ANOVA TABLE PROCESSING

2. Statistical Analysis using SPSS
by
Dr Lalit Prasad

3. Outline
• ANOVA : One Way and Two Way ANOVA
• One way ANCOVA
• MANOVA: One way and Two way MANOVA
• One way MANCOVA

4. Primary Scales of Measurement
Non-metric Scale Metric scale
Nominal Ordinal Interval Ratio
Categorical Data Continuous Data

5. Nominal scale
• When numbers assigned to objects serve as labels
for identification or categorization, then such
numbers are in nominal scale. Such numbers have
no quantitative meaning.
For e.g.
• Male = 1
• Female = 2
• The only permissible operation on such numbers is
counting. %, mode, chi-square and binomial tests
can be performed on such data.

6. Ordinal scale
• When assigned numbers indicate relation between entities in
terms of greater than, equal or less than but do not state how
much greater than or less than, then the scale is called ordinal
scale.
• For e.g. Ranks
• Rank following brands of TV on sound quality:
Rank
• Sony _____
• Videocon _____
• Samsung _____
• This means we cannot conclude about difference between
values of two objects. We can calculate median, quartiles,
deciles, percentiles & rank order correlation.

7. Interval scale
• When assigned numbers are such that difference in numbers is
valid but not ratios, then the scale is called interval scale.
• In this scale there is no true zero indicating absence of
characteristic. For e.g
• Temperature
• – To what extent do you like sound quality of LG TV?
Liked very much 5
Somewhat liked 4
Neither liked nor disliked 3
Somewhat not liked 2
Not liked at all 1
Arithmetic mean, standard deviation, product-moment
correlations can be applied to interval scale data.

8. Ratio scale
• When a scale contains absolute zero, it is
called ratio scale
• All mathematical operations (+,-,*,/) are valid
on this data
• All statistical techniques can be applied to
ratio scale data.

9. Hypothesis
H0: There is no significant difference of demographic
variables (Gender, Age Group, Income Group,
Educational Qualification, Work Experience ) on
dependent variable(s) (customer satisfaction)
H1: There is a significant difference of demographic
variables (Gender, Age Group, Income Group,
Educational Qualification, work Experience ) on
dependent variable(s) (customer satisfaction)

10. ANOVA
• ANOVA tests three or more groups for
mean differences of continuous response
variable (dependent variable).
• ANOVA compares MEAN Values.

11. ANOVA Types
• One way ANOVA compares levels
(i.e. groups ) of a single factor.
• Two way ANOVA compares levels of two or
more factors.
• Both has single continuous response
variable.

12. One Way ANOVA
Factor Dependent Variable
Independent/Predictor variable
(Categorical)
e.g. Study Period
1: Less than 5 Hours
2: 5 to 10 Hours
3: More than 10 Years
Dependent /Response Variable
(Continuous)
Example: Test Score

13. Two Way ANOVA
Factor 1
Dependent Variable
Factor 2
Independent /Predictor
Variable
(Categorical)
Factor : Level of Anxiety
Independent /Predictor
Variable
(Categorical)
Factor : Study Period
Dependent/Response
Variable
(Continuous)
Example : Test Score

14. ANCOVA: Analysis of co-variance
• “C” stands for ‘covariance’.
• Like ANOVA, ANCOVA has a single continuous
response variable.
• Unlike ANOVA, ANCOVA compares a response
variable by both a factor and a continuous
dependent variable.
• The continuous independent variable used in
ANCOVA is known as “covariate”

15. One Way ANCOVA
Factor 1
Dependent variable
Covariate
Independent /Predictor
Variable
(Continuous)
Example: Age
Independent /Predictor
Variable
(Categorical)
Factor : Diet
1: Normal Diet
2:Junk Diet
3: Health Diet
Dependent/Response
Variable
(Continuous)
Example : weight Gain

16. What is MANOVA
• MANOVA is variation of ANOVA…..with two
or more continuous response variables
• MANOVA assesses the statistical significance
of the effect of one or more independent
variables on a set of two or more dependent
variables.
• Its simply ANOVA with several dependent
variables.

17. MANOVA
• MANOVA is an ANOVA with two or
more continuous variables.
• “M” stands for multivariate.
• Like ANOVA, MANOVA has both one
way and a two way types.

18. One way MANOVA
DV1
Factor
DV2
Independent /Predictor Variable
(Categorical)
Factor : Gender
1:Male
2: Female
Dependent/Response Variable
(Continuous)
Example- Emotional
Intelligence
Dependent/Response Variable
(Continuous)
Example- Job Performance

19. Two Way MANOVA
Factor 1 DV1
Factor 2 DV2
Independent /Predictor
Variable
(Categorical)
Factor : Level of Anxiety
Dependent/Response
Variable
(Continuous)
Example- Test Scores
Dependent/Response
Variable
(Continuous)
Example- Income
Independent /Predictor
Variable
(Categorical)
Factor : Study Period

20. MANCOVA
• Both MANOVA and MANCOVA has
two or more response variables.

21. One Way MANCOVA
Factor 1 DV1
Covariate DV2
Dependent/Response
Variable
(Continuous)
Example- Test Scores
Dependent/Response
Variable
(Continuous)
Example- Income
Independent /Predictor
Variable
(Categorical)
Factor : Study Period
Independent /Predictor
Variable
(Continuous)
Example : Age

22. Summary : ANOVA Family
IV= Independent Variable,
DV=Dependent Variable
DV=1 DV>=2
Metric Metric
IV=1 Nonmetric One Way ANOVA One Way MANOVA
IV=2
Both Nonmetric Two way ANOVA Two Way MANOVA
Mixed-one
Metric(Covaraite)
& one Non-metric
One Way ANCOVA One Way MANCOVA
IV=3
All Nonmetric N-Way ANOVA N-Way MANOVA
Mixed -Two Non-
metric & one Metric
Two way ANCOVA Two way MANCOVA

23. THANK YOU