Abstract

Introduction

Materials & Methods

Results

Discussion & Conclusion

References

Discussion
Board

Figure 1 depicts the MAXCOV-HITMAX results of analysis of the real RCBSHY data.

Fig. 1: MAXCOV graph of shyness results.

Figure 2 depicts a set of 5 of the 100 simulated RCBSHY comparison data sets.

Fig. 2: MAXCOV graphs of simulated shyness results.

Figure 3 depicts the MAXCOV-HITMAX results of analysis of the real LSAS data.

Fig. 3: MAXCOV graph of social anxiety results.

Figure 4 depicts a set of 5 of the 100 simulated LSAS comparison data sets.

Fig. 4: MAXCOV graphs of simulated social anxiety results.

The percentile rank of the curve in Figure 2 and Figure 4 (shown on the right side of each graph) indicates how curved the graph is, when all simulation graphs are ordered from the least typological result to the most typological result. Simulation graphs are clearly variable enough to appear distinctly typological (such as the 90th percentile graph) and distinctly dimensional (as in the 10th and 30th percentile graphs). The central tendency of this distribution of graphs is represented by the 50th percentile graph, which is the median simulation result.

Examining the results of the RCBSHY analyses first, we see that the quadratic regression weight for the median simulation graph in Figure 2 is .00258, indicating that the dimensional simulations have a slight tendency to be curved in a nontypological direction. In contrast, the quadratic regression component of the regression line superimposed on the results of MAXCOV-HITMAX analysis of the real RCBSHY data in Figure 1 is -.00212, indicating that the plot is curved in the typological direction. Turning to Figure 3, the quadratic regression component of the regression line superimposed on the results of MAXCOV-HITMAX analysis of the real LSAS data in is -.0066, indicating that the plot is curved in the typological direction, much like the real RCBSHY results. The typological result of analyses of the LSAS is stronger, however, as indicated by the greater magnitude of the negative quadratic regression weight. The quadratic regression weight for the median simulation graph of the LSAS comparison data (Figure 4) is .00337, indicating that the plot has a slight tendency to be curved in a nontypological direction. Visual inspection of these figures suggests that both the RCBSHY and the LSAS may be based on a latent typology, however variability in the simulation results for both measures is considerable. In order for us to be confident in these results, the provisional typological results need to be considered in the context of the distribution of null (simulation) results.

The regression results of our analyses of the MAXCOV-HITMAX graphs are presented in Table 1.

Table 1
Summary of Regression Analyses Performed on Covariance Plots from
MAXCOV-HITMAX Analyses of the RCBSHY and LSAS measures

           Quadratic regression coefficients
                 of simulated data                      Real data results
--------------------------------------------------------------------------------

                                                   Quadratic
                                                   Regression
                Mean     S.D.                      Coefficient    Z-score     P

RCBSHY        .00299     .00925                      -.00212        .55      .29

LSAS          .00337     .00781                      -.00660       1.28      .10

Table 1 lists summary results of the simulated data, along with results of analysis of the real data for both the RCBSHY and LSAS measures. Columns 1 and 2 of the table list the mean and standard deviation of the quadratic regression coefficients of the simulated data. Column 3 of the table lists the quadratic regression coefficient of the line fitted to the MAXCOV-HITMAX graph of results of analysis of the real data. The last columns of the table list the z-score corresponding to the coefficient for the real data when compared to the distribution of simulation results, and its associated probability. This z-score indicates how deviant the real results are from those expected on the basis of dimensional simulation analyses. Although the RCBSHY real data results are more curved in the expected typological direction than the average simulation result, the real data results are well within the range of simulation (null) results, only differing from the mean by .55 of a standard deviation. This means that fully 29% of simulation results were more curved in the typological direction than the real data results. Results of comparable analysis of the LSAS measure are more compelling. The quadratic regression coefficient of the real LSAS data approaches the extreme of the distribution of null results, differing from the mean by 1.28 standard deviations (and being surpassed in the typological direction by only 10% of null results). One interpretation of this result is that the typological model of social phobia has moderate support. In summary, the results of MAXCOV analyses of prominent measures of shyness and social anxiety are both qualitatively typological, with one result being marginally significant. While the result appears typological, it may be that these results are due to chance fluctuations (sampling error) in the MAXCOV graph. Alternatively, it may be that a more robust typological result has been suppressed by an overly conservative data simulation control strategy. Certainly, the latter inference would be adopted by those who advocate for simply visually inspecting MAXCOV graphs for evidence of taxonic curvature³⁹.

An attempt was made to examine the effect of the conservative control strategy by bootstrapping both the real data and the simulated data to improve the power of our analyses. The regression results of our analyses of the MAXCOV-HITMAX graphs of bootstrapped data are presented in Table 2.

Table 2
Summary of Regression Analyses Performed on Covariance Plots from
MAXCOV-HITMAX Analyses of Samples of 1000 bootstrapped RCBSHY and LSAS
measures in comparison with bootstrapped simulation controls of the
same size.

             Quadratic Regression         Quadratic Regression
             Coefficients of              Coefficients of
             Bootstrapped Simulated       Bootstrapped Real
                   Data                         Data
-------------------------------------------------------------------
Sample Size    Mean      S.D.          Mean    S.D.    t     p
-------------------------------------------------------------------
  RCBSHY      .00162   .00429         .00132  .00194   .63   n.s.
  (N=1000)

  LSAS        .00065   .00210        -.00154  .00057   31.3  <.01
  (N=1000)

Table 2 lists summary results of the bootstrapped simulated data, along with results of analysis of the bootstrapped real data, for both the RCBSHY and LSAS measures. Columns 1 and 2 of the table list the mean and standard deviation of the quadratic regression coefficients of the simulated data. Columns 3 and 4 of the table list the mean and standard deviation of the quadratic regression coefficients of the lines fitted to the MAXCOV-HITMAX graphs of results of analyses of the bootstrapped real data. The last columns of the table list the t-test corresponding to the test of the difference between the mean bootstrapped real data set when compared to the mean bootstrapped dimensional simulation, and the p value of the t-test. This t-test indicates how deviant the real results are from those expected on the basis of dimensional simulations.

The results of analyses of bootstrapped RCBSHY real data are not distinguishable from the simulation results. In contrast, results of analyses of bootstrapped LSAS real data are strinkingly distinguishable from results of analyses of bootstrapped controls. These results suggest that shyness (as measures by the RCBSHY) is a dimensional construct, while social anxiety (as measured by the LSAS) is typological.

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