The nature of the statistical hypotheses used to test the operational hypothesis depends on the decision regarding the nature of the envisaged statistical analyses. The argument that the two conceptualisations of the social desirability construct, taken in conjunction with the manner in which the items were assigned to underlying factors in the scales that they were harvested from,
imply two specific measurement models points to the need to perform confirmatory factor analysis using structural equation modelling (Diamantopoulos & Siguaw, 2000). More specifically structural equation modelling utilising LISREL (Jöreskog & Sörbom, 1996) will be used to test the hypothesis that the measurement model defined by operational hypotheses 1 to 4 can closely reproduce the observed covariance matrix.
The present study investigated two substantive research hypotheses, linked to four operational research hypotheses. The statistical hypotheses indicated below represent statistical translations of the claims made by the four operational research hypotheses.
The claims made by the four operational research hypotheses that the measurement model implied by substantive hypothesis 1 or 2 can reproduce the co-variances observed between the items comprising each of the two SD subscales (self-deception enhancement and impression management),without and with method bias taken into account, translate into two overarching model fit hypotheses. More specifically the exact fit null hypotheses (H01i; i=1, 2, 3, 4)were
tested which represents the rather bold stance that the measurement model implied by the ith operational hypothesis accurately reflects the measurement model in the parameter (Browne & Cudeck, 1993).
RMSEA = 0; i=1, 2, 3, 4 : RMSEA > 0; i=1, 2, 3, 4
If it is, however, somewhat more realistically assumed that that the measurement model implied by substantive hypothesis 1 or 2,without and with method bias taken into account, approximates the processes that operated in reality to create the observed co-variance matrix, the following close fit null hypotheses (H02i; 1, 2, 3, 4) were tested (Browne & Cudeck, 1993):
: RMSEA ≤ .05; i=1, 2, 3, 4 : RMSEA > .05; i=1, 2, 3, 4
If the exact or close measurement model fit would be found for the measurement model fitted under operational research hypothesis 1 (i.e. H01i; i=1 or H02i; i=1 would not be rejected), the
57 following 12 null hypotheses on the slope of the regression of item j on latent social desirability dimension k will be tested for operational research hypothesis 1:
H0pi: jk=0;p=2, 3, …, 13; i=1; j=1, 2, …, 12; k=1, 214
Hapi: jk≠0;p=2, 3, …, 13; i=1; j=1, 2, …, 12; k=1, 2
If the exact or close measurement model fit would be found for the measurement model fitted under operational research hypothesis 2 (i.e. H01i; i=2 or H02i; i=2 would not be rejected), the
following 24 null hypotheses on the slope of the regression of item j on latent social desirability dimension k were tested for operational research hypotheses 2:
H0pi: jk=0;p=14, 15, …, 37; i=2,; j=1, 2, …, 12; k=1, 2, 3
Hapi: jk≠0;p=14, 15, …, 37; i=2,; j=1, 2, …, 12; k=1, 2, 3
If the exact or close measurement model fit would be found for the measurement model fitted under operational research hypothesis 3 (i.e. H01i; i=3 or H02i; i=3 would not be rejected), the
following 24 null hypotheses on the slope of the regression of item j on latent social desirability dimension k were tested for operational research hypothesis 3:
H0pi: jk=0; p=38, 39, …, 61; i=4; j=1, 2, …, 12; k=1, 2, 3, 4
Hapi: jk≠0; p=38, 39, …, 61; i=3; j=1, 2, …, 12; k=1, 2, 3, 4
If the exact or close measurement model fit would be found for the measurement model fitted under operational research hypothesis 4 (i.e. H01i; i=4 or H02i; i=4 would not be rejected), the
following 12 null hypotheses15 on the slope of the regression of item j on latent social desirability dimension k were tested for operational research hypotheses 4:
H0pi: jk=0;p=64, 65, 68, 69, 79, 71, 72, 73, 80, 81, 82, 83; i=4; j=2, 4, 5, 6, 10,11; k=1, 2, 3
Hapi: jk>0;p=64, 65, 68, 69, 79, 71, 72, 73, 80, 81, 82, 83; i=4; j=2, 4, 5, 6, 10, 11; k=1, 2, 3
If the exact or close measurement model fit would be found for the measurement model fitted under operational research hypothesis 4 (i.e. H01i; i=4 or H02i; i=4 would not be rejected), the
14
p is is counted across the matrix in the rows starting from the first freed factor loading for RQ27_SD
15 These hypotheses apply to the 6 items that are hypothesised to load positively on the two SD factors and the general factor
following 12 null hypotheses on the slope of the regression of item j on latent social desirability dimension k were tested for operational research hypotheses 4:
H0pi: jk=0; p=62, 63, 66, 67, 74, 75, 76, 77, 78, 79, 84, 85; i=4; j=1, 3, 7, 8, 9,12; k=1, 2, 3
Hapi: jk<0; p=62, 63, 66, 67, 74, 75, 76, 77, 78, 79, 84, 85; i=4; j=1, 3, 7, 8, 9,12; k=1, 2, 3 If the exact or close fit would be found (i.e. H01i; i=1, 2, 3, 4 or H02i; i=1, 2, 3, 4 not be rejected),
the following 48null hypotheses were tested with regards to the freed elements in the variance- covariance matricesi; i=1, 2, 3, 4 for operational research hypothesis 1 to 4:
H0pi: jj=0;p=87, 88, …, 134; i =1, 2, 3, 4; j=1, 2, ..., 12
Hapi: ijj> 0;p=87, 88, …,134; ; i =1, 2, 3, 4; j=1, 2 ..., 12
If the exact or close fit would be found (i.e. H01i; i=1 or H02i; i=1 not be rejected), the following
null hypothesis were tested with regards to the freed elements in the variance-co-variance matrix
i; i=1for operational research hypothesis 1: H0pi: jk=0; p=135; i =1; j=1; k=2
Hapi: jk> 0;p=135; i =1; j=1; k=2
If the exact or close fit would be found (i.e. H01i; i=2, 4 or H02i; i=2, 4 not be rejected), the
following 2 null hypotheses were tested with regards to the freed elements in the variance-co- variance matrix i; i=2, 4for operational research hypotheses 2 and 4:
H0pi: jk=0; p=136, 137; i =2, 4; j=1; k=216
Hapi: jk> 0;p=136, 137; i =2, 4; j=1; k=2
If the exact or close fit would be found (i.e. H01i; i=3 or H02i; i=3 not be rejected), the following
null hypothesis were tested with regards to the freed elements in the variance-co-variance matrix
i; i=3for operational research hypothesis 3: H0pi: jk=0; p=138, 139; i =3; j=1, 3; k=2, 417
Hapi: jk> 0;p=138, 139; i =3; j=1, 3; k=2, 4
16
13and23were fixed to zero 17
59
3.5. PARTICIPANTS AND PROCEDURES