4. Write short note on the following
a) Factor loading and factor analysis
FACTOR ANALYSIS
Factor analysis is a generic name given to a class of techniques whose purpose is data reduction and summarization. Very often market researchers are overwhelmed by the plethora of data. Factor analysis comes to their rescue in reducing the number of variables. Factor analysis does not entail partitioning the data matrix into criterion and predictor subsets; rather interest is centred on relationships involving the whole set of variables. In factor analysis:
The analyst is interested in examining the "strength" of the overall association among variables. The sense that he would like to account for this association in terms of a smaller set of linear composites of the original variables that preserve most of the information in the full data set. Often his interest will emphasize description of the data rather than statistical inference. No attempt is made to divide the variables into criterion versus prediction sets. The models are primarily based on linear relationships.
Factor analysis is a "search" technique. The researcher-decision maker does not typically have a clear priori structure of the number of factors to be identified. Cut off points with respect to stopping rules for the analysis is often ad hoc as the output becomes available. Even where the procedures and rules are stipulated in advance, the results are more descriptive than inferential.
The procedure involved in computation of factor analysis is extremely complicated and cannot be carried out effectively without the help of computer. Packages like SPSS , SAS and Biomedical programs (BMD) can be used to analyse various combinations leading to factor reduction. We will make an attempt to conceptualise the scenario of factor analysis with emphasis on the interpretation of figures.
The term "factor analysis" embraces a variety of techniques. Our discussion focuses on one procedure: principal component analysis and the factors derived from the analysis are expressed as linear equations. These linear equations are of the form
The factors are derived, and each variable appears in each equation. The a-co-efficients indicate the importance of each variable with respect to a particular factor. Co-efficient of zero indicating the variable is of no significance for the factor. In principal component analysis, the factors are derived sequentially, using criteria of maximum reduction in variance and non-correlation among factors.
b. Different types of experimental design
Experiments are much more effective than descriptive techniques in establishing the casual relationships. First, the units to be studied are selected by the researcher and each unit is assigned to the group determined by the researcher. The units do not select their groups, thus avoiding the self-selection bias. Second, a necessary consequence of the first, the researcher administers the predetermined treatment or treatments to the units with in each group.
The use of a control group is almost mandatory in experimental designs. The inclusion of a control group permits a better isolation of the treatment component through a proper design like a simple cross sectional design.
A major contribution that the statisticians have made to experimental design is the development of randomization concept which enables the researcher to reduce the effect of the uncontrolled variables on comparative measures of response to the variables that are under the experimenter's control. Randomization is a useful device for ensuring on the average, that uncontrolled variables do not favour one treatment versus others.
· Completely Randomized Design
· Randomized Complete Block Design
· Latin Square
· Factorial Design
· Analysis. of Covariance
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