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Case Study 177
Table 12.3 Contingency table for the study on the sectoral employment of RSEs.
Employment in
RSEs Private sector Public sector Total
With PhD 781 3 282 4 063
Without PhD 10 815 4 057 14 872

2
2
G statistics are very much larger than the critical χ statistic at the 95% level of sig-
nificance. Hence, there is very strong evidence to suggest that there is a relationship
between the PhD qualifications and sectoral employment status of RSEs. The full com-
2
putation of X contributions and adjusted residuals for each cell is shown in Table 12.4.
From the adjusted residuals there appear to be significantly more RSEs without PhDs
in the private sector than predicted by a hypothesis of independence. Conversely,
there appear to be significantly more PhD-level RSEs in the public sector than would
occur if the sectoral employment of RSEs were independent of PhD qualifications.
The actual sectoral employment data set contains more detailed classification on the
type of qualification for an RSE. Table 12.5 cross-classifies the sectoral employment
of RSEs against three qualification levels (bachelor’s, master’s or PhD). Here there
is a distinct ordering in the level of qualification. As discussed earlier, such ordinal
information can be incorporated into the analysis to achieve higher power in the
assessment of whether the probability of employment as an RSE in the private sector
is dependent on the qualification level (highest for PhD and lowest for bachelor’s).
Prior to the use of rigorous statistical hypothesis testing procedures, a preliminary
analysis can be conducted by just looking at the data shown in Table 12.5, which
includes the percentage of RSEs employed in each sector together with the usual
statistics ignoring the ordinal information. From the data, there appears to be a de-
creasing trend in the percentage of RSEs employed in the private sector at each higher
qualification level. The adjusted residuals in Table 12.5 also show a similar trend. The
adjusted residuals for the number of RSEs employed in the private sectors are both
negative at higher qualification levels corresponding the master’s and PhD degrees.

Table 12.4 Computed statistics for comparison of sectoral employment of PhD RSEs.
Employment in
Private sector Public sector p i+ Total

RSE with PhD 781 3 282 0.215 4 063
X 2 1 171 1 850
−62 62
R adj
RSE without PhD 10 815 4 057 0.785 14 872
X 2 320 505
62 −62
R adj
0.613 0.387
p + j
Total 11 596 7 339