# Using Statistical Test Method to Establish a Decision Model of Performance Evaluation Matrix
## 6 Conclusions
### Nomenclature  
\begin{tabular}{l l} \(q\) & the number of service items \\ \(X_{i}\) & the satisfaction of the \(i\)th service item \\ \(Y_{i}\) & the importance attached to the \(i\)th service item \\ \(a_{i}^{\mathrm{S}};b_{i}^{\mathrm{S}}\) & parameter of Beta distribution for satisfaction \\ \(a_{i}^{\mathrm{I}};b_{i}^{\mathrm{I}}\) & parameter of Beta distribution for importance \\ \(\theta_{i}^{\mathrm{S}}\) & satisfaction index \\ \(\theta_{i}^{\mathrm{S}}\) & the estimator of \(\theta_{i}^{\mathrm{S}}\). \\ \(\theta_{i}^{\mathrm{I}}\) & importance index \\ \(\theta_{i}^{\mathrm{I}}\) & the estimator of \(\theta_{i}^{\mathrm{I}}\) \\ \(\theta_{i}^{\mathrm{S}}\) & the average value of all satisfaction indices \\ \(C_{0}^{\mathrm{S}}\) & critical value \\ \(\theta_{i}\) & the average value of \(\hat{\theta}_{i}^{\mathrm{I}}\) \\ \((x_{i},y_{i})=\left(\hat{\theta}_{i}^{\mathrm{S}},\hat{\theta}_{i}^{\mathrm{I }}\right)\) & evaluation coordinate point \\ \(n\) & sample size \\ \(\left(X_{i1},\cdots,\ X_{i,j},\cdots,\ X_{i,n}\right)\) & the satisfaction sample data of the customer's \(i\)th service item \\ \(E\left[\hat{\theta}_{i}^{\mathrm{S}}\right]=\theta_{i}^{\mathrm{S}}\) & the expected value of \(\hat{\theta}_{i}^{\mathrm{S}}\) \\ \(\theta_{i}^{\mathrm{I}}\) & an unbiased estimator of \(\theta_{i}^{\mathrm{S}}\) \\ \(\theta_{\mathrm{S}}\) & the average value of \(\hat{\theta}_{i}^{\mathrm{S}}\) \\ \(\alpha\) & significance level \\ \(CR_{Xi}\) & the critical region for satisfaction index \(i\) \\ \(S_{Xi}\) & the standard deviation of satisfaction index \(i\) \\ \(Z_{Xi}\) & the standard score of satisfaction index \(i\) \\ \(C_{X0i}\) & the critical value of satisfaction index \(i\) \\ \((Y_{i1},\cdots,\ Y_{i,j},\cdots,\ Y_{i,n})\) & the importance sample data of the customer's \(i\)th service item \\ \(\hat{\theta}_{i}^{\mathrm{I}}\) & an unbiased estimator of importance index \(i\) \\ \(E\left[\hat{\theta}_{i}^{\mathrm{I}}\right]=\theta_{i}^{\mathrm{I}}\) & the expected value of \(\hat{\theta}_{i}^{\mathrm{I}}\) \\ \(\theta_{i}\) & the average value of \(\hat{\theta}_{i}^{\mathrm{I}}\) \\ \(CR_{Yi}\) & the critical region for importance index \(i\) \\ \(S_{Yi}\) & the standard deviation of importance index \(i\) \\ \(Z_{Yi}\) & the standard score of importance index \(i\) \\ \(C_{Y0i}\) & the critical value of importance index \(i\) \\ \(H_{0}\) & null hypothesis \\ \(H_{1}\) & alternative hypothesis \\ \(y=C_{Y0}\) & the value at which the horizontal line intersects the \(y\)-axis \\ \(x=C_{X0}\) & the value at which the vertical line intersects the \(x\)-axis \\ \(C_{X0}\) & \(Min\left\{C_{X01},C_{X02},\ldots,C_{X0q}\right\}\) \\ \(C_{Y0}\) & \(Min\left\{C_{Y01},C_{Y02},\ldots,C_{Y0q}\right\}\) \\ \(Q_{1}\) & Quadrant 1 \\ \(Q_{2}\) & Quadrant 2 \\ \(Q_{3}\) & Quadrant 3 \\ \(Q_{4}\) & Quadrant 4 \\ \(A\) & the set formed by the service items that need to be enhanced \\ \(\theta_{ij}^{\mathrm{S}}\) & the value of satisfaction index before improvement \\ \(\theta_{ai}^{\mathrm{S}}\) & the value of satisfaction index after improvement \\ \(\left(X_{i1}^{\mathrm{T}},\cdots,\ X_{i,j}^{\mathrm{T}},\cdots,\ X_{i,n}^{ \mathrm{T}}\right)\) & the satisfaction sample data is for \(i\in A\) \\ \(\theta_{i}^{\mathrm{S}}\) & the average value of satisfaction index after improvement \\ \(\theta_{pi}^{\mathrm{S}}\) & the average value of satisfaction index before improvement \\ \(Z_{hi}\) & the standard score of satisfaction index \(i\) after improvement \\ \(S_{Xai}\) & the standard deviation of satisfaction index \(i\) before improvement \\ \(S_{Xhi}\) & the standard deviation of satisfaction index \(i\) before improvement \\ \(\left[L_{bh},U\theta_{bi}\right]\) & the standard deviation of satisfaction index \(i\) before improvement \\ \(\left[L_{bh},U\theta_{bi}\right]\) & the standard deviation of satisfaction index \(i\) \\ \(S_{Xhi}\) & the standard deviation of satisfaction index \(i\) before improvement \\ \(S_{Xhi}\) & the standard deviation of satisfaction index \(i\) before improvement \\ \(\left[L_{