A Bootstrap procedure to test the cograduation between two ordinal scales: a proposal of two new indices

In psychometric sciences the choice of a good response scale is a typical problem. Several studies (see, in particular, Bonanomi, 2004) proved that different measurement scales lead to highly dissimilar evaluations of goods/services, in particular in the measurement of observable variables in latent variables models. So, this requires that proper cograduation indices should be available, in order to compare the attitude of different measurement scales (typically ordinal scales) in assigning the various and different number of allowed response modalities.