# Course Work Example: Exploratory Factor Analysis on the Data

2021-07-15
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Exploratory factor analysis is primarily used in testing the dimensionality or extracting the most meaningful or important subthemes of a particular variable based on the variability index (Henson & Roberts, 2006). This is majorly achieved through the factor analysis method of data reduction where principal component analysis iteration method and a rotation aspect of the researchers choice is presumed in order to establish (extract) the factors (subthemes or scores) that loads higher in the index or variable of interest (Hayton, Allen, & Scarpello, 2004). In this context, the experiment sought to examine the number of meaningful factors that were extracted from the subscale scores for the Weschler Intelligence Scale for Children using the PCA presuming no rotation, assuming varimax rotation and also the promax rotation. Prior to conducting the factor analysis, it was necessary to assess whether the test was statistically significant using the KMO and Bartletts test of sphericity as shown in table 1 below.

Table SEQ Table \* ARABIC 1: KMO and Bartletts test for subscale scores for the Weschler Intelligence Scale for Children

KMO and Bartlett's Test

Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .828

Bartlett's Test of SphericityApprox. Chi-Square 502.89

df55

Sig. .000

The KMO and Bartletts test of sphericity yielded a Kaiser-Meyer-Olkin Measure of Sampling Adequacy value of 0.828 which is weighed as a better while the Bartletts test of sphericity yielded x2 (55) = 502.89, p = .001 as depicted in table 1b above. Since the p<0.05 we reject the null hypothesis and conclude that the factor analysis correlational matrix thus the factor analysis or the principal component analysis can be statistically conducted. The test gives the statistical approval for exploratory analytical concepts (FA and PCA) subjection on the respective data (Conway & Huffcutt, 2003).

Firstly, the principal component analysis with no rotation was conducted for the Wechsler intelligence scale scores for the children in order to establish the most meaningful factors and the results were as presented in table 2 below.

Table SEQ Table \* ARABIC 2: Total variance explained by the subscale scores for the Weschler Intelligence Scale for Children with no rotation on the data

Total Variance Explained

Component Initial Eigenvalues Extraction Sums of Squared Loadings

Total % of Variance Cumulative % Total % of Variance Cumulative %

1 3.829 34.806 34.806 3.829 34.806 34.806

2 1.442 13.109 47.915 1.442 13.109 47.915

3 1.116 10.147 58.062 1.116 10.147 58.062

4 .890 8.092 66.153 5 .768 6.985 73.138 6 .633 5.753 78.891 7 .595 5.412 84.303 8 .522 4.749 89.051 9 .471 4.281 93.332 10 .419 3.806 97.138 11 .315 2.862 100.000 Extraction Method: Principal Component Analysis.

The analysis in table 2 above indicates the proportional variance of Weschler Intelligence Scale for Children index subscale scores can be explained by the retained factors (3 dimensional subscale scores). The subscales with higher contribution are Factor 1 (34.81%), factor 2 (13.11%) and factor 3 (10.15%) (Retained/Meaningful subscales) accounting for approximately 58.062% variance of the Weschler Intelligence Scale for Children index in this extraction method.

Exploratory Factor Analysis (Principal Components, with Varimax rotation) on the data

The principal component analysis with Varimax rotation was conducted for the Wechsler intelligence scale scores for the children in order to establish the most meaningful factors and the results were as presented in table 3 below.

Table 3: Total variance explained by the subscale scores for the Weschler Intelligence Scale for Children with Varimax rotation on the data

Total Variance Explained

Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative %

1 3.83 34.80 34.80 3.82 34.80 34.80 3.02 27.48 27.48

2 1.44 13.10 47.91 1.44 13.10 47.91 2.20 20.08 47.56

3 1.11 10.14 58.06 1.11 10.14 58.06 1.15 10.49 58.06

4 .89 8.09 66.15 5 .76 6.98 73.13 6 .63 5.75 78.89 7 .59 5.41 84.30 8 .52 4.74 89.05 9 .47 4.28 93.33 10 .41 3.80 97.13 11 .31 2.86 100.00 Extraction Method: Principal Component Analysis.

The table 3 analysis above indicates that the proportional variance of Weschler Intelligence Scale for Children index subscale scores can be explained by the retained factors (3 dimensional subscale scores). The subscales with higher contribution are Factor 1 (27.48%), factor 2 (20.08%) and factor 3 (10.49%) (Retained/Meaningful subscales) accounting for approximately 58.062% variance of the Weschler Intelligence Scale for Children index in this extraction method.

Exploratory Factor Analysis (Principal Components, with Promax rotation) on the data

The principal component analysis with Promax rotation was conducted for the Wechsler intelligence scale scores for the children in order to establish the most meaningful factors and the results were as presented in table 4 below.

Table 4: Total variance explained by the subscale scores for the Weschler Intelligence Scale for Children with Promax rotation on the data

Total Variance Explained

Component Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared LoadingsaTotal % of Variance Cumulative % Total % of Variance Cumulative % Total

1 3.829 34.806 34.806 3.829 34.806 34.806 3.485

2 1.442 13.109 47.915 1.442 13.109 47.915 2.689

3 1.116 10.147 58.062 1.116 10.147 58.062 1.159

4 .890 8.092 66.153 5 .768 6.985 73.138 6 .633 5.753 78.891 7 .595 5.412 84.303 8 .522 4.749 89.051 9 .471 4.281 93.332 10 .419 3.806 97.138 11 .315 2.862 100.000 Extraction Method: Principal Component Analysis.

a. When components are correlated, sums of squared loadings cannot be added to obtain a total variance.

The analysis in table 4 above indicates the proportional variance of Weschler Intelligence Scale for Children index subscale scores can be explained by the retained factors (3 dimensional subscale scores). The subscales with higher contribution are Factor 1 (34.81%), factor 2 (13.11%) and factor 3 (10.15%) (Retained/Meaningful subscales) accounting for approximately 58.062% variance of the Weschler Intelligence Scale for Children index in this extraction method.

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References

Conway, J. M., & Huffcutt, A. I. (2003). A Review and Evaluation of Exploratory Factor Analysis Practices in Organizational Research. Organizational Research Methods, 6(2), 147-168. Doi: 10.1177/1094428103251541

Hayton, J. C., Allen, D. G., & Scarpello, V. (2004). Factor Retention Decisions in Exploratory Factor Analysis: a Tutorial on Parallel Analysis. Organizational Research Methods, 7(2), 191-205. Doi: 10.1177/1094428104263675

Henson, R. K., & Roberts, J. K. (2006). Use of Exploratory Factor Analysis in Published Research. Educational and Psychological Measurement, 66(3), 393-416. Doi: 10.1177/0013164405282485

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