factor analysis

# factor analysis - Factor analysis is a statistical data...

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Factor analysis is a statistical data reduction and analysis technique that strives to explain correlations among multiple outcomes as the result of one or more underlying explanations, or factors. The technique involves data reduction. Factor analysis attempts to discover the unexplained factors that influence the co-variation among multiple observations. These factors represent underlying concepts that cannot be adequately measured by a single variable. Factor analysis is especially popular in survey research psychological, mathematical, and economic---where there appear to be dozens or even hundreds of variables affecting operations. By analyzing and studying the variables statistically, factor analysis can separate out a few core variables, known as factors, in which the responses to each question represent an outcome. Because multiple questions often are related, underlying factors. Interdependency Technique Seeks to find the latent factors that account for the patterns of co linearity among multiple metric variables Reduction of number of variables, by combining two or more variables into a single factor. For example, performance at running, ball throwing, batting, jumping and weight lifting could be combined into a single factor such as general athletic ability. Usually, in an item by people matrix, factors are selected by grouping related items. In the Q factor analysis technique, the matrix is transposed and factors are created by grouping related people: For example, liberals, libertarians, conservatives and socialists, could form separate groups. Why factor analysis is used? Factor analysis originated in psychometrics, and is used in behavioral sciences, social sciences , marketing , product management , operations research , and other applied sciences that deal with large quantities of data. for example, that variations in three or four observed variables mainly reflect the variations in a single unobserved variable, or in a reduced number of unobserved variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modeled as linear combinations of the potential factors. Example is a fictionalized simplification for expository purposes, and should not be taken as being realistic. Suppose a psychologist proposes a theory that there are two kinds of intelligence, "verbal intelligence" and "mathematical intelligence", neither of which is directly observed. Evidence for the theory is sought in the examination scores from each of 10 different academic fields of 1000 students. If each student is chosen randomly from a large population, then each student's 10 scores are random variables. The psychologist's theory may say that for each of the 10 academic fields, the score averaged over the group of all students who share some common pair of values for verbal and mathematical "intelligences" is some constant times their level of verbal intelligence plus another constant times their level of mathematical intelligence, i.e., it is a linear combination of those two "factors". The numbers for a

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