The determination of the appropriate number of factors is a difficult problem in PCA. Various approaches are possible, it does not really exist a state-of-art method. The only way to proceed is to try different approaches in order to obtain a clear indication about the good solution. We had shown how to program them under R in a recent paper . These techniques are now incorporated into

**Tanagra 1.4.45**. We have also added the KMO index (Measure of Sampling Adequacy – MSA) and the Bartlett's test of sphericity in the Principal Component Analysis tool.

In this tutorial, we present these new features incorporated into Tanagra on a realistic example. To check our implementation, we compare our results with those of SAS PROC FACTOR when the equivalent is available.

**Keywords**: principal component analysis, pca, sas, proc princomp, proc factor, bartlett's test of sphericity, R software, scree plot, cattell, kaiser-guttman, karlis saporta spinaki, broken stick approach, parallel analysis, randomization, bootstrap, correlation, partial correlation, varimax, factor rotation, variable clustering, msa, kmo index, correlation circle

**Components**: PRINCIPAL COMPONENT ANALYSIS, CORRELATION SCATTERPLOT, PARALLEL ANALYSIS, BOOTSTRAP EIGENVALUES, FACTOR ROTATION, SCATTERPLOT, VARHCA

**Tutorial**: en_Tanagra_PCA_New_Tools.pdf

**Dataset**: beer_pca.xls

**References**:

Tanagra - "Principal Component Analysis (PCA)"

Tanagra - "VARIMAX rotation in Principal Component Analysis"

Tanagra - "PCA using R - KMO index and Bartlett's test"

Tanagra - "Choosing the number of components in PCA"