## Sunday, 4 September 2011

### Factor analysis

Factor analysis was invented nearly 100 years ago by psychologist Charles Spearman, who hypothesized that the enormous variety of tests of mental ability--measures of mathematical skill, vocabulary, other verbal skills, artistic skills, logical reasoning ability, etc.--could all be explained by one underlying "factor" of general intelligence that he called g. He hypothesized that if g could be measured and you could select a sub population of people with the same score on g, in that subpopulation you would find no correlations among any tests of mental ability. In other words, he hypothesized that g was the only factor common to all those measures.

It was an interesting idea, but it turned out to be wrong. Today the College Board testing service operates a system based on the idea that there are at least three important factors of mental ability--verbal, mathematical, and logical abilities--and most psychologists agree that many other factors could be identified as well.

Factor analysis is a multivariate statistical technique that is concerned with the identification of structure within a set of observed variables.  It’s  appropriate use  involves  the  study  of  interrelationships  among variables  in  an effort to  find a new  set  of  variables, fewer  in  number  than  the  original  variables,  which express  that  which  is  common  among  the  original variables.

Factor analysis is used to study the patterns of relationship among many dependent variables, with the goal of discovering something about the nature of the independent variables that affect them, even though those independent variables were not measured directly. Thus answers obtained by factor analysis are necessarily more hypothetical and tentative than is true when independent variables are observed directly. The inferred independent variables are called factors. A typical factor analysis suggests answers to four major questions:

1. How many different factors are needed to explain the pattern of relationships among these variables?
2. What is the nature of those factors?
3. How well do the hypothesized factors explain the observed data?
4. How much purely random or unique variance does each observed variable include?

Factor analysis is a means by which the regularity and order in phenomena can be discerned. As phenomena co-occur in space or in time, they are patterned; as these co-occurring phenomena are independent of each other, there are a number of distinct patterns. Patterned phenomena are the essence of workaday concepts such as "table," "chair," and "house," and--at a less trivial level--patterns structure our scientific theories and hypotheses. We associate a pattern of attitudes, for example, with businessmen and another pattern with farmers. "Economic development" assumes a pattern of characteristics, as does the concept of "communist political system." The notion of conflict itself embodies a pattern of elements, i.e., two or more parties and a perception of mutually exclusive or contradictory values or goals. And to mention phenomena that everyone talks about, weather also has its patterns.

Types of Factor Analysis:

1. Exploratory: It is exploratory when you do not have a pre-defined idea of the structure or how many dimensions are in a set of variables.
2. Confirmatory: It is confirmatory when you want to test specific hypothesis about the structure or the number of dimensions underlying a set of variables (i.e. in your data you may think there are two dimensions and you want to verify that).

Importance of Factor Analysis in Marketing:

Factor analysis in marketing is important because it reflects the perception of the buyer of the product. By testing variables, it is possible for marketing professionals to determine what is important to the customers of the product. For example, if a product is only available in black and the sales reach \$150,000 in one year, but when the company adds colour options of red, blue and silver, and sales reach \$300,000, then the company can conclude through factor analysis that colour options are important to the customers of the product. Ultimately, it is imperative to use factor analysis in marketing to create the ideal product for customers, which in turn, increases the sales of the product.

Generally, companies test variables with factor analysis in marketing using tools such as focus groups and surveys. Since making changes to the product itself in order to test variables can be expensive, surveys and focus groups allows companies to gather pertinent information without increasing the cost to manufacture the product. Focus groups and surveys allow companies to gather perceptual information from current and potential customers of the product. This information is important because it allows the company to see the product from the vantage point of the customers and determine which factors in marketing are the most important to the customers. For example, a focus group may see four different package versions of a product and then ask the focus group participants to choose which package they like best and explain why. Companies can use this information to alter product packaging to attract more customers and sell more products.

Group : Marketing 5
Author : Krupa Vijura
Roll no: 13083