Factor analysis is a statistical technique used to reduce a large set of variables into a smaller set of underlying factors or dimensions. It examines the interrelationships among variables to define common dimensions called factors that can help explain correlations. Factor analysis is used to identify the underlying structure in a data set and reduce many variables into a smaller number of factors for subsequent analysis like regression or discriminant analysis.

1. FACTOR ANALYSIS

2. FACTOR ANALYSIS
 A data reduction technique designed to represent
a wide range of attributes on a smaller number of
dimensions.
DEFINITION
“ 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)”

3. What is factor analysis ?
 Factor analysis is a general name denoting a class of
Procedures primarily used for data reduction and
summarization.
 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.

4. 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.

5. Types of FA
 Exploratory FA
 Summarizing data by grouping correlated variables
 Investigating sets of measured variables related to
theoretical constructs
 Usually done near the onset of research

6. Types of FA
 Confirmatory FA
 More advanced technique
 When factor structure is known or at least theorized
 Testing generalization of factor structure to new
data, etc.

7. Assumptions
 Models are usually based on linear relationships
 Models assume that the data collected are interval scaled
 Multicollinearity 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.

8. SAMPLE SIZE
 Minimum numbers of variable for FA is 5 cases
per variable
 e.g. 20 variables should have>100 cases(1:5)
IDEAL CONDITION

9. A few examples
We can now take few examples
with hypothetical data and run
factor analysis using SPSS package.

10. How to RuN on spss