Bartlett's sphericity

Provides users with insights on the suitability of their dataset for principal component analysis (PCA).

This sub-tab within the PCA Analysis results panel shows outputs from two statistical tests that help assess if your data is suitable for Principal Component Analysis.

Bartlett's Test of Sphericity

Bartlett's Test of Sphericity

• Purpose: Tests the hypothesis that your variables are uncorrelated in the population (i.e., the correlation matrix is an identity matrix). If variables are uncorrelated, PCA is not very useful.

• Output:

  • $chisq: The test statistic value.

  • $p.value: The significance level (p-value) of the test.

  • $df: Degrees of freedom.

• Interpretation: You generally want to reject the null hypothesis. A significant p-value (typically < 0.05) indicates that the correlation matrix is significantly different from an identity matrix, meaning there are correlations between your variables, and PCA is likely appropriate. If the p-value is > 0.05, PCA might not be the best technique for your data.

Kaiser-Meyer-Olkin (KMO)

Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy

• Purpose: Measures the proportion of variance in your variables that might be common variance (i.e., shared with other variables). It assesses if the variables are suitable for factor analysis or PCA.

• Output:

  • $overall: The overall KMO index for the dataset.

  • $report: A qualitative interpretation of the overall KMO score.

  • $individual: (Optional, might be shown) KMO values for each individual variable.

• Interpretation:

  • KMO values range from 0 to 1.

  • Values closer to 1 are better, indicating that patterns of correlation are relatively compact, and PCA should yield distinct and reliable components.

  • A common guideline suggests a minimum overall KMO value of 0.6. Values below 0.5 are generally considered unacceptable.