Factor Analysis and KMO Bartlett’s Test

Factor Analysis is one of the most frequently used data reduction technique. There are three main reasons why this technique is used in research. The first reason for using factor analysis is to bring down the number of variables from big to small. Bring about in setting up underlying reasons and factors between the measured variables and their constructs and the third main reason is to provide the construct validity evidence.

There is more than one type of factor analysis. The two types are, Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA).  The main difference between the two is that EFA is being used when the concerned study does not have any basis of pre conceived theories. On the contrary, CFA is conducted when the study is being done to only either confirm or reject an already existing proposed theory.

One very important aspect of factor analysis is the KMO & Bartlett’s Test of Sphercity. It is a measure to check the sampling adequacy which is suggested to check the case to variable ratio for the different analysis to be conducted. In most of the studies pertaining to academic and business arena, it plays an important role on the acceptance of the sample adequacy. The range of the KMO falls between 0 to 1; the accepted index globally is 0.6. To recommend the suitability of the Factor Analysis, the Bartlett’s  Test of Sphercity has to be less than 0.05.

Another component without which the explanation of Factor Analysis would go incomplete is the Rotated Component Matrix. It aids in deciding whether a variable might relate to more than one factor. Rotation maximizes the loading of high items and minimizes the low item loading. It helps in producing more interpretable and simplified solution. The most commonly used rotation techniques are orthogonal rotation and oblique rotation. On one side the orthogonal varimax rotation technique produces the analysis that is uncorrelated the oblique varimax produces correlated factors. Despite the rotation method that is implemented, the key objective is to offer a better and easier interpretation of the results and give a more comprehensive and parsimonious solution.