PCA and cluster analysis were performed for the friction parameters of powder cosmetics using SPSS 25.0 Base System software (IBM, New York, USA) . These analyses were performed after each friction parameter was standardized using Eq. (3) :
where z is the standardized variate of the friction parameter, x i is the individual datum, x ̅ is the mean value, and σ is the standard deviation. PCA was performed using a correlation matrix. The similarity among objects used for the cluster analysis was calculated using squared Euclidean distance metrics, while Ward s method was used to measure the distance between clusters.
where z is the standardized variate of the friction parameter, x i is the individual datum, x ̅ is the mean value, and σ is the standard deviation. PCA was performed using a correlation matrix. The similarity among objects used for the cluster analysis was calculated using squared Euclidean distance metrics, while Ward s method was used to measure the distance between clusters.