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Table 5 G-coefficients and Ф-coefficients for different numbers of items for p × I design in D-study for four domains of quality of life instrument QLICD-PU

From: Development and validation of the peptic ulcer scale under the system of quality of life instruments for chronic diseases based on classical test theory and generalizability theory

Domain Number of items \(\sigma^{2} ({\text{P}})\) \(\sigma^{2} ({\text{I}})\) \(\sigma^{2} ({\text{PI}})\) \(\sigma^{2} (\delta )\) \(\sigma^{2} (\Delta )\) \(\sigma^{2} ({\text{X}}_{{{\text{PI}}}} )\) \({\text{E}}\rho^{2}\) \(\Phi\)
Physical domain 6 0.517 0.037 0.186 0.186 0.224 0.042 0.735 0.698
  8 0.517 0.028 0.140 0.140 0.168 0.032 0.787 0.755
  9 0.517 0.025 0.124 0.124 0.149 0.029 0.806 0.776
  11 0.517 0.020 0.102 0.102 0.122 0.024 0.836 0.809
Psychological domain 9 0.338 0.010 0.095 0.095 0.105 0.013 0.780 0.763
  11 0.338 0.007 0.069 0.069 0.076 0.010 0.830 0.815
  13 0.338 0.006 0.059 0.059 0.065 0.009 0.852 0.839
  15 0.338 0.005 0.051 0.051 0.056 0.008 0.869 0.858
Social domain 9 0.190 0.010 0.142 0.142 0.152 0.012 0.573 0.556
  11 0.190 0.008 0.116 0.116 0.124 0.010 0.622 0.605
  13 0.190 0.007 0.098 0.098 0.105 0.009 0.660 0.644
  16 0.190 0.006 0.080 0.080 0.085 0.008 0.705 0.690
  17 0.190 0.005 0.075 0.075 0.080 0.007 0.717 0.703
  27 0.190 0.003 0.047 0.047 0.051 0.005 0.801 0.790
  29 0.190 0.003 0.044 0.044 0.047 0.005 0.812 0.801
Specific domain 11 0.143 0.023 0.108 0.108 0.132 0.025 0.568 0.520
  14 0.143 0.018 0.085 0.085 0.103 0.020 0.626 0.580
  17 0.143 0.015 0.070 0.070 0.085 0.016 0.671 0.626
  20 0.143 0.013 0.060 0.060 0.072 0.014 0.705 0.663
  24 0.143 0.011 0.050 0.050 0.060 0.012 0.742 0.703
  34 0.143 0.008 0.035 0.035 0.043 0.009 0.803 0.770
  41 0.143 0.006 0.029 0.029 0.035 0.007 0.831 0.802
  1. Item number for present scale is shown in bold
  2. \(\sigma^{2} (\delta )\) is the variance components of relative error, \(\sigma^{2} (\Delta )\) is the variance components of absolute error, \(\sigma^{2} ({\text{X}}_{{{\text{PI}}}} )\), is the variance components of error when estimating the universe score by using sample mean, \({\text{E}}\rho^{2}\) is the Generalizability coefficient, \(\Phi\) is the index of dependability