Typicality tests consist in comparing the observations of a group with the ones of a reference population of which the group may or may not be a subset. Two test statistics are studied: 1) the Mahalanobis distance between points with respect to the covariance structure of the reference cloud; 2) the variance of cloud.

• Multidimensional Case (Euclidean Clouds) see pp 55–59.
  • "Target example": reference data set (Target_reference.txt) et group dataset (Target_group.txt)
  • Script R: Combinatorial_Typicality.R
• One-dimensional case (numerical variable)
  The previous R script applied to a one-dimensional cloud performs the test with the squared calibrated deviation between means as test statistic; it does not provide the directional test based on the deviation between means.

The geometric typicality test consists in comparing the mean point of a Euclidean cloud to a reference point by taking the squared Mahalanobis distance between points as a test statistic. This test can be applied to a design with two repeated measures, the basic dataset being the individual differences.

• Multidimensional Case (Euclidean clouds)
  • "Target example": Target.txt
  • R Script (see pp. 97–101): Geometric_Typicality.R
• One-dimensional case (numerical variable)
  The previous R script applied to a one-dimensional cloud provides the results corresponding to a test with the calibrated deviation between the group mean and the reference mean as test statistic.
• The case of a design with two repeated measures
      Student's Example: Student.txt

The homogeneity tests presented in this chapter consist in comparing several subclouds by taking the M-variance between the mean points of subclouds as a test statistic, that is, the variance calculated from the Mahalanobis distance between points. We study the case of several independent groups and the one of repeated measures. In the case of several independent groups, several permutation groups are studied depending on whether the comparison is global, partial or specific (see pp. 109–110).

• The R script (Homogeneity.R) presented on pages 142–147 computes the p-value and the compatibility region in the case of the partial or specific comparison of two independent groups.
• The dataset of page 142 is Target_4.txt.