How is the Sociomap formed from the data?
Distances between individuals on the Sociomap are derived from the mutual similarities of their profiles. Then the matrix of distances between individuals is created and used for calculating positions of individuals on the Sociomap.
Positions on the Sociomap
Positions of individuals (team members) on the Sociomap correspond to the similarities of their profiles in test characteristics. Those individuals whose profiles are similar are placed close to each other while those individuals whose profiles differ greatly are placed apart. The individuals whose profiles are mostly similar to the profiles of others are located in the middle of the Sociomap. On the periphery of the Sociomap, you can find the individuals whose profiles deviates the most from the other team members.
The distance of the profiles of these two individuals can be calculated in various ways. One of the most frequently used is City Block. In TPA we use another method (so called P-values) that is based on the City Block method but improves it with probability computations.
Example
In this example, the profiles of two individuals are analyzed for four test characteristics. We will mark the scores of the first individual as X and the scores of the other individual as Y. For each characteristic, we can establish the differences between their scores (percentiles) using the City Block distance calculation.
City Block (Manhattan) distance
This is a method of calculating the distance between two profiles as a sum of differences in scores for the individual test characteristics.
Example:
d= 55 + 54 + 38 + 41 = 188
The distance between individuals X and Y is therefore 188. For each set of individuals, this distance is computed and the distances are then converted to distances on the Sociomap.
For calculating distances, TPA uses a unique P-values method, which operates with a probability function and is able to establish the customariness/exceptionality of profile distances between two individuals. This enables us to test statistically in which characteristics a given group significantly differs from the population, and also differences between groups.
P-value method
In TPA, the distance between profiles of two individuals is expressed by the above mentioned P-values. This value states the probability that in the population distribution, the difference in two random variable realizations of X will be at least as high as the difference between individuals measured by the City Block metric function. The range of P-values is from 0 to 1. The higher the P-values, the more probable it is that there is a difference from the general population. The lower the P-value is the less probable it is that there is a difference from the general population.
The following graphs show the cumulative distribution function of differences between two profiles of n-dimensions.
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