The manner in which the statistical hypotheses are formulated depicts the logic underlying the proposed research design, as well as the nature of the statistical analyses. The proposed Client Risk-Tolerance reduced structural model consists of a number of endogenous and exogenous latent variables and causal paths are proposed between these variables. The notational system used in the formulation of the statistical hypotheses follows the structural equation modelling (SEM) convention associated with LISREL (Jöreskog & Sörbom, 1996b). In order to investigate the hypothesised model’s fit, an exact fit and close fit null hypothesis were tested.
The overarching substantive research hypothesis (hypothesis 1) states that the structural model depicted in figure 2.3 provides a valid account of the psychological processes that underpin Client Risk-Tolerance. If the overarching substantive
research hypothesis would be interpreted to mean that the structural model provides a perfect explanation for the psychological dynamics underlying Client Risk-
Tolerance, the substantive research hypothesis translates into the following exact fit
null hypothesis (hypothesis 2a20):
H02a: RMSEA = 0
Ha2a: RMSEA > 0
However, the probability of obtaining an exact fit is doubtful. Consequently, the close fit null hypothesis should be considered as it takes the error of approximation into account. If the difference between the observed and reproduced score is equal to or less than 0.05, it implies close fit (Theron, 2013). If the overarching substantive research hypothesis would be interpreted to mean that the structural model provides an approximate explanation of the psychological dynamics underlying Client Risk-
Tolerance, the substantive research hypothesis translates into the following close fit
null hypothesis (hypothesis 2b):
H02b: RMSEA ≤ 0.05 Ha2b: RMSEA > 0.05
The overarching substantive research hypothesis was dissected into 27 more detailed path-specific research hypotheses. Of these hypotheses, 15 were included in the reduced structural model and therefore, 15 path coefficient statistical hypotheses could be formulated and tested via SEM. These hypotheses are summarised in table 3.1. The remaining 12 hypotheses could not be tested via SEM. Instead, multiple regression analyses were conducted which did not necessitate the formulation of statistical hypotheses according to the SEM convention.
20
The overarching substantive research hypothesis can be dissected into exact and close fit null hypotheses for the measurement model (H01a and H01b) and the structural model (H02a and H02b). Due to the fact that the presentation of the measurement model results precedes that of the structural model, it was decided to assign the numbers accordingly and in that order.
Hypothesis 2: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Openness to Experience (ξ1) has a positive linear effect on Risk- Tolerance (η4)
H03: γ41 = 0 Ha3: γ41 > 0
Hypothesis 3: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Conscientiousness (ξ2) has a negative linear effect on Risk- Tolerance (η4)
H04: γ42 = 0 Ha4: γ42 < 0
Hypothesis 4: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Extraversion (ξ3) has a positive linear effect on Risk-Tolerance (η4) H05: γ43 = 0
Ha5: γ43 > 0
Hypothesis 5: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Extraversion (ξ3) has a positive linear effect on Sensation Seeking (η1)
H06: γ13 = 0 Ha6: γ13 > 0
Hypothesis 6: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Agreeableness (ξ4) has a positive linear effect on Risk-Tolerance (η4)
H07: γ44 = 0 Ha7: γ44 > 0
Hypothesis 7: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Neuroticism (ξ5) has a negative linear effect on Risk-Tolerance (η4) H08: γ45 = 0
Ha8: γ45 < 0
Hypothesis 8: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Sensation Seeking (η1) has a positive linear effect on Risk- Tolerance(η4)
H09: β41 = 0 Ha9: β41 > 0
Hypothesis 9: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Delay of Gratification (η3) has a negative linear effect on Risk- Tolerance (η4)
H010: β43 = 0 Ha10: β43 < 0
Hypothesis 10: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Extraversion (ξ3) has a negative linear effect on Delay of Gratification (η3)
H011: γ33 = 0 Ha11: γ33 < 0
Hypothesis 11: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Openness to Experience (ξ1) has a positive linear effect on Delay of Gratification (η3)
H012: γ31 = 0 Ha12: γ31 > 0
Hypothesis 12: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Conscientiousness (ξ2) has a positive linear effect on Delay of Gratification(η3)
H013: γ32 = 0 Ha13: γ32 > 0
Hypothesis 13: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Emotional Self-Management (η2) has a positive linear effect on Risk-Tolerance (η4)
H014: β42 = 0 Ha14: β42 > 0
Hypothesis 14: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Emotional Self-Control (ξ6) has a positive linear effect on Risk- Tolerance (η4)
H015: γ46 = 0 Ha15: γ46 > 0
Hypothesis 15: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Extraversion (ξ3) has a positive linear effect on Emotional Self- Management (η2)
H016: γ23 = 0 Ha16: γ23 > 0
Hypothesis 16: In the proposed Client Risk-Tolerance structural model it was
hypothesised that Neuroticism (ξ5) has a negative linear effect on Emotional Self- Management (η2)
H017: γ25 = 0 Ha17: γ25 < 0
Table 3.1
Path coefficient statistical hypotheses
Hypothesis 2 H03: γ41 = 0 Ha3: γ41 > 0 Hypothesis 3 H04: γ42 = 0 Ha4: γ42 < 0 Hypothesis 4 H05: γ43 = 0 Ha5: γ43 > 0 Hypothesis 5 H06: γ13 = 0 Ha6: γ13 > 0 Hypothesis 6 H07: γ44 = 0 Ha7: γ44 > 0 Hypothesis 7 H08: γ45 = 0 Ha8: γ45 < 0 Hypothesis 8 H09: β41 = 0 Ha9: β41 > 0 Hypothesis 9 H010: β43 = 0 Ha10: β43 < 0 Hypothesis 10 H011: γ33 = 0 Ha11: γ33 < 0 Hypothesis 11 H012: γ31 = 0 Ha12: γ31 > 0 Hypothesis 12 H013: γ32 = 0 Ha13: γ32 > 0 Hypothesis 13 H014: β42 = 0 Ha14: β42 > 0 Hypothesis 14 H015: γ6 = 0 Ha15: γ46 > 0 Hypothesis 15 H016: γ23 = 0 Ha16: γ23 > 0 Hypothesis 16 H017: γ25 = 0 Ha17: γ25 < 0
3.4. Research Design and Procedure