Factor Analysis

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Factor analysis is a general name denoting a class of procedures primarily used for data reduction and summarization. It is used in the following circumstances: •To identify underlying dimensions or factors, that explains the correlations among the set of variables. •To identify new, smaller set of uncorrelated variables to replace the original set of correlated variables in subsequent multivariate analysis. •To identify smaller set of salient variables from a larger set for use in subsequent multivariate analysis. In our research, we are using factor analysis to find out a smaller set of uncorrelated factors to replace the original correlated variables like fear of side effects, packaging, brand image, quality, availability, ingredients, promotion, income group, frequency of purchase, color cosmetics, peer influence, price, fragrance, brand loyalty, age. . We have in all 15 independent variables. We are doing principal component analysis to determine the minimum number of factors that will account for maximum variance in the data for use in the subsequent multi variant analysis.

KMO and Bartlett’s test of sphericity
Bartlett’s test of sphericity can be used to test the null hypothesis that the variables are uncorrelated in the population or the population correlation matrix is an identity matrix .The test statistics for sphericity is base in a Chi square transformation of the determinant of the correlation matrix. A large value of test statistic will favor the rejection of null hypothesis and hence will favor factor analysis. Its significance value should be less than 0.005 to favor Factor analysis. The KMO statistic measures sampling adequacy .This index compares the magnitudes of the observed correlation coefficients to the magnitudes of partial correlation coefficients. Small values of the KMO statistic indicate that the correlations between the pair of variable s cannot be explained by other variables and that factor analysis may not...
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