = 1.84) compared to all other time points. In addition,
performance at TIME 3 (M = 5.94 , SD = 1.33) was greater
than TIME 2 (M = 5.29 , SD = 1.56), which indicated that
children significantly developed their social skills in
between each time of assessment.
• All effects are significant!
Report the main effects:
For IV#2: TEMP
The main effect of temperamental status on children’s social
functions was significant., (F(1, 36) = 4.412, p = .043), indicating
that calm children (M = 6.67 , SD = 1.20) had higher social skills
than the anxious children (M = 5.75 , SD = 1.49).
-----------------------------------------------------------------------------You can see the descriptives seperately from the this command
COMPUTE SF_Mean=(SF_TIME_1 + SF_TIME_2 + SF_TIME_3
+ SF_TIME_4) / 4.
Conduct independent-samples t-tes TEMP by SF_Mean
There is an increase at each time
point; however, the increase for
calm individuals seems to be
greater than anxious children.
• To examine the mean differences causing interaction effect,
conduct multiple t-tests.
• Include only two levels of within-subj. IV
(TEMP by SF_TIME_1 vs. SF_TIME_2; SF_TIME_1 vs.
SF_TIME_4; SF_TIME_3 vs. SF_TIME_4…)
The difference between calm and anxious individuals is
significant only for SF_TIME_4.
Report the means and based on the descriptives of the t-test.
Reporting interaction effect
“The interaction effect of temperamental reactivity on the children’s
level of social skills was signigicant, (F(2.60, 93.66,) = 28.592p <
.000), revealing that the amount of increase across years are
different for calm and anxious children. Although calm and anxious
children did not differ with respect to social functions at TIME_1,
TIME_2, and TIME_3(M = 6.16, SD = 1.17) , calm children
outperformed anxious children at TIME_4(M = 10.33, SD=1.27. This
indicated that the increase from TIME 3 to TIME 4 was greater for
calm children than the anxious ones.
If the categorical IV has more than two levels, then conduct:
Simple effects analyses as described in the previous lecture
(this slide )
Follow the same logic that analyzed each level of IV seperately.
• Assignments are due the final date, but it is better to
complete them before the final so that you can ask questions..
• Send your output and also a word documents in which you
summarized your findings. Please email to both me and Ezgi.