CHAPTER 3: METHODOLOGY
3.9. Trustworthiness
3.9.1. Realibility and Validity
3.9.1.2. Exploratory Factor Analysis (EFA)
The researcher used EFA to explore and discover the main constructs or dimensions of the 40- items survey. EFA is one of the oldest structural models, having been developed by Spearman in 1904, to discover the main constructs or dimensions (Olkin, 2001). It is a means of determining to what degree individual items are measuring a something in common, such as a factor (Naomi et al., 2018). The EFA was performed using Statistical Product and Service Solutions (SPSS v.26) software, with a Principal Component Analysis (PCA) extraction method and Varimax rotation.
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Before running the EFA, the following assumptions were tested: sample size, correlation between pairs of survey variables (questions), and data sampling adequacy to factor analysis.
3.9.1.2.1. Sample Size
There are varying opinions and several guiding rules of thumb that can be used to determine if the sample size is suitable for the factor analysis. At least 300 cases are needed for factor analysis (Tabachnick, 2007). Hair et al (1995) suggested that sample size should be at least 100 cases. Guadagnoli and Velicer (1988) proposed that if the dataset has several high factor loading scores (> 0.80), then a smaller small size (n > 150) should be sufficient. One requirement for small sample size is that variables communalities have to be high enough (> 0.5) after extraction, according to Field (2005). From another point of view, sample size can be determined using the sample to variable ratio, denoted as N:p, where N refers to the number of participants and p refers to the number of variables (Hogarty et al., 2005). That is, rules of thumb suggest ratios such as 3:1, 6:1, 10:1, 15:1, or 20:1, based on several studies. Hogarty et al. (2005) and MacCallum et al. (1999) have conducted studies to test these guides, and Hogarty et al. (2005) noted that their results showed that there was not a minimum level of N or N:p ratio to achieve good factor solution.
In the study at hand, a total of 240 participants exists, which meets the minimum requirement by Hair et al (1995). Moreover, the N:p ratio is 240:40, which meets the 6:1 ratio rule of thumb, indicating that sample size is sufficient to run the factor analysis.
3.9.1.2.2. Correlation Analysis
A correlation matrix is used in EFA process displaying the associations between pairs of individual variables of the survey, with correlation coefficients above 0.3 (Tabachnick and Fidell, 2007). The correlation matrix is attached to Appendix H, displayed in two tables to fit the
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page width. Correlation coefficients ranged between 0.082 and 0.603, with more than 57% of correlation coefficients above the minimum threshold of 0.3, see Figure 3.. Correlated variables indicate that they measure the same underlying dimension, which means that the dataset is factorable.
On the other hand, extremely high correlation coefficients (close to 1) would indicate the possibility of having the problem of multicollinearity as this would cause difficulties in determining the unique contribution of the variables to a latent factor (Field, 2000). Checking the correlation matrix, the maximum correlation coefficient was 0.603, indicating that there is no multicollinearity problem.
Figure 3.2: Correlation Matrix
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3.9.1.2.3. EFA Assumptions
a) Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy
Prior to proceeding with the factor analysis results, Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy, and Bartlett’s Test of Sphericity were checked. According to the results presented in Table 1.4, the KMO is equal to 0.942, which exceeds the minimum threshold of 0.5 (Hair et al., 1995; and Tabachnick et al., 2007). Moreover, the Bartlett’s Test of Sphericity is significant (p < 0.001) (Hair et al., 1995; and Tabachnick et al., 2007). Therefore, factor analysis is suitable for the data at hand.
Table 1.4: Kaiser-Meyer-Olkin Measure of Sampling Adequacy
b) Anti-image Correlation Matrix
The Measures of Sampling Adequacy (MSA) for individual variables are printed as the diagonal elements of the Anti-image Correlation matrix in the "Anti-image Matrices" table of the Factor output. The diagonals of the anti-image correlation matrix, presented in Table , were all over 0.5, so all items may reasonably be retained for the EFA.
c) Communalities
The communality is the variance in the observed variables which are accounted for by a common factor or common variance (Child, 2006). The communalities, reported in 3.5 were all above 0.3, except the four items:11, 14, 16, and 17, with communalities below 0.3 but above 0.2, so they
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can be retained in the analysis based on what Child (2006) stated: “Often times variables with low communalities (less than .20 so that 80% is unique variance) are eliminated from the analysis since the aim of factor analysis is to try and explain the variance through the common factors”. This further confirms that each item shared some common variance with other items.
Table 3.5: Extraction Communalities and Measures of Sampling Adequacy (MSA)
Questionnaire Items Extraction MSA
1. I understand the importance of working in groups. .474 .953
2. I get along with other team members in my group. .545 .931
3. I respect / accept every team member in my group who is from different culture and background.
.601 .936
4. I respect / accept every team member in my group who has different ability and learning style.
.572 .937
5. I respect / accept different opinions in my group. .471 .961 6. I question the way other team members in my group do and try to think of a
better way.
.559 .958
7. I feel that my ideas and suggestions are important to others. .628 .945 8. I feel excited and satisfied to work with my group. .582 .941
9. I like to help my team members in my group. .453 .903
10. I like to think differently in doing activities in my group. .383 .953 11. I like to share ideas and suggestions in my group. .247 .896 12. I really enjoy working collaboratively with other students. .442 .922
13. I prefer to have a leadership role in my group. .490 .969
14. I am an important member in my group. .242 .931
15. I work hard and effectively in my group. .385 .938
16. My teacher encourages us to work collaboratively in class. .272 .939 17. My teacher encourages us to discuss topics in class. .295 .945 18. My teacher encourages us to think critically and solve problems. .474 .940 19. My teacher encourages us to be independent and creative. .330 .944 20. My teacher encourages us to reflect on our actions to see whether we
could improve on what we did.
.329 .946
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Questionnaire Items Extraction MSA
21. My teacher monitors / controls students’ interaction in class. .332 .943 22. My teacher asks useful questions to deepen the study and link to previous
topics.
.574 .954 23. My teacher uses differentiated questions that fit students’ abilities and
learning style.
.463 .901
24. My teacher shares information that was collected from the group. .575 .937
25. My teacher treats us fairly and equally. .557 .954
26. Working collaboratively with my group improves the content and the structure of my writing.
.501 .936
27. Working collaboratively with my group makes me think differently. .523 .940 28. Working collaboratively with my group makes me think critically. .489 .957 29. Working collaboratively with my group makes me more creative. .383 .917 30. Working collaboratively with my group makes me learn new ideas. .489 .948 31. Working collaboratively with my group makes me solve problems faster. .528 .946 32. Working collaboratively with my group makes me learn values and new
concepts.
.436 .938
33. Working collaboratively with my group makes me learn and grow from other differences.
.497 .958
34. Working collaboratively with my group changes the way I look at myself. .552 .916 35. Working collaboratively with my group makes me feel better student. .501 .941 36. Working collaboratively with my group increases my desire to learn. .565 .948 37. Working collaboratively with my group is better than working
individually.
.435 .967
38. Working collaboratively with my group makes my communication skills better.
.408 .938
39. Working collaboratively with my group encourages me to be more responsible.
.535 .945
40. Working collaboratively with my group creates better opportunity for my learning.
.366 .947
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Given those overall indicators, factor analysis was deemed to be factorable with all 40 questionnaire items.