# Factor Analysis

Typical Problem Studied with factor analysis: Factor analysis is typically used to study a complex product or service in order to identify the major characteristics (or “factors”) considered to be important by consumers of the product or service. For example researchers for an automobile company may ask a large sample of potential buyers to report (using a 7 – or 10 – or 11 – point scale) the extent of their agreement or disagreement with a number of statements such as “The side profile of a car should be sleek,” and “A car’s brakes are its most critical part.” Researchers apply factor analysis to such a set of data to identify which factors such as “safety”, “exterior styling,” “Interior roominess” or “economy of operation” are considered important by potential buyers. Once this information is available, it can be used to guide the overall characteristics to be designed into the product or to identify advertising themes that potential buyers would consider important.

What Factor Analysis Does: Using data from a large sample, factor analysis applies an advanced form of correlation analysis to the responses to a number of statements. The purpose of this analysis is to determine if the responses to several of the statements are highly correlated. If the responses to three or more statements are highly correlated, it is believed that the statements measure some factor common to all of them. Since such studies usually involve many statements, there are likely to be several sets of such correlated statements. The statements in any one set are highly correlated with each other but are not highly correlated with the statements in any of the other sets.

For each such set of highly correlated statements, the researchers use their own judgment to determine what the single “theme” or “factor” is that ties the statements together in the minds of the respondents. For example, regarding the automobile study mentioned above, researchers may find high correlations among the responses to the following three statements: A car’s brakes are its most critical part; I want my next car to be equipped with an “air bag”; a collapsible steering column should be standard equipment on all new cars. Researchers may then make the judgment that agreement with the set of statements indicates an underlying concern with the factor of “safety”.

Types of Variables used in Factor analysis: Factor analysis can only be applied to continuous variables or interval scaled variables.

Factor Analysis Identifies Interdependencies among variables: Factor analysis like cluster, uses more than one variable to identify a class or a category (e.g. “safety” “economy of operation”) that is important from a marketing stand point. Recall that cluster analysis identifies respondents who gave the same answers to a number of questions. Factor analysis identifies two or more questions that result in sets of responses that are highly correlated. In these ways, both methods look for interdependencies or inter-relationships among the data, and so are different from the four methods of analysis listed in the top half. An awareness of this characteristic can help the reader better understand when to use factor analysis rather than some other method.

An Example of factor analysis Application: A manufacturer of compact automobiles wanted to know which automobile characteristics (or “factors”) were considered very important by compact car buyers. To study this topic, the company prepared 100 statements that related to all characteristics of automobiles that they believed were important. Three hundred potential buyers of compact cars were selected on a probability basis and were asked to read the 100 statements, five of which are listed below. They were then asked to report on a seven point scale the extent to which they agreed or disagreed with each statement.

The side profile of a compact car should be sleek. A compact car’s brakes are its most critical part. Interior appointments in a compact car should be attractive. Four adults should be able to sit comfortably in a compact car. Gasoline mileage in a compact car should be at least 30 miles per gallon.

This resulted in a set of data in which each of 300 individuals gave a response to each of 100 statements. For any given statement, some individuals were found to agree strongly, some were found to disagree slightly, some neither agreed nor disagreed with the statement and so on. Thus, for each statement, there was a distribution of 300 responses on a seven point scale, and there were 100 such distributions, one for each of the 100 statements.

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