# Principal Component Analysis and Factor Analysis: How much are they similar?

Principal Component Analysis

Principal Component analysis is the procedure that helps in the identification of a smaller number of uncorrelated variables. These are called the principal components and are derived from a large set of data. The purpose of principal component analysis is to further explain the maximum amount of variance with the fewest number of principal components. It is mostly found getting used in the field of social sciences, market research and other industries that have been using large data sets.

This type of analysis is commonly seen getting used as a single step in the series of analysis. It is seen getting used by researchers to bring down the number of variables and put off multi collinearity or when there are too many predictors relative to the number of observations that are there.

Factor Analysis

It is the method that helps in explaining the structure of the data and explains the correlations between the variables. It the technique that helps to summarize the data into fewer dimensions and condenses the large number of variables into a smaller set of latent variables or so called factors. The areas of research where it is commonly seen getting used are market research, social sciences and various other industries that have been seen using large data sets.

Both the techniques, principal component analysis and Factor Analysis have similar traits because both of them have been seen getting used for simplification of the structure of a set of variables.

There are certain differences in the analysis which can be briefly understood in this way:

1. When using Minitab, only raw data can be entered in the case of PCA. However, the case of Factor Analysis, raw data, correlation covariance or the loadings from the previous analysis can be added.
2. When we talk of principal component analysis , the calculations would be as linear combinations of the original variables under study while in the case of Factor Analysis, the original variables are seen to be defined as linear combinations of the factors.
3. When we try and distinguish the two on the basis of the goal, the goal of PCA is to explain the total variance in the variables as possible. The goal of Factor Analysis is to explain the covariance between the variables