In this study of academic self-concept, items are categorized into four subscales; English self- concept, Arabic self-concept, Science self-concept and Mathematics self-concept respectively. For the reliability test, the coefficient alpha is calculated for each subscale. The alpha value ranged between .902 - .948 which indicates a high internal consistency. In addition to the
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Subject Specific Reliability Test, all items that constitute the ASDQII in this study were subject to a reliability analysis test. The coefficient alpha for the 20 items together was found to be .956, which indicates a high reliability measurement.
The Construct Validity was also tested in this study. The Construct validity refers to the degree to which a measure reflects the construct that it intended to measure (Gorard, 2001, Cohen et al, 2007, Bryman, 2001). A Construct Validity of a measure is tested through an Exploratory Factor Analysis (EFA).
However, Field (2013) suggested conducting a r-matrix analysis (correlation matrix) prior factor analysis. R-matrix calculates the relationships between variables. Variables that correlate higher than 0.9 or lower than 0.3 would raise a problem and they should be eliminated (Field, 2013). The 20 items in the ASDQII used in this study were subject to a r-matrix test. The correlational table (see Appendix H) showed no excessively large correlation coefficient among items. None of the correlation was greater than .9. Most correlations are around .5 which indicates fair correlations between variables. Therefore, all items in the ASDQII to be initially retained for a factor analysis.
The main factor analysis is conducted in two stages: factor extraction and factor rotation. Factor extraction determines how many factors to be retained. Similar procedures conducted in the EFA of the ability test will be followed on the ASDQII. Factor extraction process will conduct a Scree Plot and Principle Axis Factoring (PAF).
Scree plot showed the eigenvalues of each factor in graphical figure. The following figure (3.3) showed the scree plot of the 20 ASDQII items:
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Figure 3.3: Scree Plot in exploratory factor analysis
As shown in figure (3.3) every factor of 20 ASDQII is associated with an eigenvalue. The point where the slop of the line that drawn on the eigenvalues starts of changes up, is called the point of inflexion. The point of inflexion determines the cut-off point of which factors to be retained. In Figure (3.3), the point of inflexion is 5. Any factor in the left side of the inflexion point should be retained. This means that four factors to be retained in the ASDQII in this study.
Principle Axis Factoring (PAF) is recommended when the data is not normally distributed as in the case of the current study (Costello & Osborne, 2005). PFA assumes that the communality is greater than 1.0. Since communality concerns the shared or common variance between variables that constitute correlation matrices, PFA calculates the correlations between variables and factors and then loads the highest correlated variables with a factor (de Winter & Dodou,
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2012). The 20 items of the ASDQII used in this study were subject to an extraction factoring. The following tables (3.2) showed the SPSS output of the extraction factoring:
Total Variance Explained
Factor
Initial Eigenvalues
Extraction Sums of Squared Loadings
Rotation Sums of Squared Loadings
Total
% of
Variance Cumulative % Total
% of
Variance Cumulative % Total
% of Variance Cumulative % 1 10.005 50.025 50.025 9.682 48.408 48.408 3.603 18.013 18.013 2 2.045 10.223 60.248 1.744 8.721 57.129 3.391 16.954 34.968 3 1.447 7.237 67.485 1.188 5.940 63.069 3.292 16.458 51.426 4 1.083 5.414 72.898 .778 3.888 66.956 3.106 15.531 66.956 5 .842 4.210 77.109 6 .551 2.757 79.866 7 .448 2.239 82.105 8 .441 2.206 84.311 9 .408 2.038 86.349 10 .356 1.782 88.132 11 .341 1.707 89.839 12 .332 1.662 91.501 13 .301 1.506 93.006 14 .267 1.335 94.341 15 .241 1.206 95.547 16 .226 1.131 96.678 17 .192 .961 97.640 18 .175 .875 98.515 19 .165 .825 99.340 20 .132 .660 100.000
Table 3.2: Extraction Method: Principal Axis Factoring.
The Principle Axis Factoring (PAF) extracted all factors that have eigenvalues greater than 1.0 (based on Kaiser’s Criterion). The results showed that all variables in the ASDQII are extracted into four factors. This means that the eigenvalues associated with each factor represent the variance explained by those four factors. The ASDQII in this study is designed to measure four factors: Arabic self-concept, English self-concept, Math self-concept and Science self-concept.
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However, factor extraction is not enough to conclude the ASDQII items or variables measures the four factors. There is a need for further step to test the rotation of factors.
Factor rotation is conducted using oblique rotation. Oblique rotation is used when the factors are expected to be related. Oblique rotation is more common in social sciences, particularly in the field of Education; however, it depends on the theoretical ground of the research. Since this study measures four different factors; four subjects’ self-concepts, and those subjects’ self- concept contribute to the overall academic self-concept, it is expected that factors will be related. Therefore, oblique rotation is best to suite the purpose of this study.
SPSS offers different methods of Oblique rotation. One of them is the direct oblimin. This method is suitable for a small data set (Field, 2013). The 20 items in the ASDQII used in this study were tested using the direct oblimin factor rotation and the results are presented in the following table 3.3:
99 Factor 1 2 3 4 Q9 .921 Q10 .837 Q11 .827 Q12 .694 Q4 .407 Q6 .880 Q8 .878 Q7 .826 Q5 .740 Q19 -.986 Q18 -.850 Q17 -.718 Q20 -.699 Q13 -.892 Q15 -.805 Q14 -.764 Q16 -.663 Q3 -.507 Q1 .312 -.354 Q2
Table 3.3: Rotated factor Matrix for the ASDQII
The factor rotation table showed that variables loaded on four factors. The loading value is greater than .3 which indicates a significant loading of factors as proposed by Stevens (2002). Factor 1 represent the Arabic self-concept. Factor 2 represents The English self-concept. Factor 3 represents the Math self-concept.. Q5, Q6, Q7, Q8 represent Arabic self-concept factor, Q9, Q10, Q11, Q12 represent English self-concept factor, Q13, Q14, Q15, Q16 represent Science Self-concept factor, and Q17, Q18, Q19, Q20 represent Math self-concept factor. Q1, Q2, Q3, Q4 were designed to measure general school self-concept; therefore, they were not expected to to load on any factor. However, they loaded on different factors. Q1 loaded on Arabic and Math self-concept. Q2 did not load on any factor. Q3 loaded on only the Math self-concept. And Q4 loaded on only the Arabic self-concept. Therefore, for the sake of the reliability of the measure,
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a decision was made by the researcher to exclude the first 4 items of the ASDQII from the study.
In a summary, the factor analysis, factor extraction and factor rotation, showed that the ADSQII measures four factors: Arabic self-concept, English self-concept, Science Self-concept and Math Self-concept. Correlation matrices were measured indicate fair correlation between variables; .5 correlation value. Variables were expected to be related since they contribute to the overall academic self-concept. Factor extraction analysis was conducted and the results showed four main factors to represents the variables. Factor rotation, on the other hand, showed that The ASDQII items loaded on four factors that represent four subjects’ self-concepts. However, factor rotation discovered that the first four items seemed to be problematic since they were not designed to measure the factors that they loaded into. Therefore, those items were excluded from the measure.
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