Principal Component Analysis versus Factor Analysis

Unfortunately, principal components are often confused with factors, and the two terms and related methods are sometimes used as synonyms, although the mathematical background and goals of the two methods are really different.

PCA is used to reduce the number of variables by creating principal components that then can be used in further projects instead of the original variables. This means that we try to extract the essence of the dataset in the means of artificially created variables, which best describe the variance of the data:

FA is the other way around, as it tries to identify unknown, latent variables to explain the original data. In plain English, we use the manifest variables from our empirical dataset to guess the internal structure of the data: