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Dentists’ Working Patterns, Motivation and Morale - 2018/19 and 2019/20 Methodology

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Annex F – Detailed Regression Results and Assumption Testing

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Annex F – Detailed Regression Results and Assumption Testing

As discussed in Annexes D and E, several analytical assumptions have been made to investigate motivation in dentists. Many of these assumptions relate to the calculation of the average ‘motivation index’ and its modelling by linear regression. This Annex gives the linear regression results for 2019/20 each country in more detail and tests the assumptions around the use of the multivariate analysis for the ‘motivation index’.

England

Table F1 shows the parameter estimate results listed in table 1.7 (England – 2019/20, Multivariate Analysis) of the main report together with the p-value for each and the adjusted R-squared results. The intercept represents value of the ‘motivation index’ when all explanatory variables are zero.

Table F1: Parameter estimates and p-values for ‘motivation index’ by dental type using multiple linear regression, England, 2019/20

 Dental Type Sample Parameter Estimate Intercept Weekly Hours NHS% Clinical% Leave Age Adjusted R2 Providing-Performer 1,059 Estimate 64.092 -0.183 -0.232 0.074 0.964 -0.010 0.155 P-value <.0001 0.001 <.0001 0.060 0.007 0.890 Associate 2,437 Estimate 66.366 -0.095 -0.204 0.079 0.472 -0.137 0.078 P-value <.0001 0.023 <.0001 0.010 0.012 0.000

Based on the results it is possible to predict the ‘motivation index’ for both dental types. For example, for Providing-Performers this is given as:

64.092 - (0.183 x WH) - (0.232 x NHS%) + (0.074 x Clinical%) + (0.964 x Leave) - (0.010 x Age)

As described in Annex E, residual plots for Providing-Performers are shown in figure F1.

Figure F1: Providing-Performer dentists, plot of residuals for average ‘motivation index’ versus individual independent variables, England, 2019/20

Overall, the residual plots support the first three assumptions of multiple linear regression for average ‘motivation index’ as listed in paragraph E4 in Annex E. Figure F2 shows the normal quantile plot of the residuals for Providing-Performers.

Figure F2: Providing-Performer dentists, normal quantile plot of residuals for average ‘motivation index’, England, 2019/20

The result is a linear pattern plot with no significant departure from normality. Similar plots to the above are shown for Associate dentists in figures F3 and F4.

Figure F3: Associate dentists, plot of residuals for average ‘motivation index’ versus individual independent variables, England, 2019/20

Figure F4: Associate dentists, normal quantile plot of residuals for average ‘motivation index’, England, 2019/20

The residual plots for Associate dentists appear to support the first three assumptions for multiple linear regression of the average ‘motivation index’ as does the almost linear quantile plot.

Different Dental Populations

Table F2 shows the parameter estimate results listed in table 1.8 (Chapter 1) together with the p-value for each and the adjusted R-squared results.

Table F2: Parameter estimates and p-values for ‘motivation index’ by dental type and split populations using multiple linear regression, England, 2019/20

 Dental Type Population Sample Parameter Estimate Intercept Weekly Hours NHS% Clinical% Leave Age Adjusted R2 Providing-Performer All 1,059 Estimate 64.092 -0.183 -0.232 0.074 0.964 -0.010 0.155 P-value <.0001 0.001 <.0001 0.060 0.007 0.890 <35 Hours 229 Estimate 53.070 0.195 -0.163 0.014 1.129 -0.031 0.092 P-value <.0001 0.330 <.0001 0.827 0.084 0.837 ≥35 Hours 830 Estimate 71.710 -0.331 -0.252 0.073 1.098 0.004 0.171 P-value <.0001 <.0001 <.0001 0.143 0.011 0.960 Mainly NHS 552 Estimate 94.117 -0.314 -0.472 0.030 0.712 0.025 0.062 P-value <.0001 <.0001 <.0001 0.612 0.197 0.815 Mainly Private 240 Estimate 65.084 0.106 -0.414 0.132 1.058 -0.299 0.040 P-value <.0001 0.337 0.020 0.046 0.079 0.058 Male 764 Estimate 54.243 -0.211 -0.241 0.124 0.986 0.108 0.180 P-value <.0001 0.002 <.0001 0.011 0.017 0.216 Female 295 Estimate 76.329 0.006 -0.236 0.014 0.571 -0.186 0.115 P-value <.0001 0.953 <.0001 0.829 0.414 0.164 Associate All 2,437 Estimate 66.366 -0.095 -0.204 0.079 0.472 -0.137 0.078 P-value <.0001 0.023 <.0001 0.010 0.012 0.000 <35 Hours 1,065 Estimate 62.668 0.012 -0.170 0.006 0.757 -0.074 0.064 P-value <.0001 0.896 <.0001 0.891 0.010 0.207 ≥35 Hours 1,372 Estimate 76.397 -0.308 -0.244 0.126 0.251 -0.157 0.097 P-value <.0001 0.001 <.0001 0.003 0.306 0.003 Mainly NHS 1,700 Estimate 74.233 -0.142 -0.282 0.070 0.576 -0.110 0.022 P-value <.0001 0.006 <.0001 0.059 0.007 0.022 Mainly Private 285 Estimate 62.358 0.149 -0.518 0.131 0.050 -0.191 0.041 P-value <.0001 0.200 0.002 0.127 0.941 0.096 Male 1,110 Estimate 60.355 -0.144 -0.214 0.151 0.209 -0.079 0.093 P-value <.0001 0.024 <.0001 0.002 0.461 0.161 Female 1,327 Estimate 68.601 0.029 -0.204 0.022 0.692 -0.172 0.071 P-value <.0001 0.628 <.0001 0.571 0.006 0.003

Northern Ireland

Table F3 shows the parameter estimate results listed in table 2.7 (Northern Ireland – 2019/20, Multivariate Analysis) of the main report together with the p-value for each and the adjusted R-squared results. The intercept represents value of the ‘motivation index’ when all explanatory variables are zero.

Table F3: Parameter estimates and p-values for ‘motivation index’ by dental type using multiple linear regression, Northern Ireland, 2019/20

 Dental Type Sample Parameter Estimate Intercept Weekly Hours NHS% Clinical% Leave Age Adjusted R2 Principal 138 Estimate 64.148 -0.067 -0.279 -0.080 2.440 0.004 0.195 P-value 0.000 0.623 <.0001 0.525 0.019 0.982 Associate 200 Estimate 101.366 0.101 -0.372 0.049 0.068 -0.970 0.190 P-value <.0001 0.567 <.0001 0.694 0.956 <.0001

Based on the results it is possible to predict the ‘motivation index’ for dentists. For example, for Principal dentists in Northern Ireland this is given as:

64.148 - (0.067 x WH) - (0.279 x NHS%) - (0.080 x Clinical%) + (2.440 x Leave) + (0.004 x Age)

As described in Annex E, residual plots for Principal dentists in Northern Ireland are shown in figure F5.

Figure F5: Principal dentists, plot of residuals for average ‘motivation index’ versus individual independent variables, Northern Ireland, 2019/20

Overall, the residual plots support the first three assumptions of multiple linear regression for average ‘motivation index’ as listed in paragraph E4 in Annex E. In terms of constant variance of the errors, most plots appear well balanced with no clear errors. Figure F6 shows the normal quantile plot of the residuals for Principals.

Figure F6: Principal dentists, normal quantile plot of residuals for average ‘motivation index’, Northern Ireland, 2019/20

The result is a linear pattern plot with no significant departure from normality. Similar plots to the above are shown for Associate dentists in Northern Ireland in figures F7 and F8.

Figure F7: Associate dentists, plot of residuals for average ‘motivation index’ versus individual independent variables, Northern Ireland, 2019/20

Figure F8: Associate dentists, normal quantile plot of residuals for average ‘motivation index’, Northern Ireland, 2019/20

Like the results for Principals in Northern Ireland, the residual plots for Associates appear to support the four assumptions for multiple linear regression of the average ‘motivation index’.

Scotland

Tables F4 shows the parameter estimate results listed in table 3.7 (Scotland 2019/20 – Multivariate Analysis) of the main report together with the p-value for each and the adjusted R-squared results. The intercept represents value of the ‘motivation index’ when all explanatory variables are zero.

Table F4: Parameter estimates and p-values for ‘motivation index’ by dental type using multiple linear regression, Scotland, 2019/20

 Dental Type Sample Parameter Estimate Intercept Weekly Hours NHS% Clinical% Leave Age Adjusted R2 Principal 332 Estimate 54.068 -0.221 -0.166 0.214 1.227 -0.073 0.104 P-value <.0001 0.033 <.0001 0.014 0.069 0.519 Associate 770 Estimate 60.985 -0.091 -0.209 0.262 0.490 -0.326 0.082 P-value <.0001 0.294 <.0001 <.0001 0.291 <.0001

Based on the results it is possible to predict the ‘motivation index’ for dentists. For example, for Principal dentists in Scotland this is given as:

54.068 - (0.221 x WH) - (0.166 x NHS%) + (0.214 x Clinical%) + (1.227 x Leave) - (0.073 x Age)

As described in Annex E, residual plots for Principal dentists in Scotland are shown in figure F9.

Figure F9: Principal dentists, plot of residuals for average ‘motivation index’ versus individual independent variables, Scotland, 2019/20

Overall, the residual plots support the first three assumptions of multiple linear regression for average ‘motivation index’ as listed in paragraph E4 in Annex E. In terms of constant variance of the errors, most plots appear well balanced with no clear errors. Figure E10 shows the normal quantile plot of the residuals for Principals.

Figure F10: Principal dentists, normal quantile plot of residuals for average ‘motivation index’, Scotland, 2019/20

The result is a linear pattern plot with no significant departure from normality. Similar plots to the above are shown for Associate dentists in Scotland in figures F11 and F12.

Figure F11: Associate dentists, plot of residuals for average ‘motivation index’ versus individual independent variables, Scotland, 2019/20

Figure F12: Associate dentists, normal quantile plot of residuals for average ‘motivation index’, Scotland, 2019/20

Like the results for Principals in Scotland, the residual plots for Associates appear to support the four assumptions for multiple linear regression of the average ‘motivation index’.

Wales

Table F5 shows the parameter estimate results listed in table 4.7 (Wales 2019/20 – Multivariate Analysis) of the main report together with the p-value for each and the adjusted R-squared results. The intercept represents value of the ‘motivation index’ when all explanatory variables are zero.

Table F5: Parameter estimates and p-values for ‘motivation index’ by dental type using multiple linear regression, Wales, 2019/20

 Dental Type Sample Parameter Estimate Intercept Weekly Hours NHS% Clinical% Leave Age Adjusted R2 Providing-Performer 92 Estimate 20.685 -0.090 -0.165 0.121 0.768 0.538 0.102 P-value 0.320 0.662 0.015 0.445 0.344 0.042 Associate 253 Estimate 78.937 -0.322 -0.249 0.142 1.056 -0.353 0.135 P-value <.0001 0.024 <.0001 0.135 0.126 0.003

Based on the results it is possible to predict the ‘motivation index’ for dentists, shown in Chapters 4. For example, for Providing-Performer dentists in Wales this is given as:

20.685 - (0.090 x WH) - (0.165 x NHS%) + (0.121 x Clinical%) + (0.768 x Leave) + (0.538 x Age)

As described in Annex E, residual plots for Providing-Performer dentists in Wales are shown in figure F13.

Figure F13: Providing-Performer dentists, plot of residuals for average ‘motivation index’ versus individual independent variables, Wales, 2019/20

Overall, the residual plots support the first three assumptions of multiple linear regression for average ‘motivation index’ as listed in paragraph E4 in Annex E. In terms of constant variance of the errors, most plots appear well balanced with no clear errors. Figure F14 shows the normal quantile plot of the residuals for Providing-Performers.

Figure F14: Providing-Performer dentists, normal quantile plot of residuals for average ‘motivation index’, Wales, 2019/20

The result is a linear pattern plot with no significant departure from normality. Similar plots to the above are shown for Associate dentists in Wales in figures F15 and F16.

Figure F15: Associate dentists, plot of residuals for average ‘motivation index’ versus individual independent variables, Wales, 2019/20

Figure F16: Associate dentists, normal quantile plot of residuals for average ‘motivation index’, Wales, 2019/20

Like the results for Providing-Performers in Wales, the residual plots for Associates appear to support the four assumptions for multiple linear regression of the average ‘motivation index’.

Last edited: 27 August 2020 10:35 am