Analysis of Variance and its impact for statistical analysis

1. Analysis of Covariance (ANCOVA)
by
Dr Lalit Prasad

2. Outline
• What is ANCOVA?
• Assumptions
• An example : One Way ANCOVA

3. ANCOVA: Analysis Of Covariance
• “C” stands for ‘covariance’.
• Like ANOVA, ANCOVA has a single continuous
response variable.
• ANCOVA compares a response variable by both a
factor and a continuous independent variable.
• The continuous independent variable used in
ANCOVA is known as “covariate”

4. 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

5. Assumptions of ANCOVA
• The groups are independent to each other.
• Normality Distribution : The dependent variable must
be normally distributed within each subpopulation.
• Linearity: the relation between the covariate(s) and the
dependent variable must be linear.
• Homogeneity of regression slopes (interaction effect :
(factor variable*covariate) sig value>0.05): The b-
coefficient(s) for the covariate(s) must be equal among
all subpopulations.
• Homogeneity of Variance (Levene test -sig value >0.05):
The variance of the dependent variable must be equal
over all subpopulations.

6. Topic:
A study on covariating effect of Age between
diet types and weight gain

7. Objectives
• To study the age, diet types and weight
gain of the respondents.
• To study the covariating effect of age
between diet types and weight gain of the
respondents.

8. Hypotheses
Null Hypothesis: H0: There is no significant
difference of diet types on weight gain
with covariate “age” of the respondents.
Alternative Hypothesis: H1: There is a
significant difference of diet types on
weight with covariate “age” of the
respondents.

9. Data and Data Analysis

10. Reporting of Result (Output)
• The data collected for analysis holds all the
assumptions of ANCOVA.
• The significant value in ANCOVA table (Test of
between subjects) is 0.069>0.05, So it has sufficient
evidence as per the decision rule to accept the null
hypothesis. Hence, H0 i.e. Null Hypothesis is accepted.
• It means, there is no significant difference between diet
types and weight gain with covariate “age” of the
respondents.
• But, if we remove the covariate “age” and run One way
ANOVA, the significant value between diet types and
weight gain is 0.039<0.05 , which is significant. So
There is a significant difference between diet types and
weight gain if we do not control the covariate “Age”.

11. Thank You

12. Research Topics
• A study of gender (Male , Female) on academic scores of students in B-Schools of Pune
– Independent Sample t-test
• A study of attendance level (>75%, 60%-75%, less than 60%) on academic scores of
students in B-Schools of Pune-One Way ANOVA
• Interaction effect of attendance level (>75%, 60%-75%, less than 60%) and
educational background (BBA,BE,B COM, BA) on academic scores: An empirical
study in B-Schools of Pune –Two Way ANOVA
• A study of educational background on academic scores using covariate IQ score : An
empirical study in B-Schools of Pune : One Way ANCOVA
• Interaction effect of attendance level, educational background on academic scores
using covariate IQ score : An empirical study in B-Schools of Pune : Two Way
ANCOVA
• Interaction effect of Gender, attendance level, educational background on academic
scores : An empirical study in B-Schools of Pune: N -Way ANOVA
• Interaction effect of Gender, attendance level, educational background on academic
scores using covariate IQ score : An empirical study in B-Schools of Pune – N -Way
ANCOVA