Factorial analysis of the revised OGE

The preliminary analysis seen above led to the removal of constructs and suppression of particular items from specific constructs. The means and standard deviations of these 19 proposed items for a revised version of the OGE, one which would be adequate for this particular sample, can be seen below (Table 32).

Nonetheless, these values denote a wide dispersion (see Figure 14) signalling a lack of consensus amongst the answers given. This lack of consensus could result in diminishing the likelihood of reaching any significant conclusions. Hence, a statistical analysis was required to verify whether these proposed items could be used regardless of this observed dispersion.

Table 32

Means and Variations of 19 proposed items for a Revised OGE Mean Variance Skewness

Statistic Statistic Statistic Std. Error

q2 2.69 1.427 .227 .230

q9 4.07 1.132 -.985 .230

q14 4.48 .729 -2.284 .230

q15 4.35 .616 -1.417 .230

q19 2.87 1.268 .059 .230

q24 3.75 .925 -.033 .230

q30 3.96 1.081 -.924 .230

q31 2.95 1.226 -.180 .230

q3rec 2.69 1.830 .265 .230

q5rec 3.90 1.412 -.873 .230 q12rec 3.49 1.775 -.419 .230 q16rec 4.26 .801 -1.252 .230 q26rec 3.97 1.476 -.978 .230 q27rec 3.45 1.223 -.360 .230 q28rec 3.66 .978 -.322 .230 q21rec 2.41 1.161 .374 .230

q20rec 2.84 .890 .469 .230

q6rec 3.39 1.635 -.369 .230

q22 2.83 1.704 .050 .230

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Although the items did not demonstrate a normal distribution, independently of the p-value of the researcher, Analysis of the Mardia's (1970) multivariate asymmetry Skewness did not result in a strong asymmetry within the distribution (Table 33), enabling the usage of the 19 proposed items.

Table 33

Analysis of the Mardia's (1970) multivariate asymmetry skewness of the 19 proposed Items for a Revised OGE

Coefficient Statistic df P Skewness 105.422 1932.731 1330 1.0000 Skewness corrected for small sample 105.422 1990.822 1330 1.0000

Maximum Likelihood (ML) was used to extract factors. Maximum Likelihood

“aims to find the parameter values that make the observed data most likely (or conversely maximise the likelihood of the parameters given the data” (Brown, 2006, p.75).

Figure 14. Mean and Variance Statistics of 19 proposed Items for a Revised OGE

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Exploratory Factor Analysis (EFA) is a highly used statistical method in the creation, assessment and improvement of scales in the Social Sciences field and even more so in Psychology (Floyd & Widaman, 1995). As several anomalies were found in the psychometric study of the scale (as was confirmed by Gagné, 2018), it was important to consider regrouping the items differently. For a new structure to be developed, the EFA was needed in order to identify the underlying relationships between the measured variables (Norris & Lecavalier, 2009).

The implementation of the EFA confirmed the feasibility of dividing the data matrix into factors. The assessment was carried out using two methods; the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy and Bartlett’s test of sphericity.

According to Pasquali (1999) both tests revealed statistically favourable values (Table 34). KMO was found to be 0.767 and the Barlett test (with levels of significance p >

0.05 resulted in a value of 721.8 (p=0.000). These results demonstrate that the items can be separated into factors.

Table 34

Kaiser-Meyer-Olkin (KMO) and Bartlett’s Test of the 19 proposed items for a Revised OGE

Determinant of the matrix = 0.000834779746694 Bartlett's statistic = 721.8 (df = 171; P = 0.000010) Kaiser-Meyer-Olkin (KMO) test = 0.76724 (fair)

In order to determine what factors need to be retained, two methods were used:

the Hull method as well as the Kaiser-Guttman criteria more known as eigenvalue > 1 (Patil et al., 2008). Despite the latter suggesting the existence of seven factors, goodness of fit statistics (0.975) and degrees of freedom of each of the models shed light on the possibility of a more favourable solution, one which supported using only four factors (Table 35).

119 Table 35

Statistics and Goodness of Fit of the Revised OGE Root Mean Square Error of Approximation (RMSEA)

= 0.074; (between 0.050 and 0.080: fair)

Comparative Fit Index (CFI) = 0.947; (between 0.920 and 0.950: fair)

Goodness of Fit Index (GFI) = 0.975

This solution was reinforced by the data shown on Table 36 where the explained proportion of variance significantly reduced from the fourth to the fifth factor. Hence, four factors were retained which explain 56.53% of the total variance. The first factor explains 26% of the variance, the second factor 14%, the third factor explains 9.8% and the fourth explains 6.7%.

Table 36

Variance based on eigenvalues – Total Variance Explained for the Revised OGE Variable Eigenvalue Proportion of

variance

Cumulative Proportion of variance 1 6.50069 0.26091 0.26091 2 3.48126 0.13972 0.40063 3 2.44755 0.09823 0.49886 4 1.65700 0.06650 0.56536 5 1.53761 0.06171

6 1.35131 0.05423 7 1.22140 0.04902 8 0.89586 0.03596 9 0.84197 0.03379 10 0.75037 0.03012 11 0.72713 0.02918 12 0.66319 0.02662 13 0.58395 0.02344 14 0.51934 0.02084 15 0.45525 0.01827 16 0.39213 0.01574 17 0.37329 0.01498 18 0.32797 0.01316 19 0.18860 0.00757

(loadings lower than absolute 0.300 omitted)

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The implementation of the Factorial Analysis in its initial matrix did not facilitate the interpretation of the extracted factors; there was more than one situation where the contribution of the variables on the factor was unclear. In order to give more loading to the factors, a rotation of axes was carried out. This had the objective of simplifying factor extraction. After reviewing the literature, an oblique rotation method referred to as Promax was selected. Other researchers (Tirri, Tallent-Runnels, Adames, Yuen, & Patrick, 2002) have also opted for a similar data analysis to discern the main factors in Gagné and Nadeau’s (1991) attitude scale. This method allows the new axes to take any position in the factor space and allows for gains in simplicity in interpretation (Hair et al. 2006).

Loading values were found to be weak in Question 24 (0.324) to very strong in Question 31 (0.977) (Table 37). Both Question 15 and Question 24 had inferior loadings to 0.5. but were maintained in order to maintain the original structure of the scale.

Table 37

Rotated Loading Matrix – Promax for the Revised OGE

F1 F2 F3 F4

Q24 0.324 Q15 0.411 Q16 0.579

Q9 0.660

Q14 0.818

Q6 0.599

Q20 0.611

Q2 0.747

Q21 0.748

Q12 0.627

Q30 0.641

Q26 0.646

Q28 0.666

Q27 0.669

Q3 0.681

Q5 0.798

Q19 0.743

Q22 0.921

Q31 0.977

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Based on the factorial analysis, correlations among the variables and the review of the literature as well as taking into consideration the original conceptualisation of the OGE, below is a statistically more robust and revised structure for Secondary teachers of English in Portugal.

Needs and support (Table 38): This subscale consists of five items and measures teachers’ beliefs in the needs of gifted students and their support for adequate specialised services for this sub-population of children. High scores indicate positive attitudes towards the gifted.

Table 38

Needs and support

Q9 Gifted children are often bored in school.

Q14 The specific educational needs of the gifted are too often ignored in our schools.

Q15 The gifted need special attention in order to fully develop their potential Q16 (rec) Our schools are already adequate in meeting the needs of the gifted.

Q24 In order to progress, a society must develop the talents of gifted individuals to a maximum.

Resistance to objections (Table 39): This subscale, entailing 7 items, focussed on the measurement of teachers’ objections based on their ideologies. Positive attitudes denoted favourable attitudes towards the gifted and their education.

Table 39

Resistance to objections

Q3(rec) Children with difficulties have the most need of special educational services.

Q5(rec) Special educational services for the gifted are a mark of privilege.

Q12(rec) We have a greater moral responsibility to give special help to children with difficulties than to gifted children.

Q26(rec) Taxpayers should not to pay for special education for the minority of children who are gifted.

Q27(rec) Average children are the major resource of our society; so, they should be the focus of our attention.

Q28(rec) Gifted children might become vain or egoistical if they are given special attention.

Q30 Since we invest supplementary funds for children with difficulties, we should do the same for the gifted.

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Rejection (Table 40): Attitudes towards the isolation of gifted persons by others in the immediate environment were measured using the following three questions. High scores indicated positive attitudes towards the gifted population.

Table 40 Rejection

Q19 A child who has been identified as gifted has more difficulty in making friends.

Q22 Some teachers feel their authority threatened by gifted children.

Q31 Often children are rejected because people are envious of them.

Ability Grouping (Table 41): This subscale measures respondents’ attitudes towards special homogenous groups or schools with the below four items. Positive attitudes denoted positive attitudes towards homogenous grouping for the gifted.

Table 41

Ability grouping

Q2 The best way to meet the needs of the gifted is to put them in special classes.

Q6(rec) When the gifted are put in special classes, the other children feel devalued.

Q20 (rec) Gifted children should be left in regular classes, since they serve as an intellectual stimulant for the other children.

Q21 (rec) By separating students into gifted and their groups, we increase the labelling of children as strong-weak, good-less good, etc.

The Needs and Support construct consisted of five items (α = 0.682), and Resistance to Objections consisted of seven items (α = 0.713). Cronbach’s Alphas for the three items in the Rejection construct and the four items in the Ability Grouping were observed to have an internal consistency of 0.742 and 0.630 respectively.

III. 2.2. Reliability of the Revised Classroom Practices Questionnaire