Factor analysis is one of the most powerful and one of the most frequently misunderstood analytical techniques in Kenyan postgraduate research. It appears across disciplines — management, education, public health, psychology, agriculture, economics — wherever a study uses a multi-item questionnaire to measure constructs that cannot be observed directly. Yet in practice, many students run SPSS factor analysis output, paste the tables into Chapter 4, and report a few numbers without understanding what any of them mean, what decisions they required, or how a panel examiner will probe their choices.
Factor analysis requires more researcher judgment than almost any other statistical procedure. Every step — from deciding whether your data is suitable, to choosing an extraction method, to determining how many factors to retain, to selecting a rotation method, to deciding which items to remove — involves a decision that your panel can and will interrogate. At Tobit Research Consulting, we have helped hundreds of Masters and PhD students across KU, UoN, JKUAT, MKU, Strathmore, Laikipia, Egerton, and Moi navigate these decisions correctly. This guide gives you the complete framework.
Table of Contents
- What Factor Analysis Is — and Why Kenyan Postgraduate Research Uses It
- EFA, PCA, and CFA: Three Related but Distinct Techniques — and How to Choose
- Sample Size Requirements for Factor Analysis
- Testing Data Suitability: KMO and Bartlett’s Test of Sphericity
- Extraction Methods: Principal Axis Factoring vs. Principal Component Analysis
- How Many Factors to Retain: Eigenvalues, Scree Plot, and Variance Explained
- Rotation Methods: Varimax, Direct Oblimin, and When to Use Each
- Reading the Rotated Factor Matrix: Loadings, Communalities, and Cross-Loadings
- Item Retention and Removal Decisions: The Rules and the Judgment
- Naming and Interpreting Your Extracted Factors
- Running EFA in SPSS: Complete Step-by-Step Procedure
- Reporting Factor Analysis in APA 7th Edition — Full Template
- Panel Questions on Factor Analysis — and How to Answer Each One
- How Tobit Research Consulting Can Help
1. What Factor Analysis Is — and Why Kenyan Postgraduate Research Uses It
Factor analysis is a statistical technique for identifying the underlying structure in a set of observed variables. When researchers measure constructs that cannot be observed directly — employee motivation, organisational performance, perceived service quality, financial literacy, leadership style — they typically do so through multiple questionnaire items, each designed to capture a different facet of the underlying construct. Factor analysis answers the question: Do these items actually cluster together in the way the researcher’s theory predicts?
In practice, factor analysis serves three distinct purposes in Kenyan postgraduate research. First, it is used as a construct validity test — demonstrating that the items in each subscale of your instrument genuinely measure the same underlying construct and that different subscales are statistically distinguishable from each other. Second, it is used for data reduction — replacing a large number of correlated items with a smaller number of interpretable factor scores that can be used in subsequent analyses. Third, it is used for scale development and refinement — identifying which items perform well and which should be removed or revised when developing a new measurement instrument.
The core logic: If ten questionnaire items all measure “employee commitment,” they should all correlate with each other and, when analysed together, should load onto a single common factor. If some items load on a separate factor, this reveals that your questionnaire is actually measuring two or more distinct constructs — which may require you to revise your conceptual framework, rename your constructs, or redesign your instrument. Factor analysis is the statistical test that makes this visible.
2. EFA, PCA, and CFA: Three Related but Distinct Techniques — and How to Choose
One of the most common sources of confusion in Kenyan postgraduate factor analysis work is the conflation of three related but distinct techniques: Exploratory Factor Analysis (EFA), Principal Component Analysis (PCA), and Confirmatory Factor Analysis (CFA). Using the wrong term — or worse, using one technique while claiming to use another — is a panel correction waiting to happen. The choice between them must be driven by your research purpose, not by whichever option appears first in the SPSS menu.
| Technique | Purpose | What It Assumes | When to Use It | Software |
|---|---|---|---|---|
| Exploratory Factor Analysis (EFA) | Discover the underlying factor structure of a set of items when the structure is unknown or uncertain | No prior theory about factor structure; factors are latent — they cause the item responses (common factor model) | When developing or adapting an instrument; when you are unsure whether your subscales hold together as theorised; when validating a questionnaire in a new population or context | SPSS (Analyze → Dimension Reduction → Factor) |
| Principal Component Analysis (PCA) | Reduce a large number of correlated variables into a smaller number of uncorrelated components that capture maximum variance | Components are mathematical summaries of the data — they are not assumed to be latent causes; PCA accounts for all variance including unique and error variance | When the goal is data reduction for subsequent analysis (e.g., creating composite index scores); when you are not making claims about latent constructs. Not appropriate as a validity test for construct measurement | SPSS (same menu as EFA — select Principal Components as extraction method) |
| Confirmatory Factor Analysis (CFA) | Test whether a specific, theoretically specified factor structure fits the observed data | You already know (from theory or prior EFA) how many factors exist and which items load on each; tests model fit against the data | When using an established scale; at PhD level for construct validity; when testing measurement invariance across groups; when your conceptual framework specifies a precise factor structure | SPSS AMOS, R (lavaan), LISREL, EQS — not standard SPSS |
At Masters level at KU, UoN, JKUAT, and MKU, EFA run in SPSS is the standard approach for construct validation when using an adapted or newly developed questionnaire. If you are using a well-established validated scale from prior research without modification, you may reference the original validation study rather than re-running EFA — but you must still run reliability analysis on your own sample’s data. At PhD level, and for Masters studies at institutions with more demanding measurement standards (such as Strathmore University Business School), CFA using SPSS AMOS or R is increasingly expected as the gold standard for construct validity, with model fit indices reported alongside factor loadings. Know your institution’s expectations before deciding which approach to take.
3. Sample Size Requirements for Factor Analysis
Factor analysis is sensitive to sample size. Insufficient sample sizes produce unstable factor solutions that do not replicate — meaning the factors you extract from your data may be an artefact of your specific sample rather than a real reflection of the underlying construct structure. Your panel will ask about your sample size relative to the number of items, and you need to have a principled answer.
The most widely cited sample size guidance for EFA comes from Comrey and Lee (1992), who described N = 100 as poor, N = 200 as fair, N = 300 as good, N = 500 as very good, and N = 1,000 as excellent. However, the number of items relative to sample size is equally important: with more items, you need a larger sample for stable factor loadings. A study with 30 items and 150 respondents (5:1 ratio) is at the minimum floor; the same 30 items with 300 respondents (10:1 ratio) produces a more reliable solution. Where your sample is smaller than ideal, acknowledge this as a limitation but proceed if the 5:1 minimum is satisfied — factor analysis with small samples is still better than not validating your instrument at all.
4. Testing Data Suitability: KMO and Bartlett’s Test of Sphericity
Before running factor analysis, you must demonstrate that your data is suitable for the procedure — specifically, that the inter-item correlations in your dataset are large enough to make factor extraction meaningful. Two statistics are used for this: the Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy and Bartlett’s Test of Sphericity. Both are automatically produced by SPSS when you run the factor analysis procedure, and both must be reported in your Chapter 4.
The KMO statistic ranges from 0 to 1 and indicates the proportion of variance in your items that is common variance — that is, variance potentially caused by underlying factors. A KMO value close to 1.0 means that patterns of correlations are compact and therefore factor analysis should yield distinct and reliable factors. Kaiser (1974) described the interpretation of KMO values as follows: values in the 0.90s are “marvelous”; 0.80s are “meritorious”; 0.70s are “middling”; 0.60s are “mediocre”; 0.50s are “miserable”; and values below 0.50 are “unacceptable.” In practice, a KMO of 0.60 or above is the minimum for proceeding with factor analysis; 0.70 or above is recommended; and values of 0.80 and above indicate genuinely strong factorability. If your overall KMO is below 0.60, examine the individual item KMO values (Anti-Image Correlation matrix diagonal values) and remove items with values below 0.50 — these items have insufficient shared variance with the other items to contribute meaningfully to a factor structure.
Bartlett’s Test of Sphericity tests the null hypothesis that the correlation matrix of your items is an identity matrix — meaning all items are uncorrelated with each other. If all items are uncorrelated, factor analysis is meaningless because there are no common patterns to extract. A significant result from Bartlett’s test (p < .05) rejects this null hypothesis, confirming that the correlations between items are sufficiently large to warrant factor analysis. In practice, for samples above 200, Bartlett’s test is almost always significant regardless of the actual correlation structure — it is very sensitive to sample size. Do not rely on Bartlett’s test alone; always interpret it alongside the KMO statistic. In your reporting, state both: the chi-square statistic, degrees of freedom, and p-value for Bartlett’s test, and the KMO value.
“Prior to factor extraction, the suitability of the data for factor analysis was assessed. The Kaiser-Meyer-Olkin measure of sampling adequacy was .83, exceeding the recommended threshold of .60 (Kaiser, 1974), indicating that the pattern of correlations was compact and factor analysis was appropriate. Bartlett’s test of sphericity was statistically significant, χ²(231) = 1,847.34, p < .001, confirming that the inter-item correlations were sufficiently large for factor analysis to be conducted (Field, 2018).”
5. Extraction Methods: Principal Axis Factoring vs. Principal Component Analysis
When you open the SPSS Factor Analysis procedure, you must choose an extraction method. The two most commonly used are Principal Axis Factoring (PAF) and Principal Component Analysis (PCA). The choice between them is theoretically significant — and your panel may ask you to justify it.
PAF is based on the common factor model, which assumes that the observed item responses are caused by a set of underlying (latent) factors plus unique variance specific to each item. It extracts only the common variance shared among items — it does not attempt to account for the unique variance in each variable. This makes PAF the theoretically appropriate method when your purpose is construct validity — you want to identify the latent constructs causing your items’ responses. Most methodologists recommend PAF (or Maximum Likelihood extraction if data are normally distributed) for EFA in social science research. In SPSS, select PAF from the Extraction Method dropdown.
PCA extracts components that account for the maximum total variance in the item set — including unique variance and measurement error, not just common variance. PCA components are mathematical summaries of the data, not latent constructs. They do not represent underlying causes of item responses in the way that factors in a common factor model do. PCA is appropriate when your goal is data reduction — creating composite scores or indices from a set of correlated variables — not when you are making claims about the underlying construct structure of a measurement instrument. A common error in Kenyan postgraduate dissertations is running PCA and then describing the results as confirming “construct validity” — this conflates two different analytical purposes and two different statistical models, and it will draw a panel correction.
The most common factor analysis error in Kenyan dissertations: Running Principal Components Analysis (PCA), producing a rotated component matrix, and describing the output as “Exploratory Factor Analysis confirming construct validity.” PCA and EFA are not the same. PCA does not test the common factor model. If your purpose is construct validity, use Principal Axis Factoring (PAF) as your extraction method and describe the procedure accurately as EFA.
6. How Many Factors to Retain: Eigenvalues, Scree Plot, and Variance Explained
Determining how many factors to extract is the most consequential decision in EFA — and the one that requires the most researcher judgment. SPSS will produce multiple statistics to guide this decision, but none of them mechanically determines the right answer. You must triangulate across multiple criteria and apply theoretical knowledge of your constructs to make a defensible final decision.
An eigenvalue represents the amount of variance in the total item set explained by a given factor. Under the Kaiser criterion (Kaiser, 1960), factors with eigenvalues greater than 1.0 are retained — the logic being that a factor should explain at least as much variance as a single observed variable (which by standardisation has a variance of 1.0). This criterion is the SPSS default and produces a factor solution automatically. However, the Kaiser criterion is widely criticised for overextracting factors — it frequently retains more factors than are theoretically meaningful, particularly in large item sets. Use it as a starting point, not a final answer. Always complement it with the scree plot.
A scree plot graphs the eigenvalue (y-axis) of each factor against its factor number (x-axis), producing a descending curve. The number of factors to retain is determined by identifying the point of inflection — the “elbow” in the curve — where the slope changes from steep to relatively flat. Factors to the left of (and including) the elbow are retained; factors below the flat portion add little to the explanation of variance and are discarded. When the scree plot elbow and the Kaiser criterion agree — both suggesting the same number of factors — you have strong grounds for your decision. When they disagree, the scree plot is generally considered the more theoretically informative criterion. Use both and note any discrepancy.
The Total Variance Explained table in SPSS shows the cumulative percentage of variance in the item set accounted for by the retained factors. As a general rule, the retained factor solution should explain at least 50% of the total variance (Streiner, 1994; Field, 2018). Solutions explaining less than 50% suggest that the extracted factors are not adequately capturing the shared structure of the items. In some fields and with complex constructs, 60% or higher is the expected standard. Report both the individual variance explained by each factor and the cumulative total for the retained solution.
Parallel analysis is considered the most rigorous criterion for factor retention. It compares your observed eigenvalues to eigenvalues generated from randomly simulated data with the same number of items and participants. Factors whose observed eigenvalues exceed the corresponding randomly generated eigenvalues are retained — those that do not are rejected as no more meaningful than random noise. Parallel analysis consistently outperforms the Kaiser criterion in accuracy and tends to prevent over-extraction. It is not available in standard SPSS but can be run using an external macro (O’Connor, 2000) or in R. At PhD level and in rigorous Masters research, parallel analysis is increasingly expected at Kenyan institutions where supervisors are active researchers themselves.
7. Rotation Methods: Varimax, Direct Oblimin, and When to Use Each
After factor extraction, the initial factor solution is mathematically indeterminate — many different rotations of the factor axes would fit the data equally well. Rotation is applied to simplify and clarify the factor structure by redistributing the variance among factors so that each item loads highly on one factor and as near to zero as possible on all others. This produces the “simple structure” ideal that makes factors interpretable. The choice of rotation method is a theoretical decision that your panel will probe.
| Rotation Method | Type | Assumption | When to Use | SPSS Output Table |
|---|---|---|---|---|
| Varimax | Orthogonal | Factors are uncorrelated with each other | When your theoretical framework treats the constructs as distinct and independent — e.g., measuring separate dimensions of a service quality framework that are theoretically unrelated | Rotated Component/Factor Matrix |
| Direct Oblimin | Oblique | Factors are allowed to correlate | When your constructs are theoretically related — which is the case in most social science research. If you are measuring constructs in the same broad domain (e.g., different dimensions of leadership, or different components of organisational culture), they are likely to correlate. This is the more realistic and more commonly appropriate choice for Kenyan postgraduate social science research. | Pattern Matrix (primary loadings) + Structure Matrix (total correlations) |
| Promax | Oblique | Factors are allowed to correlate | An alternative to Direct Oblimin; begins with a Varimax solution and then allows factors to correlate. Often produces similar results to Oblimin; Oblimin is generally preferred for scale development work | Pattern Matrix + Structure Matrix |
| Quartimax | Orthogonal | Factors are uncorrelated | Maximises loadings of variables on a single factor rather than spreading variance across factors — tends to produce a large general factor. Rarely used in Kenyan postgraduate research | Rotated Factor Matrix |
The practical default for most Kenyan postgraduate studies: If your constructs are plausibly related — which they usually are in business, management, education, and health research — use an oblique rotation (Direct Oblimin or Promax). If the correlation between factors turns out to be low (below r = .32), an orthogonal solution would have been equally appropriate; but choosing oblique rotation when factors are actually correlated is correct methodology, while choosing orthogonal rotation and ignoring real inter-factor correlations is a methodological error. When in doubt, choose oblique and report the factor correlations.
8. Reading the Rotated Factor Matrix: Loadings, Communalities, and Cross-Loadings
The rotated factor matrix (or Pattern Matrix for oblique rotations) is the central output of EFA — it is what you will spend most time interpreting and reporting. For each item, the matrix shows the factor loading on each extracted factor. Understanding what these loadings mean and what thresholds to apply is essential for making defensible item retention decisions.
A factor loading is the correlation between an item and a factor (for orthogonal rotations) or the unique contribution of the item to the factor after controlling for other factors (for oblique rotation Pattern Matrix). Loadings range from −1 to +1. The minimum acceptable loading for an item to be considered to clearly belong to a factor is widely debated, but the most commonly applied thresholds in postgraduate research are: ≥ 0.32 as the absolute minimum (accounts for at least 10% of shared variance — Tabachnick & Fidell, 2019); ≥ 0.40 as the preferred minimum for a clean, interpretable solution; and ≥ 0.50 for a strong loading that unambiguously assigns an item to a factor. For a sample of 200, loadings of 0.40 are significant at the 0.01 level (Stevens, 2012). Items that do not load above your chosen threshold on any factor should be removed.
Communality (h²) is the proportion of variance in each item that is explained by the extracted factors collectively. It ranges from 0 to 1, with values closer to 1 indicating that the item shares substantial variance with the factor structure. The widely accepted minimum communality threshold is h² ≥ 0.30, with some methodologists (Hair et al., 2010) recommending h² ≥ 0.50 for a stable solution. Items with communalities below 0.30 are not well explained by any of the extracted factors — they contain mostly unique variance — and should be considered for removal. Check the Communalities table (Extraction column) in the SPSS output for every item. Do not confuse the Initial and Extraction communality values — only the Extraction communalities (after factors have been identified) are relevant for your decisions.
A cross-loading occurs when an item loads substantially on two or more factors simultaneously — meaning the item cannot be cleanly assigned to a single construct. The standard for identifying a problematic cross-loading is when an item has loadings of ≥ 0.32 on two or more factors. When a cross-loading is identified, you have three options: remove the item; retain it on the factor with the highest loading if the difference between its primary and secondary loading exceeds .20 (and the cross-loading can be theoretically explained); or revise the item wording and re-pilot if time permits. Cross-loadings are not always a problem — in some cases, they genuinely reflect items that measure the overlap between two related constructs, which has theoretical meaning. But they must be acknowledged and addressed, not silently ignored.
9. Item Retention and Removal Decisions: The Rules and the Judgment
Factor analysis is an iterative process. Rarely does the initial solution produce a perfectly clean structure where every item loads strongly on exactly one factor with no cross-loadings and no low communalities. In practice, you will need to remove problematic items and re-run the analysis — sometimes multiple times — until a clean, interpretable, theoretically coherent solution is achieved. The following decision rules guide this process.
10. Naming and Interpreting Your Extracted Factors
Once a clean factor solution has been achieved, each factor must be named and interpreted. Factor naming is a creative, theoretically grounded act — the name you assign to a factor should capture the meaning shared by the items that loaded on it. This step is where your substantive knowledge of the research area matters more than your statistical knowledge.
To name a factor, examine the items with the highest loadings on it (typically the three to five items with the strongest primary loadings). What do they have in common? What theme or construct do they collectively represent? The name should be: specific enough to distinguish this factor from others; consistent with established terminology in your research field; and defensible in terms of the theoretical framework guiding your study. If a factor that was supposed to measure “transformational leadership” actually contains items about leader-member exchange and task delegation, the factor may be better named “relational leadership” or “delegation-oriented leadership” — and your interpretation must acknowledge the divergence from your original conceptualisation.
11. Running EFA in SPSS: Complete Step-by-Step Procedure
- Access the Factor Analysis procedure. Go to Analyze → Dimension Reduction → Factor. Move all items belonging to the subscale (or full instrument, if running a single EFA) into the Variables box. Do not mix items from different conceptual subscales if you are testing whether those subscales hold up as distinct factors — move all items in together and let the factor solution reveal the structure.
- Set Descriptives. Click the Descriptives button. Under Statistics, tick Initial solution. Under Correlation Matrix, tick KMO and Bartlett’s test of sphericity, and also tick Anti-image (to see individual item KMO values). Click Continue.
- Set Extraction method. Click the Extraction button. From the Method dropdown, select Principal Axis Factoring (recommended for construct validity testing). Under Analyse, select Correlation matrix. Under Extract, select Eigenvalues over 1 initially (you will compare this to the scree plot). Tick Unrotated factor solution and Scree plot. Click Continue.
- Set Rotation method. Click the Rotation button. Select Direct Oblimin (or Varimax if you have strong theoretical grounds for factor independence). Under Display, tick Rotated solution and Loading plot(s). Click Continue.
- Request Scores and Options. Click the Options button. Under Coefficient Display Format, tick Suppress absolute values less than .40 — this prevents small, irrelevant loadings from cluttering your output, making the pattern matrix easier to read. Click Continue. Then click OK.
- Review the output tables in order: (1) KMO and Bartlett’s Test — confirm suitability. (2) Communalities — note any items with extraction communality below 0.30. (3) Total Variance Explained — note how many factors have eigenvalues above 1 and the cumulative variance. (4) Scree Plot — identify the elbow point. (5) Pattern Matrix — identify primary loadings, cross-loadings, and items with no strong loading. (6) Factor Correlation Matrix — check whether factors are actually correlated (if they are close to zero, an orthogonal solution would have been equally appropriate).
- Make item removal and re-run decisions iteratively until the solution is clean: all retained items have primary loadings ≥ 0.40, communalities ≥ 0.30, no significant cross-loadings, and at least three items per factor.
12. Reporting Factor Analysis in APA 7th Edition — Full Template
Data suitability paragraph: “An exploratory factor analysis using Principal Axis Factoring with Direct Oblimin rotation was conducted on the 22 items of the organisational performance instrument. Prior to extraction, data suitability was confirmed: the Kaiser-Meyer-Olkin measure of sampling adequacy was .81, exceeding the recommended minimum of .60 (Kaiser, 1974), and Bartlett’s test of sphericity was statistically significant, χ²(231) = 2,104.17, p < .001, indicating sufficient inter-item correlations for factor analysis (Field, 2018).”
Factor retention paragraph: “Initial extraction produced four factors with eigenvalues exceeding 1.0 (7.42, 2.81, 1.94, 1.22), collectively explaining 61.4% of the total variance. Inspection of the scree plot supported a four-factor solution, with the curve levelling after the fourth factor. Principal Axis Factoring with Direct Oblimin rotation was therefore retained with four factors.”
Item removal paragraph: “Two items were removed during the iterative refinement process. Item 7 (‘The organisation meets its annual budget targets’) exhibited a communality of .21, below the accepted threshold of .30 (Field, 2018), and was removed. Item 14 (‘Staff morale is consistently high’) cross-loaded on Factors 1 and 3 (loadings of .48 and .44 respectively), with an insufficient primary-secondary difference of .04; it was removed as it could not be unambiguously assigned to a single construct. Re-analysis of the remaining 20 items produced a clean four-factor solution with all item loadings exceeding .40, communalities ranging from .31 to .76, and no cross-loadings above .32.”
Factor description paragraph: “The four retained factors explained 63.2% of total variance. Factor 1 (six items, eigenvalue = 7.18) was labelled Financial Performance, capturing items related to revenue growth, profitability, and cost efficiency. Factor 2 (five items, eigenvalue = 2.74) was labelled Customer Performance, reflecting items on client retention, satisfaction, and new market acquisition. Factor 3 (five items, eigenvalue = 1.89) was labelled Internal Process Efficiency, comprising items on operational quality and cycle time. Factor 4 (four items, eigenvalue = 1.19) was labelled Learning and Innovation, capturing staff development and process improvement items. The factor structure aligns with the Balanced Scorecard framework (Kaplan & Norton, 1996) underpinning the study’s conceptual framework.”
Reliability follow-up: “Following EFA, Cronbach’s Alpha was computed for each factor-derived subscale to confirm internal consistency. Alpha coefficients were: Financial Performance, α = .83; Customer Performance, α = .79; Internal Process Efficiency, α = .77; Learning and Innovation, α = .74. All values met the accepted minimum threshold of .70 (Nunnally & Bernstein, 1994).”
13. Panel Questions on Factor Analysis — and How to Answer Each One
| Panel Question | What They Are Testing | How to Prepare Your Answer |
|---|---|---|
| “Why did you conduct factor analysis in your study?” | Whether your use of factor analysis was purposeful — not a default procedure applied to all questionnaire data | State the purpose: to establish construct validity by testing whether the items in each subscale cluster as theoretically predicted, and to confirm that different constructs are statistically distinguishable from each other |
| “What is the difference between EFA and CFA?” | Whether you understand the distinction between exploratory and confirmatory approaches | EFA is data-driven: it discovers factor structure without pre-specifying it. CFA is theory-driven: it tests whether a specified factor structure fits the data. EFA is appropriate when the structure is unknown or uncertain; CFA tests an established model. Run in SPSS (EFA) vs. AMOS or R (CFA) |
| “Why did you use Principal Axis Factoring and not Principal Component Analysis?” | Whether you understand the conceptual difference between the two approaches | PAF is based on the common factor model and extracts only shared variance — appropriate for identifying latent constructs. PCA accounts for all variance including unique and error variance and is a data reduction technique, not a construct validity test. My purpose was construct validity, so PAF was the correct choice |
| “How did you decide how many factors to retain?” | Whether you applied a principled, multi-criterion approach — not just accepted whatever SPSS produced by default | State the criteria used: Kaiser criterion (eigenvalues > 1), scree plot inspection, and total variance explained. State what each criterion suggested, whether they agreed, and how you resolved any discrepancy. Reference the 50% total variance threshold |
| “Why did you use Varimax / Direct Oblimin rotation?” | Whether your rotation choice was theoretically justified | For Varimax: the constructs are theoretically independent. For Oblimin: the constructs are theoretically related and expected to correlate — which is the more realistic assumption in most social science contexts, and the factor correlation matrix confirmed moderate inter-factor correlations |
| “What is a factor loading and what threshold did you apply?” | Whether you understand what loadings mean and can justify your cut-off | A factor loading is the correlation between an item and a factor (for orthogonal rotation) or the item’s unique contribution to the factor (Pattern Matrix, oblique). I applied a minimum loading threshold of 0.40, which is the most widely used standard in social science EFA (Field, 2018; Hair et al., 2010) |
| “What is a communality and what happened to items with low communalities?” | Whether you understand item-level fit in the factor solution and acted on it | Communality (h²) is the proportion of an item’s variance explained by the extracted factors. Items with h² below 0.30 are not well accounted for by the factor structure. Name any such items, state their communality values, and explain whether they were removed and why |
| “Did any items cross-load and how did you handle them?” | Whether your final solution genuinely achieves simple structure — or whether you just ignored cross-loading problems | Define cross-loading (substantial loadings on two or more factors simultaneously — above 0.32 on a secondary factor). State which items (if any) cross-loaded, the loading values, the primary-secondary difference, and the decision made: removal, retention with justification, or theoretical discussion |
| “What does the factor structure tell you about your conceptual framework?” | Whether you can connect your statistical findings to your theoretical argument | State whether the empirical factor structure matches your theoretical framework. If it does, this supports the validity of your measurement model. If it diverges (more or fewer factors, or differently grouped items), discuss what this means theoretically and acknowledge it as a finding rather than a problem |
Factor Analysis Reporting: What to Include and What to Avoid
✅ Always Include in Factor Analysis Reporting
- State the extraction method (PAF or PCA) and justify the choice
- State the rotation method and justify it theoretically
- Report KMO value and Bartlett’s test (χ², df, p)
- Report the number of factors retained and the criteria used (eigenvalues, scree plot, variance explained)
- Report the total variance explained by the retained solution
- Present a clean rotated factor matrix table with loadings ≥ 0.40 shown and smaller loadings suppressed
- Report communalities for all retained items
- Describe any items removed and the statistical and theoretical basis for removal
- Name and interpret each retained factor based on the items loading on it
- Follow up with Cronbach’s Alpha for each factor-derived subscale
- State the sample-to-items ratio as evidence of adequacy
❌ Common Factor Analysis Errors in Kenyan Dissertations
- Running PCA and describing it as EFA or “factor analysis for construct validity”
- Accepting the SPSS default number of factors without checking the scree plot or variance explained
- Pasting raw SPSS output tables directly into Chapter 4 — these must be reformatted into APA tables
- Suppressing loadings below 0.40 in the SPSS output but then not explaining that suppression was applied
- Retaining cross-loading items without acknowledging them or providing justification
- Removing items to reach a target alpha without noting the factor analysis rationale for removal
- Failing to name and interpret each extracted factor — simply numbering them “Factor 1, Factor 2” without substantive meaning
- Running factor analysis on all items together when different subscales measure entirely different constructs — this produces a meaningless mixed solution
Expert Factor Analysis Support for Kenyan Masters and PhD Students
At Tobit Research Consulting, our statisticians conduct and interpret full factor analysis for students at KU, UoN, JKUAT, MKU, Strathmore, Laikipia, Egerton, Moi, and all other Kenyan universities. We handle every stage — from data suitability testing through iterative item refinement to APA-formatted results write-up. Our factor analysis services include:
- KMO and Bartlett’s test of sphericity with data suitability assessment
- Exploratory Factor Analysis (EFA) using Principal Axis Factoring with appropriate rotation
- Factor retention decisions using eigenvalues, scree plots, and variance explained — with parallel analysis available
- Full iterative item refinement: communality checking, cross-loading resolution, and re-run until clean solution
- Factor naming and theoretical interpretation aligned to your conceptual framework
- Post-EFA reliability analysis: Cronbach’s Alpha for each factor-derived subscale
- Confirmatory Factor Analysis (CFA) using SPSS AMOS or R for PhD-level construct validation, with CFI, RMSEA, SRMR, and AVE reporting
- Complete Chapter 4 write-up in APA 7th edition format with professional factor loading tables
- Panel preparation: coaching on how to explain and defend your factor analysis decisions under examination
Whether you are running EFA for the first time or revising a factor structure after a panel query, we are here to help you produce results that are methodologically sound, clearly reported, and fully defensible.
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This guide is part of Tobit Research Consulting’s Data Analysis Series. Key methodological sources include: Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.), SAGE; Hair, J.F. et al. (2010). Multivariate Data Analysis (7th ed.), Pearson; Tabachnick, B.G. & Fidell, L.S. (2019). Using Multivariate Statistics (7th ed.), Pearson; Comrey, A.L. & Lee, H.B. (1992). A First Course in Factor Analysis (2nd ed.), Lawrence Erlbaum; Kaiser, H.F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141–151; Kaiser, H.F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31–36; Streiner, D.L. (1994). Figuring out factors: the use and misuse of factor analysis. Canadian Journal of Psychiatry, 39(3), 135–140; Stevens, J.P. (2012). Applied Multivariate Statistics for the Social Sciences (5th ed.), Routledge; Costello, A.B. & Osborne, J.W. (2005). Best practices in exploratory factor analysis. Practical Assessment, Research & Evaluation, 10(7); and Child, D. (2006). The Essentials of Factor Analysis (3rd ed.), Continuum.
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