#### Psychometric properties of the ComColors questionnaire

The statistical validation of the ComColors questionnaire was carried out under the supervision of a Doctor of Psychology who applied current psychometric methodology using the most up-to-date tools available at the time (2012).

The first step was to create a questionnaire that allowed for an exploratory factor analysis. This work measured the psychological dimensions of the six personality types of the ComColors model. In order to proceed, a first series of questions was created and tested on a group of approximately 130 people. This allowed us to separate reliable psychological dimensions from those that did not lead to accurate measures. We repeated this procedure four times to arrive at a clear measure of the psychological dimensions we were trying to examine.

Table 1 is the result of the final exploratory factor analysis, showing, as expected, that the items of one colour (blue, for example) are heavily saturated with only one factor, and very slightly saturated with the factors of the other colours.

Table 1. Result of the principal component analysis with varimax rotation

(B = blue; J = yellow; O = orange; R = red; Ve = green; Vi = purple)

After we completed this last exploratory factor analysis, we proceeded with a more profound validation of the structure of the questionnaire by conducting a confirmatory factor analysis on 352 participants.

A confirmatory factor analysis (CFA) is a statistical technique that is an extension of an exploratory factor analysis. The goal of a confirmatory factor analysis is to test the solidity of the theoretical model that appeared in the exploratory analysis. A confirmatory factor analysis is therefore a more advanced step in the research process than an exploratory factor analysis.

Figure 1. Structural model

The point of the confirmatory analysis is to confirm that the theoretical model is the same as the observed model. In order to verify this similarity, indicators are calculated to measure the goodness of fit between the theoretical model and the observed model. The first indicator to consider is χ^{2 }because it allows us to calculate the spread between the observed covariance matrix and the estimated covariance matrix. If the ideal is to accept the null hypothesis, this test is problematic because it depends on the sample size and on the number of parameters of the tested model. In order to avoid these distortions, the interpretation of different indicators aims to obtain a better estimation of the goodness of fit. In this research, we retained a certain number of indicators of good fit that are widely accepted as measures of quality of the observed model.

The Comparative Fit Index and the Tucker-Lewis Index are indicators based on the spread of the independence model. These indicators examine the difference between the chi^{2} of the tested model and the chi^{2} of the theoretical model. Their value may range from 0 to 1 with values of at least .90 indicating good fit.

The Root Mean Square Error of Approximation allows us to evaluate the standardized deviation between the observed matrix and the estimated matrix. The authors consider that a value equal to or lower than .06 is indicative of good fit.

A final indicative category focuses on the explained variance. The Standardized Root Mean Residual is the square root of the average of the sum of the squares of the remainders of each cell in the matrix. The authors consider that a value equal to or less than .05 is the sign of good fit.

The Goodness of Fit Index allows us to take into account the variation of the observed matrix on which the model is based. This value may range from 0 to 1 with values of at least .90 indicating good fit.

Indicators |
χ^{2} |
p |
df |
RMSEA |
GFI |
TLI |
CFI |
SRMR |

COMCOLORS model | 467.2 | <.001 | 259 | .059 | .91 | .92 | .93 | .048 |

Table 2. Indicators of good fit

As we can see in Table 2, all of the indicators of good fit are equal to or better than the recommended figures. It is therefore justified to say that the model adjusts correctly to the data and can be considered as structurally valid.