3. 4
◉ The one-way multivariate analysis of variance (one-way MANOVA) is
used to determine whether there are any differences between
independent groups on more than one continuous dependent
variable. In this regard, it differs from a one-way ANOVA, which only
measures one dependent variable.
◉ MANOVA can be used in place of ANOVA with repeated measures; in
which case no sphericity assumption needs to be met when using
MANOVA. In this case, you treat the repeated levels as dependent
variables.
4. 5
For example: perceptions of attractiveness and intelligence of drug
users in movies
◉ the two dependent variables are "perceptions of attractiveness" and
"perceptions of intelligence",
◉ independent variable is "drug users in movies", which has three
independent groups: "non-user", "experimenter" and "regular
user").
6. 7
◉ MANOVA is used under the same circumstances
as ANOVA but when there are multiple
dependent variables as well as independent
variables within the model which the researcher
wishes to test. MANOVA is also considered a
valid alternative to the repeated measures
ANOVA when sphericity is violated.
8. 9
Like an ANOVA, MANOVA examines the
degree of variance within the independent
variables and determines whether it is smaller
than the degree of variance between the
independent variables. If the within subjects
variance is smaller than the between subjects
variance it means the independent variable had a
significant effect on the dependent.
9. ASSUMPTIONS
Two or more dependent
variables should be measured
at the interval or ratio
level (i.e., they are continuous)
Independent variable should
consist of two or more
categorical, independent
groups
You should have independence
of observations, which means
that there is no relationship
between the observations in
each group or between the
groups themselves
10
1 2 3
You should have an adequate
sample size.
4 5 There is a linear relationship
between each pair of
dependent variables for each
group of the independent
variable.
10. Example #1
The pupils at a high school come from three different primary
schools. The head teacher wanted to know whether there were academic
differences between the pupils from the three different primary schools. As
such, she randomly selected 20 pupils from School A, 20 pupils from
School B and 20 pupils from School C, and measured their academic
performance as assessed by the marks they received for their end-of-year
English and Math exams. Therefore, the two dependent variables were
"English score" and "Math score", while the independent variable was
“School”, which consisted of three categories “School A", "School B" and
"School C".
11
11. 12
Hypothesis:
Is there a significant differences in the academic performance
between the pupils from the three different primary schools?
Ho = There is no significant differences in the academic
performance between the pupils from the three different
primary schools.
H1 = There is significant differences in the academic
performance between the pupils from the three different
primary schools.
12. 1. Click Analyze > General Linear
Model > Multivariate... on the
top menu as shown below:
13
You will be presented with the
following Multivariate dialogue
box:
13. 2. Transfer the independent
variable, School, into the Fixed
Factor(s): box and transfer the
dependent
variables, English_Score and Maths_S
core, into the Dependent
Variables: box. You can do this by
drag-and-dropping the variables into
their respective boxes or by using
the arrow button
14
Note: For this analysis, you will not need to use
the Covariate(s): box (used for MANCOVA) or
the WLS Weight: box.
14. 3. Click on the PLOTS button. You will be
presented with the Multivariate: Profile
Plots dialogue box:
15
15. 4. Transfer the independent variable, School,
into the Horizontal Axis: box, as shown below:
16
16. 5. Click on the ADD button. You will see that
"School" has been added to the Plots: box,
as shown below, then Click on
the Continue button and you will be
returned to the Multivariate dialogue box.
17
17. 6. Click on the Post Hoc button. You will be
presented with the Multivariate: Post Hoc
Multiple Comparisons for Observed
Means dialogue box.
18
18. 7. Transfer the independent
variable, School, into the Post Hoc Tests
for: box and select the Tukey checkbox in
the –Equal Variances Assumed– area, as
shown below, then Click on
the Continue button and you will be
returned to the Multivariate dialogue box.
19
Note: You can select other post hoc tests depending on your data and study design. If your
independent variable only has two levels/categories, you do not need to complete this
post hoc section.
19. 8. Click on the EM Means button. You will be
presented with the Multivariate:
Estimated Marginal Means dialogue box.
20
20. 9. Transfer the independent variable,
"School", from the Factor(s) and Factor
Interactions: box into
the Display Means for: box. You will be
presented with the following screen,
then Click on the Continue button and
you will be returned to
the Multivariate dialogue box
21
21. 10. Click on the Options button. Select
the Descriptive
statistics and Estimates of effect
size checkboxes in the –Display– area.
You will be presented with the screen,
Click on the Continue button and you
will be returned to
the Multivariate dialogue box.
22
22. 11. Click on the Generate button to generate the
output.
23
25. 26
Conclusion:
◉ A p-value higher than 0.05 (> 0.05). This means
we retain the null hypothesis and reject the
alternative hypothesis
◉ There was a no statistically significant difference
in academic performance based on a pupil's
prior school .
◉ H0 = Failed to reject
26. Example #2
A counseling researcher studying the effects of cognitive-
behavioral therapy on clients’ levels of depression and anxiety. She
randomly assign 40 clients to one of two treatment conditions: a
cognitive-behavioral therapy condition and a wait-list/control
condition. After 10 weeks intervention period, where the cognitive-
behavioral group received the treatment and the wait-list control group
did not, she measure both groups of clients on their levels of depression
and anxiety (treating these variables as continuous). Let’s treat the variable
“treat” as a nominal variable coded 1=cognitive-behavioral treatment,
2=wait-list control group.
27
27. 28
Hypothesis:
Is there is significant effects of cognitive-behavioral
therapy on clients’ levels of depression and anxiety?
Ho = There is no significant effects of cognitive-behavioral
therapy on clients’ levels of depression and anxiety
H1 = There is significant effects of cognitive-behavioral therapy
on clients’ levels of depression and anxiety
33. 34
Conclusion:
◉ A p-value lower than 0.01 (< 0.05). This means we
reject the null hypothesis.
◉ There was significant effects of cognitive-
behavioral therapy on clients’ levels of
depression and anxiety
◉ H0 = reject the null hypothesis
34. Try to answer this!
1. A researcher randomly assigns 33 subjects to one of three groups. The first group receives technical
dietary information interactively from an on-line website. Group 2 receives the same information
from a nurse practitioner, while group 3 receives the information from a video tape made by the
same nurse practitioner. The researcher looks at three different ratings of the presentation,
difficulty, usefulness and importance, to determine if there is a difference in the modes of
presentation. In particular, the researcher is interested in whether the interactive website is superior
because that is the most cost-effective way of delivering the information.
2. A clinical psychologist recruits 100 people who suffer from panic disorder into his study. Each
subject receives one of four types of treatment for eight weeks. At the end of treatment, each subject
participates in a structured interview, during which the clinical psychologist makes three
ratings: physiological, emotional and cognitive. The clinical psychologist wants to know which type
of treatment most reduces the symptoms of the panic disorder as measured on the physiological,
emotional and cognitive scales.
35
38. References
One-way MANOVA in SPSS Statistics - Step-by-step procedure with screenshots | Laerd
Statistics. (2018b). Laerd Statistics. Retrieved July 13, 2022, from
https://statistics.laerd.com/spss-tutorials/one-way-manova-using-spss-
statistics.php
Crowson, Ph.D., M. (2019, October). Multivariate statistics for the real world - MANOVA and
discriminant analysis. Https://Sites.Google.Com/View/Statistics-for-the-Real-
World/Contents/Manova-and-Discriminant-Analysis. Retrieved July 15, 2022, from
https://sites.google.com/view/statistics-for-the-real-world/contents/manova-and-
discriminant-analysis
2020 Statistical Supporting Unit (STATS-U). (2020). MANOVA and MANCOVA.
Www.Sites.Education.Miami.Edu/. Retrieved July 15, 2022, from
https://sites.education.miami.edu/statsu/2020/10/16/manova-and-mancova/
39
