STATISTICAL HYPOTHESIS

The format in which the statistical hypotheses are formulated depends on the logic underlying the proposed research design as well as the nature of the envisaged statistical analyses. One option to examine the construct validity of the 15FQ+ would have been to use an unrestricted, exploratory factor analytic approach in which no statistical hypotheses would have been formulated (Donnelly, 2009). In an unrestricted, exploratory factor analytic approach no a priori stance is taken on the number of factors underlying the observed covariance matrix, their identity and the manner in which the items load on the factors (Ferrando & Lorenzo-Seva, 2000).

This option seems inappropriate for this study since it ignores the design intentions of the developers of the 15FQ+.

The test developers of the 15FQ+ took a very specific stance on the number of personality factors underlying the observed covariance matrix, their identity and the manner in which the items load on the personality factors. Personality items were intentionally developed to reflect specific dimensions of the personality construct.

Therefore it is clear that the 15FQ+ items were specifically written for test takers to respond with behaviour which would lead to a behavioural expression of a specific latent personality dimensions. The scoring key of the 15FQ+ reflect these design intentions. It is, however, very difficult to isolate behaviour in such a manner that the response on an item will be a behavioural expression of a specific first-order personality factor. Behaviour reflects the whole personality which results in a test taker’s response to an item to be positively or negatively affected by all the remaining personality factors as well, albeit to a lesser degree (Gerbing & Tuley, 1991). These patterns of positive and negative loadings on the remaining factors cancel each other out when composite scores are calculated through the suppressor action effect (Gerbing & Tuley, 1991). Therefore the suppressor action allows for a relatively uncontaminated measure of the latent personality variable where variance in the responses of the test takers predominantly reflects variance in the factor of interest.

78 It seems more reasonable to first evaluate whether the intentional instrument design of the test developers did succeed in providing a comprehensive and relatively uncontaminated empirical grasp on the personality construct as the 15FQ+ manual defines it. Consequently a hypothesis testing, restricted, confirmatory factor analytic approach should rather be followed. In terms of this approach specific structural assumptions with regard to the number of latent variables underlying the 15FQ+, the relations among the latent variables and the specific pattern of loadings of indicator variables on these latent variables are made (Ferrando & Lorenzo-Seva, 2000;

Jöreskog & Sörbom, 1993). More specifically assumptions are made on how these structural assumptions apply across the Black, Coloured and White ethnic groups.

Moyo (2009) argued that if the verdict would go against the claims made by the test developers it would be more reasonable to use an unrestricted, exploratory factor analytical approach where no priori stance is taken on the number of factors underlying the observed co-variance matrix. This will lead to estimation of the number of factors underlying the observed co-variance and identify the manner in which the items load on the factors (Moyo, 2009).

Moyo (2009) stated that the measurement model should also acknowledge the pattern of positive and negative loadings of the items on the remaining factors.

Excluding the suppressor action from the measurement model would not fully acknowledge the design intention of the developers of the 15FQ+ and thereby result in an unfair evaluation of the extent to which the test developers succeeded in their design intention to measure the personality construct as they defined it in the manner that they intended. Excluding the suppressor action from the measurement model could lead to poor model fit which would result in the unwarranted conclusion that the measurement intention of the test developers has failed. The vexing question, however, is how the suppressor effect should be accommodated in the single- and multi-group measurement models that are fitted. The suppressor effect implies that all elements of X are freed to be estimated but that only the factor loadings of the items on the first-order factor they are meant to reflect are freed unconditionally. The suppressor effect further implies that for the remaining 15 first-order factors the factor loadings of the items of a specific subscale are freed to be estimated but constrained to range in a narrow band straddling zero. Although such a model would still be identified with positive degrees of freedom, the problem is that

79 it is not practically possible to free measurement model parameters in LISREL under a range condition. The amount of memory and processing capacity that would be required would in addition probably exceed even the capabilities of the current 64 bit version of LISREL 9.0. To fix the loadings of items on non-target latent variables to some specific low positive or negative values would be possible in LISREL but would not accurately model the hypothesized suppressor effect.

Moyo (2009) argued that the formation of item parcels presents a way of capturing the suppressor effect in the measurement model in that the item parcels allowed the suppressor action to operate. The suppressor action originates from the fact that the items of the 15FQ+ reflect the whole personality. Although each item is designed to primarily reflect a specific personality dimension, each item simultaneously also reflect, albeit to a lesser degree, positively and negatively, the remaining personality dimensions (Gerbing & Tuley, 1991). Moyo (2009) argued that when fitting the measurement model with the items of a subscale combined into parcels, the suppressor effect that is assumed to operate when calculating the subscale scores should also operate when calculating the item parcels. The greater the number of items that are included in an item parcel the more likely it becomes that the suppressor effect would also operate when calculating the item parcel scores. The disadvantage of using parcels on the other hand is that it offers the opportunity for insensitive, hermit, biased items to hide away in item parcels. Increasing the number of item parcels decreases the latter problem but makes it less likely that the suppressor effect will operate effectively when calculating item parcel scores.

A compromise position was taken in this study, partly because of restrictions imposed by limitations imposed by the LISREL software. Six item parcels containing 2 items each were used to represent each of the 16 first-order personality factors in the single- and multi-group measurement models. The formation of the item parcels are discussed in greater detail in paragraph 5.6.2.1 below.

Structural equation modelling utilizing LISREL 9.0 (Du Toit & Du Toit, 2000;

Jöreskog & Sörbom, 1996a) was used to test the operational hypotheses listed in paragraph 5.1.

Hypotheses 1a, 1b and 1c were tested by fitting three single-group measurement models separately to the data of the three ethnic groups. In estimating the

80 hypothesised models’ fit the extent to which the model is consistent with the obtained empirical data will be tested. In order to investigate the hypothesised models’ fit exact fit null hypotheses and close fit null hypotheses were tested (Diamantopoulos

& Siguaw, 2000). The ideal would be to find an exact fit. Exact fit means that the 15FQ+ flawlessly explains the covariances between the indicator variables across the three ethnic groups. More specifically the following exact fit null hypothesis was tested:

H01i: Σ= Σ(Ө); i=1, 2, 3 Ha1i: Σ≠ Σ(Ө); i=1, 2, 3

Where Σ is the observed population co-variance matrix and Σ(Ө) is the derived or reproduced co-variance matrix obtained from the fitted model (Kelloway, 1998). In its alternative format the exact fit hypothesis could be formulated as (Browne & Cudeck, 1993):

H01i: RMSEA=0;i=1, 2, 3 Ha1i: RMSEA>0i=1, 2, 3;

However, the possibility of exact fit is highly improbable in that models are only approximations of reality and, therefore, rarely exactly fit in the population. The close fit null hypothesis takes the error of approximation into account and is therefore more realistic (Diamantopoulos & Siguaw, 2000). If the error due to approximation in the population is equal to or less than .05 the model can be said to fit closely (Diamantopoulos & Siguaw, 2000).

Therefore the following close fit null hypothesis was also tested:

H02i: RMSEA≤.05; i=1, 2, 3 Ha2i: RMSEA>.05; i=1, 2, 3

Conditional on the decision on H01 and H02 a further series of hypotheses on the slope and intercepts of the regression for the items on the respective latent personality dimensions were tested⁶.

6Due to the complexity of the model, these hypotheses were not written out individually.

81 Conditional on the decision on H01 and H02, hypothesis 2 was tested by testing the null hypothesis that the multi-group configural invariance model shows close fit.

H03: RMSEA≤.05 Ha3: RMSEA>.05

Conditional on the decision on H03, hypotheses 3 - 6 were tested by testing the null hypotheses that the multi-group weak, strong, strict and complete invariance models show close fit.

H0j: RMSEA≤.05; j=4, 5, 6, 7 Haj: RMSEA>.05; j=4, 5, 6, 7

Conditional on the decision on H0j; j= 4, 5, 6, 7 hypothesis 7 - 10 were tested by determining the practical significance of the difference in fit between the multi-group weak, strong, strict and complete invariance models and the multi-group configural invariance model.

H0j: RMSEA≤.05; j=8, 9, 10, 11 Haj: RMSEA>.05; j=8, 9, 10, 11

The results of these analyses formed the basis for examining the merits of the claim made by the developers of the test that the 15FQ+ successfully measures the sixteen primary personality dimensions it intends to measure and in the manner that it intends to do according to the scoring key.

5.4 SAMPLE

The data used for this study was drawn from a large archival database of the 15FQ+

psychometric test scores provided by a test distributor company in South Africa. The database included the following ethnic groups: Blacks, Coloureds and Whites. Item raw scores were provided for all relevant ethnic groups and self-reported biographical information included gender, age, language, education and ethnic group membership. Given the objective of the study the item raw scores for the sample of Black, Coloured and White respondents of the 15FQ+ were needed and therefore separated. The sample could be considered a non-probability sample of respondents

82 comprising of Black, Coloured and White South African test takers who completed the 15FQ+.

The objective of this study was to determine measurement equivalence and measurement invariance of the 15FQ+ across the Black, Coloured and White groups. Respondents qualified for inclusion in the sample if they completed the 15FQ+ and if information was available on the ethnic group they belong to. The total sample size consisted of 10019 respondents of which 4440 were Black (44.3%), 1049 were Coloured (10.5%) and 4532 were White (45.2%). The large sample size and the demographic information available allowed for the generalizations of the results of the study.