Factor analysis Guide, Meaning , Facts, Information and Description

Factor analysis is a statistical technique that originated in mathematical psychology. It is used in the social sciences and in marketing, product management, operations research, and other applied sciences that deal with large quantities of data. The objective is to discover patterns among variations in the values of multiple variables. This is done by generating artificial dimensions (called factors) that correlate highly with the real variables.

Table of contents

1 Factor analysis in marketing 1.1 Information collection 1.2 Analysis 1.3 Advantages 1.4 Disadvantages 2 Factor analysis in psychometrics 2.5 History 2.6 Applications in psychology 2.7 Advantages 2.8 Disadvantages 2.9 Bibliography 2.10 See also

Factor analysis in marketing

The basic steps are:

• Identify the salient attributes consumers use to evaluate products in this category.
• Use quantitative marketing research techniques (such as surveys) to collect data from a sample of potential customers concerning their ratings of all the product attributes.
• Input the data into a statistical program and run the factor analysis procedure. The computer will yield a set of underlying attributes (or factors).
• Use these factors to construct perceptual maps and other product positioning devices.

Information collection

The data collection stage is usually done by marketing research professionals. Survey questions ask the respondant to rate a product from one to five (or 1 to 7, or 1 to 10) on a range of attributes. Anywhere from five to twenty attributes are chosen. They could include things like: ease of use, weight, accuracy, durability, colourfulness, price, or size. The attributes chosen will vary depending on the product being studied. The same question is asked about all the products in the study. The data for multiple products is codified and input into a statistical program such as SPSS or SAS.

Analysis

The analysis will isolate the underlying factors that explain the data. Factor analysis is an interdependence technique. The complete set of interdependent relationships are examined. There is no specification of either dependent variables, independent variables, or causality. Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions. This reduction is possible because the attributes are related. The rating given to any one attribute is partially the result of the influence of other attributes. The statistical algorithm deconstructs the rating (called a raw score) into its various components, and reconstructs the partial scores into underlying factor scores. The degree of correlation between the initial raw score and the final factor score is called a factor loading. There are two approaches to factor analysis: "principal component analysis" (the total variance in the data is considered); and "common factor analysis" (the common variance is considered).

The use of principle components in a semantic space can vary somewhat because the components may only "predict" but not "map" to the vector space. This produces a statistical principle component use where the most salient words or themes represent the preferred Basis

Advantages

• both objective and subjective attributes can be used
• it is fairly easy to do, inexpensive, and accurate
• it is based on direct inputs from customers
• there is flexibilty in naming and using dimensions

Disadvantages

• usefulness depends on the researchers ability to develop a complete and accurate set of product attributes - If important attributes are missed the procedure is valueless.
• naming of the factors can be difficult - multiple attributes can be highly correlated with no appearent reason.
• factor analysis will always produce a pattern between variables, no matter how random.

Factor analysis in psychometrics

History

Charles Spearman pioneered the use of factor analysis in the field of psychology, measuring the intelligence of children in a village school. During his testing, he discovered a high correlation between all scores on the tests. Spearman believed that the empirically observed correlation was less than the true correlation between two test participants. Using a correctional formula devised from knowledge of the degree of the unreliability of the observed factors, he discovered a perfect correlation between all kinds of intelligence. This lead to the postulation of a general intelligence, or g, that is innate in all humans. Spearman went on to test the theory of specialized intelligence, or s. S, supposedly, deals with specific areas, such as logic or verbal ability. According to his theory, all tasks require some use of g and an s factor, so it could be concluded that someone with a high g will perform well on another test for g.

Raymond Cattell expanded on Spearman’s idea of a two-factor theory of intelligence after performing his own tests and factor analysis. He used a multi-factor theory to explain intelligence. Cattell’s theory addressed alternate factors in intellectual development, including motivation and psychology. Cattell also developed several mathematical methods for adjusting psychometric graphs, such as his "scree" test and similarity coefficients. His research lead to the development of his theory of crystallized and fluid intelligence, in which crystallized is a set memory and reflexive actions, and fluid is the ability for a person to adjust or reason (think on their feet). Cattell was a strong advocate of factor analysis and psychometrics. He believed that all theory should be derived from research, which supports the continued use of empirical observation and objective testing to study human intelligence. All of their research, of course, is based on the idea that intelligence is measureable.

Applications in psychology

Factor analysis has been used in the study of human intelligence as a method for comparing the outcomes of (hopefully) objective tests and to construct matrices to define correlations between these outcomes, as well as finding the factors for these results. The field of psychology that measures human intelligence using quantitative testing in this way is known as psychometrics (psycho=mental, metrics=measurement).

Advantages

• Offers a much more objective method of testing intelligence in humans
• Allows for a satisfactory comparison between the results of intelligence tests
• Provides support for theories that would be difficult to prove otherwise

Disadvantages

• "...each orientation is equally acceptable mathematically. But different factorial theories proved to differ as much in terms of the orientations of factorial axes for a given solution as in terms of anything else, so that model fitting did not prove to be useful in distinguishing among theories." (Sternberg, 1977). This means that even though all rotations are mathematically equal, they all come up with different results, and it is impossible to judge the proper rotation.
• "[Raymond Cattell] believed that factor analysis was 'a tool that could be applied to the study of behavior and ... might yield results with an objectivity and reliability rivaling those of the physical sciences (Stills, p. 114).'" [1] In other words, one’s gathering of data would have to be perfect and unbiased, which will probably never happen.
• Interpreting factor analysis is based on using a “heuristic”, which is a solution that is "convenient even if not absolutely true" (Richard B. Darlington). More than one interpretation can be made of the same data factored the same way.

Bibliography

• Charles Spearman. Retrieved July 22, 2004, from http://www.indiana.edu/~intell/spearman.shtml
• Factor Analysis. (2004). Retrieved July 22, 2004, from http://comp9.psych.cornell.edu/Darlington/factor.htm
• Factor Analysis. Retrieved July 23, 2004, from http://www2.chass.ncsu.edu/garson/pa765/factor.htm
• Raymond Cattell. Retrieved July 22, 2004, from http://www.indiana.edu/~intell/rcattell.shtml
• Sternberg, R.J.(1990). The geographic metaphor. In R.J. Sternberg, Metaphors of mind: Conceptions of the nature of intelligence (pp.85-111). New York: Cambridge.
• Stills, D.L. (Ed.). (1989). International encyclopedia of the social sciences: Biographical supplement (Vol. 18). New York: Macmillan.

See also

• product positioning
• perceptual mapping
• marketing research
• product management
• list of marketing topics
• Recomendation system

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