4.2 Data Analysis
4.2.1 Factor Analysis and Reliability
4.2.1.1 Factor Analysis
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44 Table 4.2. 2. Communalities Test
Source: data analysis – SPSS 16.0 c. Total Variance Explained
Table 4.2. 3. Total Variance Explained
45 Source: Data analysis – SPSS 16.0
From table 4.2.3 above, it show lists the eigenvalues associated with each linear component (factor) before extraction, after extraction and after rotation. Before extraction, SPSS has identified 23 linear components within the data set. The eigenvalues associated with each factor represent the variance explained by that particular linear component and SPSS also displays the eigenvalue in term of the percentage of variance explained (so, factor 1 explains 50.414% of total variance). It should be clear that the first few factors explain relatively large amounts of variance (especially factor 1) whereas subsequent factors explain only small amounts of variance. SPSS the extracts all factors with eigenvalues greater than 1, which leaves us with five factors. The eigenvalues associated with these factors are again displayed (and the percentage of variance explained) in the columns labelled Extraction Sums of Squared Loading. The values in this part of the table are the same as the values before extraction, expect that the values for the discarded factors are ignored (hence, the table is blank after the fifth factor). In the final part of table (labelled Rotation Sum of Squared Loadings), the eigenvalues of the factors after rotation are displayed. Rotation has the effect of optimizing the factor structure and one consequence for these data is that the relative important of the five factors is equalized. Before rotation, factor 1 accounted for considerably more variance than the remaining four (50.414% compared to 10.457, 6.041, 4.709, and 4.585%).
However, after extraction it accounts for only 16.598% of variance (compared to 15.858%, 15.598%, 15.512%, and 12.674 % respectively).
d. Rotated Component Matrix
From the table 4.2.4 below, it shows the rotated component matrix (also called the rotated factor matrix in factor analysis) which is a matrix of the factor loading for each variable onto each factor. This matrix contains the same information as the component matrix in Table 4.2.3 except that it is calculated after rotation.
Since there are number 05, 06, and 25 do not only converge in one factor. Hence, there is divergent validity problem.
46 Table 4.2. 4. Rotated Component Matrix
Source: data analysis – SPSS 16.0
After several times removing the entire variable less than 0.5 and re-run SPSS, here are the best output following below:
Table 4.2. 5. KMO and Bartlett’s Test
Source: primary data-SPSS 16.0
From table 4.2.5 above, it showed the Bartlett’s test of Sphericity is 0.000 <0.05 (Sig.), thus the hypothesis that the intercorrelation matrix involving these five variables is an identify matrix is reject. As Bartlett’s test is almost always significant,
47 a more discriminating index of factor analyzability is the KMO From this table, KMO = 0.873, which is very large, so the KMO also support factor analysis.
Table 4.2. 6. Communalities
Source: primary data- spss16.0
From table 4.2.6 above, the Communalities (Extraction, as the Initial are always 1.000) range from 0.560 to 0.840, thus most of variance of these variables was accounted for by this two dimensional factor solution. It means all of variable with high values are well represented in common.
Table 4.2. 7. Total Variance Explained
Source: primary data- SPSS 16.0
48 From table 4.2.7 above, it shows lists eigenvalues associated with each linear component (factor) before extraction, after extraction and after rotation. Before extraction, SPSS has identified 11 linear components within the data set. The eigenvalues associated with each factor represent the variance explained by that particular linear component and SPSS also displays the eigenvalue in term of the percentage of variance explained (so, factor 1 explains 50.339% of total variance). It should be clear that the first few factors explain relatively large amounts of variance (especially factor 1) whereas subsequent factors explain only small amounts of variance. SPSS the extracts all factors with eigenvalues greater than 1, which leaves us with three factors. The eigenvalues associated with these factors are again displayed (and the percentage of variance explained) in the columns labelled Extraction Sums of Squared Loading. The values in this part of the table are the same as the values before extraction, expect that the values for the discarded factors are ignored (hence, the table is blank after the three factor). In the final part of table (labelled Rotation Sum of Squared Loadings), the eigenvalues of the factors after rotation are displayed. Rotation has the effect of optimizing the factor structure and one consequence for these data is that the relative important of the three factors is equalized. Before rotation, factor 1 accounted for considerably more variance than the remaining four (50.339% compared to 12.560% and 10.030%). However, after extraction it accounts for only 27.626% of variance (compared to 24.717%, and 20.587% respectively). For this table, the cumulative of three factor explained 72.930% of the variance in the original data.
From table 4.2.8 below, once the number of factors has been determined, one can start trying to interpret what they represent. To assist in this process the factors can be “rotated”. Rotation does not change the underlying solution, but rather present the pattern of loading in way that is easier to interpret (Pallant, 2005). Factor rotation can be done in several ways.
49 Table 4.2. 8. Rotated Component Matrix
Source: primary data- SPSS 16.0
The next step is to look at the content of question that loads onto the same factor to try to identify the common themes. After using factor analysis, there are three factors in this research:
Factor 1 includes three questions from Reliability part of Service quality in questionnaire. There are statements of 01: “Staff’s uniform is tidy and elegant”; 02:
“Knowledge and skill of staff”; 03: “customer can contact easily with the staff who responsible for the customer service”. Therefore, the researcher gave the name for the first factor is “Reliability”.
Factor 2 includes four questions from questionnaire. There are statements of 08:
“The working hours of the bank that you cooperate are flexible and convenient for customer”; 09: “The ATMs of bank with sufficient in number”, 10: “The bank has parking place is convenient for customers”; 14: “The branches of bank are convenient for customer’s transaction”. Therefore, the researcher gave the name for second factor is “Tangible”.
50 Factor 3 includes four questions from the questionnaire. There are statements of number 23: “The bank offer low interest rates on loans”; number 24: “The bank offer higher return (interest) on savings”; number 25: “The bank collects low commission / charges”; number 28: “The bank has stable finance”. Therefore, the researcher gave the name for third factor is “financial benefit”.