FACTOR ANALYSIS AND ANOVA
A data reduction technique designed to represent
a wide range of attributes on a smaller number of
“ A statistical approach that can be used to analyze
interrelationship among a large number of
variables and a explain these variables in terms
of their common underlying dimension(factor).”
What is Factor Analysis ?
Factor analysis is a general name denoting a class of
Procedures primarily used for data reduction and
Variables are not classified as either dependent or
independent. Instead, the whole set of interdependent
relationships among variables is examined in order to
define a set of common dimensions called Factors.
Purpose of Factor Analysis
To identify underlying dimensions called Factors, that explain
the correlations among a set of variables.
lifestyle statements may be used to measure the
psychographic profile of consumers.
To identify a new, smaller set of uncorrelated variables to
replace the original set of correlated variables for subsequent
analysis such as Regression or Discriminant Analysis.
psychographic factors may be used as independent
variables to explain the difference between loyal and
non loyal customers.
Types of Factor Analysis
Exploratory Factor Analysis
Summarizing data by grouping correlated variables
Investigating sets of measured variables related to
Usually done near the onset of research
Types of Factor Analysis
Confirmatory Factor Analysis
More advanced technique
When factor structure is known or at least
Testing generalization of factor structure to new
Models are usually based on linear relationships
Models assume that the data collected are interval scaled
Multi collinearity in the data is desirable because the objective is to
identify interrelated set of variables.
The data should be amenable for factor analysis. It should not be
such that a variable is only correlated with itself and no correlation
exists with any other variables. This is like an Identity Matrix.
Factor analysis cannot be done on such data.
• ANOVA is an abbreviation for the full name of the method: Analysis Of
Invented by R.A. Fisher in the 1920’s.
• ANOVA is used to test the significance of the difference between more
than two sample means and to make inferences about whether our
samples are drawn from population having same means.
ANOVA is comparison of means. Each possible value of a
factor or combination of factor is a treatment.
The ANOVA is a powerful and common statistical
procedure in the social sciences. It can handle a variety of
Why ANOVA instead of multiple ttests?
If you are comparing means between more than two
groups, why not just do several two sample t-tests to
compare the mean from one group with the mean from each
of the other groups?
Before ANOVA, this was the only option available to
compare means between more than two groups.
The problem with the multiple t-tests approach is that as the
number of groups increases, the number of two sample ttests also increases.
As the number of tests increases the probability of making
a Type I error also increases.
ANALYSIS OF HYPOTHESIS:ASSUMPTONS
We assume independent random sampling from
each of the r populations
We assume that the r populations under study:
– are normally distributed,
– with means i that may or may not be equal,
– but with equal variances, i2.
The Null hypothesis for ANOVA is that the
means for all groups are equal:
The Alternative hypothesis for ANOVA is that at
least two of the means are not equal.
The test statistic for ANOVA is ANOVA Fstatistic.
APPLICATION OF ANNOVA
ANOVA is designed to detect differences among
means from populations subject to different treatments.
ANOVA is a joint test.
The equality of several population means is tested
simultaneously or jointly.
ANOVA tests for the equality of several population
means by looking at two estimators of the population
variance (hence, analysis of variance).
APPLICATION OF ANNOVA IN
Product testing, ad copy testing and concept testing are
some common applications, though ANOVA Analysis
Surveys can be used in retail environments or simulated
We can manipulate certain variables (like promotion, ad
copy, display at the point of purchase), and observe changes
in other variables (like sales, or consumer preferences,
behavior or attitude). The application areas for experiments
are wide .
OTHER ANNOVA PROCEDURES
One-way ANOVA is Analysis of Variance for one factor.
More than one factor can be used for a two, three or four-
A continuous variable can be added to the model – this is
Analysis of Covariance (ANCOVA).
Repeated Measures ANOVA can handle replicated
measurements on the same observation unit (subject).
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