Internal Validity

The high Cronbach’s alpha scores show the reliability of the BFI but what they do not show is the internal validity. Although many researchers infer a unidimensional construct from high alpha scores this is not correct because a scale can be multidimensional and

still have high alpha scores because of the sheer number of items. For assessing validity, a factor analysis with varimax rotation was applied.

Because the BFI should assess the personality of the participants within the FFM a factor analysis should extract those five factors from the gathered data. The extraction of the factors is also called variable reduction because several similar variables (in this case the items of the BFI) are reduced to new and from each other distinctly different variable constructs (factors). The factor analysis is a highly complex mathematical procedure. The explanation of this procedure would exceed the extent of this work. Thus, each step will only be described briefly. In a first step the metrical scores of the items are transformed to standardized Z-scores. Next the standardized scores are analyzed on their correlation to each other and those bivariate correlation coefficients are put into a correlations matrix.

In a third step the eigenvalues and eigenvectors are computed with the principal component method. In this case, the eigenvalues are statistics that state which part of the total variance of all the standardized item scores is explained solely by a newly computed factor. The eigenvalues are sorted in descending order and build the basis for the factor extraction. It is common procedure to extract each factor which eigenvalue is higher than 1 (Eckstein, 2012). The eigenvectors of the items are correlation coefficients between the standardized items and the extracted factors. They can take on values between -1 and 1 and signify the factor load (Eckstein, 2012; Abdi, 2010). An item loads high on a factor when the absolute value of its eigenvector (factor load) is higher than .50. It is important to mention that an item can exceed this critical value and thus load high on several factors.

After the extraction of meaningful factors with the factor analysis those factors need to be interpreted. Interpretation of a factor is easy if some items load only high on one factor while other items only load high on another factor. To achieve such a simple solution, it can make sense to rotate the extracted factors because the rotation maximizes the variance and results in items that load only high on a small number of factors (Abdi, 2010).

When applying the conventional method of extracting each factor with eigenvalue higher than 1 the factor analysis determines nine separate dimensions for the data gather with the BFI. Those nine dimensions explain 59 % of the total variance. When looking at the rotated factor matrix in Appendix A one can see that every Conscientiousness item except one loads high on Factor 2, thus Factor 2 can clearly be interpreted as the

Conscientiousness dimension of the FFM. The same goes for Factor 1 where all items except two load high and hence can be read as Extraversion and Factor 3 which can be interpreted as Neuroticism since all items of the respective scale besides two load high on this factor. The remaining two personality dimensions are not represented in a single factor. Most items of the Openness scale load high on Factor 4 and 7. Factor 4 could be interpreted as intelligence or mental creativity while Factor 7 comprises items with cultural aspects. While the interpretation of those two factors makes logical sense, and is not at all surprising because intelligence and culture were formerly used labels for the construct instead of Openness (John et al., 2008), it is unfortunate that the Openness dimensions is not replicated in a single factor. A similar situation arises for the Agreeableness dimension where the scale items load high on Factor 5, 6, 8 and 9. Most of the items load high on Factor 5 which can be interpreted as sociability or good-naturedness, however the high loading items of Factor 8 also fit into this picture. Besides items of the Agreeableness scale the items “Can be somewhat careless” of the Extraversion scale and the item “Can be moody” of the Neuroticism scale are also loading high on Factor 6, which hence could be interpreted as reluctance. Factor 9 with the items

“Tends to find fault with others” and “Likes work that is the same every time (routine)”

is not logically interpretable in an obvious way.

The factor analysis failed to replicate the conceptualize five personality dimensions of the FFM when applying the conventional Kaiser criterion of extracting factors with eigenvalues higher than 1. However, another common approach is the limitation of the extraction of factors. Such an approach is justified when the eigenvalues of the extracted dimensions show a sharp decline from one to another and therefore can be classified as meaningful and meaningless (Eckstein, 2012). The eigenvalues of the first five factors are 7.35, 3.77, 3.75, 3.06 and 2.41. The eigenvalues of the factors six to seven are only 1.59, 1.24, 1.16 and 1.03 respectively. These differences in eigenvalues justify a limitation to five main factors (Lang et al., 2001).

When limiting the analysis to five principle factors, the extracted dimensions explain 46.8 % of the total variance. The rotated factor matrix in Appendix B shows that the Big Five dimensions are almost perfectly replicated. All the items of the Agreeableness scale load highest on Factor 5 and all but two surpass the critical mark of .50. The same goes

for the items of the Conscientiousness scale and Factor 2, where all but one item have a high load. Factor 1 represents Extraversion. All but one item reach a load higher than 0.50. The Neuroticism dimension is represented through Factor 4. Six of the eight items of the scale exceed the critical value and one item is close to doing so. However, the item

“Is depressed, blue” has the highest load on a different factor. Instead of Factor 4 it loads negatively high on Factor 1 Extraversion although not reaching the critical value. At last the items of the Openness scale load high on Factor 3. Only the item “Likes work that is the same every time (routine)” has a scattered load over all five factors without being close to the critical value once. Nonetheless, the items replicate the five dimensions properly. Under the prerequisite of five dimensions the scale items show a good item-correlation, which makes the BFI a suitable instrument for a personality assessment and thus the gathered data valid.

As shown above reliability and validity of the personality assessment are constituted through the applied tests in an adequate manner. Therefore, the participants individual scores can be computed and used for further investigation of choice overload.