Exploratory Factor Analysis

Interim analysis from an ongoing dissertation study. Data collection is still in progress, and this work is not published.

Status

Interim. The results here are based on the responses collected so far. They may change as more data comes in, and nothing here should be treated as final.

What is in this repository

File	What it is
Phase_3_analysis.jasp	JASP file with the analysis and all output tables
Item_Mapping.docx	Document comparing the expected item grouping with the factor results

A note on what has been removed

The survey items and the names of the constructs have been removed from everything in this repository. The instrument is still under development and is not yet published, so items are referred to only by their variable codes (for example Q9_1, Q10_6).

This means the analysis can be read and checked, but the instrument itself is not reproduced here.

Method

• 39 items, each answered on a 1–5 scale
• Sample: 239 completed responses, no missing values
• Software: JASP
• Extraction: principal axis factoring
• Rotation: oblimin (oblique)

Principal axis factoring was used because the items are not normally distributed, which is expected for Likert data. An oblique rotation was used because the dimensions were expected to be related rather than independent.

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Results

1. Descriptive statistics

All 39 items have 239 valid responses and no missing values. Every item uses the full 1–5 range.

Standard error of skewness is 0.157 and standard error of kurtosis is 0.314 for every item.

Item	Mean	SD	Skewness	Kurtosis	Shapiro-Wilk W	p
Q9_1	2.431	1.320	0.670	-0.707	0.853	< .001
Q9_2	2.778	1.318	0.360	-1.073	0.882	< .001
Q9_3	2.715	1.284	0.377	-0.945	0.892	< .001
Q9_4	1.828	1.092	1.243	0.736	0.754	< .001
Q9_5	2.548	1.208	0.521	-0.672	0.885	< .001
Q9_6	3.029	1.255	0.112	-1.004	0.907	< .001
Q9_7	3.498	1.263	-0.412	-0.971	0.881	< .001
Q10_1	2.916	1.178	0.257	-0.910	0.901	< .001
Q10_2	2.946	1.316	0.190	-1.183	0.891	< .001
Q10_3	2.335	1.211	0.835	-0.218	0.844	< .001
Q10_4	2.749	1.295	0.453	-0.917	0.879	< .001
Q10_5	2.259	1.170	1.021	0.300	0.820	< .001
Q10_6	2.598	1.289	0.487	-0.871	0.880	< .001
Q10_7	2.402	1.266	0.825	-0.304	0.841	< .001
Q10_8	1.933	1.179	1.231	0.614	0.766	< .001
Q10_9	2.598	1.246	0.391	-0.836	0.895	< .001
Q10_10	2.544	1.242	0.549	-0.662	0.882	< .001
Q10_11	1.874	1.042	1.446	1.922	0.762	< .001
Q10_12	2.715	1.217	0.335	-0.869	0.900	< .001
Q10_13	2.285	1.175	0.997	0.252	0.824	< .001
Q11_1	2.937	1.223	0.232	-1.025	0.897	< .001
Q11_2	2.251	1.179	0.990	0.232	0.827	< .001
Q11_3	2.042	1.137	1.198	0.788	0.795	< .001
Q11_4	2.318	1.202	0.728	-0.351	0.862	< .001
Q11_5	2.289	1.165	0.641	-0.458	0.869	< .001
Q11_6	2.590	1.270	0.411	-0.898	0.890	< .001
Q11_7	2.393	1.201	0.658	-0.439	0.873	< .001
Q11_8	2.498	1.152	0.438	-0.609	0.896	< .001
Q11_9	3.628	1.226	-0.609	-0.648	0.869	< .001
Q11_10	2.887	1.216	0.190	-0.949	0.908	< .001
Q11_11	2.013	0.981	1.349	2.035	0.783	< .001
Q12_1	2.326	1.001	0.778	0.412	0.863	< .001
Q12_2	2.264	1.120	0.588	-0.581	0.869	< .001
Q12_3	2.213	1.096	0.783	0.034	0.860	< .001
Q12_4	1.665	0.858	1.670	3.500	0.723	< .001
Q12_5	2.075	1.128	0.950	0.108	0.826	< .001
Q12_6	2.460	1.099	0.466	-0.469	0.895	< .001
Q12_7	2.226	1.049	0.815	0.355	0.860	< .001
Q12_8	2.523	1.236	0.647	-0.507	0.871	< .001

Normality. All 39 items return p < .001 on Shapiro-Wilk, so none is consistent with a normal distribution. This is expected for five-point Likert items and is why principal axis factoring was used rather than maximum likelihood.

By magnitude the departures are more modest. Seven items fall outside a skewness range of −1 to +1, and two items fall outside a kurtosis range of −2 to +2.

	Items outside range	Which
Skewness beyond ±1	7	Q9_4, Q10_5, Q10_8, Q10_11, Q11_3, Q11_11, Q12_4
Kurtosis beyond ±2	2	Q11_11, Q12_4

Q12_4 is the most extreme item on every distributional measure: the lowest mean (1.665), the smallest standard deviation (0.858), the highest skewness (1.670), the highest kurtosis (3.500) and the lowest Shapiro-Wilk W (0.723).

2. Factorability

Test	Result
Kaiser-Meyer-Olkin (overall MSA)	0.922
Bartlett's test of sphericity	χ² = 5193.286, df = 741, p < .001

Both tests pass comfortably. An overall MSA of 0.922 falls in the highest conventional band, and Bartlett rejects the hypothesis that the correlation matrix is an identity matrix.

Item-level measures of sampling adequacy:

Item	MSA	Item	MSA	Item	MSA	Item	MSA
Q9_1	0.922	Q10_4	0.946	Q11_1	0.944	Q11_11	0.920
Q9_2	0.952	Q10_5	0.953	Q11_2	0.927	Q12_1	0.892
Q9_3	0.943	Q10_6	0.949	Q11_3	0.924	Q12_2	0.812
Q9_4	0.848	Q10_7	0.937	Q11_4	0.947	Q12_3	0.800
Q9_5	0.920	Q10_8	0.834	Q11_5	0.834	Q12_4	0.811
Q9_6	0.938	Q10_9	0.817	Q11_6	0.965	Q12_5	0.691
Q9_7	0.918	Q10_10	0.947	Q11_7	0.957	Q12_6	0.729
Q10_1	0.919	Q10_11	0.881	Q11_8	0.869	Q12_7	0.927
Q10_2	0.930	Q10_12	0.940	Q11_9	0.943	Q12_8	0.951
Q10_3	0.943	Q10_13	0.951	Q11_10	0.932

Item MSA ranges from 0.691 (Q12_5) to 0.965 (Q11_6). Q12_5 is the only item below 0.70. The lowest values cluster in the Q12 block.

3. Number of factors

Three factors were retained. The scree plot with parallel analysis is included in the JASP file.

	SumSq. loadings	Proportion var.	Cumulative
Unrotated
Factor 1	12.743	0.327	0.327
Factor 2	3.510	0.090	0.417
Factor 3	1.366	0.035	0.452
Rotated
Factor 1	10.192	0.261	0.261
Factor 2	4.899	0.126	0.387
Factor 3	2.528	0.065	0.452

The three factors together explain 45.2% of the variance. After rotation the first factor accounts for 26.1%, the second 12.6% and the third 6.5%.

4. Factor loadings

Oblimin rotation. Loadings below approximately 0.40 are suppressed, so a blank cell is a small loading rather than a zero. Uniqueness is the proportion of an item's variance not explained by the three factors.

Item	Factor 1	Factor 2	Factor 3	Uniqueness
Q9_6	0.838			0.383
Q9_7	0.816			0.466
Q9_2	0.774			0.484
Q10_6	0.767			0.358
Q11_1	0.766			0.405
Q10_7	0.756			0.344
Q9_3	0.711			0.411
Q10_2	0.686			0.423
Q10_10	0.645			0.494
Q10_5	0.625			0.453
Q9_1	0.622			0.606
Q12_8	0.618			0.534
Q10_3	0.601			0.517
Q11_9	0.587			0.600
Q10_1	0.556			0.536
Q10_12	0.539			0.565
Q10_4	0.527			0.508
Q11_7	0.508			0.466
Q10_13	0.430		0.439	0.427
Q11_6	0.426			0.570
Q12_4		0.707		0.542
Q10_11		0.702		0.514
Q12_5		0.606		0.665
Q11_3		0.580		0.455
Q10_8		0.576		0.610
Q12_6		0.542		0.721
Q11_11		0.509		0.365
Q11_2		0.497		0.592
Q11_5		0.496		0.633
Q12_2		0.491		0.762
Q9_4		0.450		0.753
Q10_9		0.442		0.622
Q12_1		0.418		0.644
Q12_7			0.512	0.452
Q11_10			0.419	0.637
Q9_5				0.758
Q11_4				0.474
Q11_8				0.738
Q12_3				0.894

5. Summary of the solution

	Count
Items loading on Factor 1 only	19
Items loading on Factor 2	13
Items loading on Factor 3 only	2
Items loading on two factors	1
Items with no loading above the threshold	4
Total	39

Points to note:

• The three factors do not correspond to the four dimensions the instrument was designed around. Factor 1 draws items from all four.
• Factor 3 has only two items loading on it cleanly, which is below the usual minimum of three for a stable factor. It also explains the least variance at 6.5%.
• Q10_13 loads on two factors at almost the same strength: 0.430 on Factor 1 and 0.439 on Factor 3. Whether Factor 3 reaches three items depends on how this one item is assigned.
• Four items do not reach the threshold. Uniqueness distinguishes two situations among them: Q12_3 (0.894), Q9_5 (0.758) and Q11_8 (0.738) share very little with the rest of the set, while Q11_4 (0.474) has variance that is shared but spread across factors rather than concentrated in one.
• Q11_11 has the lowest uniqueness in the solution at 0.365 and Q12_3 the highest at 0.894.

Reuse

This is unpublished dissertation work. Please do not reuse or cite it without asking first.

Contact

This is work in progress and feedback is welcome — umerfarooq@tamu.edu