This document provides an overview of various multivariate analysis of variance (MANOVA) techniques, including one-way MANOVA, two-way MANOVA, and multivariate analysis of covariance (MANCOVA). It defines each technique, provides examples, and outlines the assumptions that must be met to use each one. Key assumptions for MANOVA include having continuous dependent variables, categorical independent groups, independence of observations, adequate sample sizes, no outliers, multivariate normality, linear relationships between dependent variables, no multicollinearity, and homogeneity of variance-covariance matrices. The document also describes how to test assumptions and interpret MANOVA results in SPSS.

1. MANOVA - SPSS
DR ATHAR KHAN
ASSOCIATE PROFESSOR
DEPARTMENT OF COMMUNITY MEDICINE
LIAQUAT COLLEGE OF MEDICINE & DENTISTRY
KARACHI – PAKISTAN
drathar15@gmail.com

2. One-way ANOVA has one continuous response variable (e.g. Test Score)
compared by three or more levels of a factor variable (e.g. Level of
Education).2/11/2019 DR ATHAR 2

3. Two-way ANOVA has one continuous response variable (e.g. Test Score)
compared by more than one factor variable (e.g. Level of Education and
Zodiac Sign).2/11/2019 DR ATHAR 3

4. ANCOVA compares a continuous response variable (e.g. Test Score) by
levels of a factor variable (e.g. Level of Education), controlling for a
continuous covariate (e.g. Number of Hours Spent Studying).2/11/2019 DR ATHAR 4

5. One-way MANOVA compares two or more continuous response variables
(e.g. Test Score and Annual Income) by a single factor variable (e.g. Level
of Education).2/11/2019 DR ATHAR 5

6. Two-way MANOVA compares two or more continuous response variables
(e.g. Test Score and Annual Income) by two or more factor variables (e.g.
Level of Education and Zodiac Sign).2/11/2019 DR ATHAR 6

7. ANCOVA compares two or more continuous response variables (e.g. Test
Scores and Annual Income) by levels of a factor variable (e.g. Level of
Education), controlling for a covariate (e.g. Number of Hours Spent
Studying).2/11/2019 DR ATHAR 7

8. 2/11/2019 DR ATHAR 8

9. 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.
One-way Multivariate Analysis Of Variance
(One-way MANOVA)
2/11/2019 DR ATHAR 9

10. One-way MANOVA compares two or more continuous response variables
(e.g. Test Score and Annual Income) by a single factor variable (e.g. Level
of Education).2/11/2019 DR ATHAR 10

11. Drug users in movies
▪ Non-user
▪ Experimenter
▪ Regular user
Perceptions of attractiveness
Perceptions of intelligence
2/11/2019 DR ATHAR 11

12. Duration of Lecture
▪ 30 minutes
▪ 60 minutes
▪ 90 minutes
▪ 120 minutes
Short-term memory recall
Long-term memory recall
2/11/2019 DR ATHAR 12

13. Assumption #1: Your two or more dependent variables
should be measured at the interval or ratio level (i.e., they
are continuous).
Assumption #2: Your independent variable should
consist of two or more categorical, independent groups.
Assumption #3: You should have independence of
observations, which means that there is no relationship
between the observations in each group or between the
groups themselves.
2/11/2019 DR ATHAR 13

14. Assumption #4: You should have an adequate sample
size.
20 in each level of Independent variable OR
Number of levels in independent variable x number of
dependent variables = _______ in each level of
Independent variable
Assumption #5: There are no univariate or multivariate
outliers. First, there can be no (univariate) outliers in each
group of the independent variable for any of the
dependent variables.2/11/2019 DR ATHAR 14

15. 2/11/2019 DR ATHAR 15

16. For continuous variables, univariate outliers can be considered
standardized cases that are outside the absolute value of 3.29.2/11/2019 DR ATHAR 16

17. 2/11/2019 DR ATHAR 17

18. 2/11/2019 DR ATHAR 18

19. 2/11/2019 DR ATHAR 19

20. 2/11/2019 DR ATHAR 20

21. DATA → Sort Cases → MAH → Descending
DATA → Sort Cases → SNO
2/11/2019 DR ATHAR 21

22. Maximum Value is Critical Value
If greater than 13.82 (2 dependent variables ) is Outlier
If greater than 16.27(23dependent variables) is Outlier
2/11/2019 DR ATHAR 22

23. Assumption #6: There is multivariate normality.
2/11/2019 DR ATHAR 23

24. Assumption #6: There is multivariate normality.
Shapiro-Wilk test of normality
Sig > 0.05 Normally distributed
Sig < 0.05 Not normally distributed
Linear combination of the variables is also normally
distributed
2/11/2019 DR ATHAR 24

25. Assumption #7: There is a linear relationship between
each pair of dependent variables for each group of the
independent variable.
.
2/11/2019 DR ATHAR 25

26. Assumption #8: There is no multicollinearity.
2/11/2019 DR ATHAR 26

27. Assumption #8: There is no multicollinearity.
2/11/2019 DR ATHAR 27

28. If the correlations are low (< 0.2), you might be better off
running separate one-way ANOVAs, and if the
correlation(s) are too high (greater than 0.9), you could
have multicollinearity.
2/11/2019 DR ATHAR 28

29. Assumption # 9: There is homogeneity of variance-
covariance matrices. You can test this assumption in
SPSS Statistics using Box's M test of equality of
covariance.
Sig > 0.001 Meet the assumption
2/11/2019 DR ATHAR 29

30. 2/11/2019 DR ATHAR 30

31. 2/11/2019 DR ATHAR 31

32. 2/11/2019 DR ATHAR 32

33. if sample size is equal Tukey
If NO then Scheffe2/11/2019 DR ATHAR 33

34. 2/11/2019 DR ATHAR 34

35. 2/11/2019 DR ATHAR 35

36. If meet all
assumptions
If NOT meet all
assumptions
Therefore, we can conclude that IQ
Score and Test Score were
significantly dependent on type of
students(p < .001)
2/11/2019 DR ATHAR 36

37. There is a statistically
significant difference across
levels of ID on a linear
combination of VD’s
If NOT meet all
assumptions
27.1 % variance in dependent
variables can be explained by
IV
2/11/2019 DR ATHAR 37

38. There was a statistically significant difference in
academic performance based on a pupil's prior school ,
F (4, 72) = 6.676, p < .001; Pillai’s Trace = 0.541, partial
η2 = .27.
If you had not achieved a statistically significant result,
you would not perform any further follow-up tests
2/11/2019 DR ATHAR 38

39. 49.3 % variance in dependent
variable can be explained by IV
Univariate ANOVAs
To determine how the dependent variables differ for the
independent variable
2/11/2019 DR ATHAR 39

40. We can see from this table that type of course has a statistically significant
effect on IQ score (F (2, 36) = 17.51; p < .001; partial η2 = .493) and not
significant effect on Test scores (F (2, 36) = 1.41; p < .255; partial η2 = .073).
It is important to note that you should make an alpha correction to account
for multiple ANOVAs being run, such as a Bonferroni correction. As such, in
this case, we accept statistical significance at p < .025.2/11/2019 DR ATHAR 40

41. Mean scores for IQ were statistically significantly different
between Physics and chemistry student (p < .001)
2/11/2019 DR ATHAR 41

42. 2/11/2019 DR ATHAR 42

43. ANCOVA compares two or more continuous response variables (e.g. Test
Scores and Annual Income) by levels of a factor variable (e.g. Level of
Education), controlling for a covariate (e.g. Number of Hours Spent
Studying).2/11/2019 DR ATHAR 43