## 4 Results and Analysis
### Process of the Usability Experiment
#### 4.3.4 Evaluation of weight function  
In order to determine the influence of the lower levels on the higher levels, the weight functions should be determined by methods such as AHP [20], tabulated judgment method [21] and so forth. In this study, the tabulated judgment method was used for determining the weight functions.  
The procedure is described as follows:  
1. Determining the relative importance of pairwise items including the F1, F2, F3 and F4 child items.
2. List the test items into rows and columns in a table.
3. Filling in the scores of pairwise importance into the corresponding columns according to the following principles. If two child items have the same importance as the higher level, both child items were given a score of two points. For example, if F2 is more important than F1, than F2 gets 3 points and F1 gets 1 point. If F1 is much more important than F4, F1 gets 4 points and F4 has zero point. No value is filled into the diagonal columns as this is comparison to itself.
4. The summation of all child items _Ki_ can be obtained by summing up the comparison value of each row.
5. The summation of all child items can be aggregated into the grand total of a system with \(n\) items by the following equation. \[\sum\
olimits_{i=1}^{n}{{K_{i}}}=\left\{{{\left({{n^{2}}-{n}}\right)}/{2}} \right\}\times 4=2{{\left({{n^{2}}-{n}}\right)}}\] (2)
6. The weight function of each item can be expressed by \(\text{Wi}=\text{Ki}/\sum\
olimits_{i=1}^{n}{{K_{i}}}\), which is the weight of the \(n^{\text{th}}\) item.  
By implementing the above-mentioned method, the degree of influence of the five items and their child items can be determined as shown in Figure 13 and Table 6.  
Figure 12: The objective tree of a stereo system.  
All of the weights can be calculated by the above-mentioned method and the results are summarized in Table 7.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Item** & **F1** & **F2** & **F3** & **F4** & **F5** & \(\mathbf{K_{l}}\) & \(\mathbf{\sum K_{l}}\) & \(\mathbf{W_{l}}\) \\ \hline F1 & 2 & 1 & 2 & 1 & 6 & 40 & 0.15 \\ \hline F2 & 2 & 1 & 2 & 1 & 6 & 40 & 0.15 \\ \hline F3 & 3 & 3 & 3 & 1 & 10 & 40 & 0.25 \\ \hline F4 & 2 & 2 & 1 & 2 & 7 & 40 & 0.175 \\ \hline F5 & 3 & 3 & 3 & 2 & 11 & 40 & 0.275 \\ \hline \end{tabular}
\end{table}
Table 6: Weights of five items.  
\begin{table}
\begin{tabular}{c c} \hline \hline  & Precision of the audio source button (W11) & 0.375 \\ \cline{2-2}
**Efficiency Factor (W1)** & Message reception promptness (W12) & 0.25 \\ \cline{2-2}
**0.15** & Message reception clarity (W13) & 0.25 \\ \cline{2-2}  & Fast taking/placing CD (W14) & 0.125 \\ \hline \multirow{4}{*}{**Memorability Factor (W2)**} & Visibility of button design (W21) & 0.375 \\ \cline{2-2}
**Memorability Factor (W2)** & Complexity of interface design (W22) & 0.125 \\ \cline{2-2}
**0.15** & CD-ROM’s location and external style and dimensions (W23) & 0.29 \\ \cline{2-2}  & CD-ROM’s way of mechanical operation (W24) & 0.21 \\ \hline \multirow{4}{*}{**Functional Factor (W3)**} & Other ways of placement (W31) & 0.29 \\ \cline{2-2}
**0.25** & Adequacy of the product’s spatial arrangement (W32) & 0.29 \\ \cline{2-2}  & Angle of product’s speakers and the consistency of sound (W33) & 0.17 \\ \cline{2-2}  & Easy moving (W34) & 0.25 \\ \cline{2-2}  & Novelty of style (W41) & 0.25 \\ \cline{2-2}
**Emotional Factor (W4)** & Preference of style design (W42) & 0.25 \\ \cline{2-2}
**0.175** & Audible added value of the style (W43) & 0.17 \\ \cline{2-2}  & Enhanced overall atmosphere when listening to music (W44) & 0.33 \\ \hline \multirow{4}{*}{**Satisfaction Factor (W5)**} & Proportion and arrangement of the product’s screen and speakers (W51) & 0.33 \\ \cline{2-2}
**0.275** & The frequency of using other functions in addition to CD (W52) & 0.25 \\ \cline{2-2}  & Durability (W53) & 0.25 \\ \cline{2-2}  & Cleanness (W54) & 0.17 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Weights of all items.  
Figure 13: Hierarchy of five items of a stereo system.