SPSS
Validity Testing
KMO & Bartlett’s Test
Construct Validity
Factor Analysis
Kenya Research
Tobit Research Consulting | Statistical Analysis & Thesis Support Series | Reading time: ~14 minutes
What you will learn: Why validity and reliability are two separate tests answering two different questions, and why examiners ask for both; how to run the Kaiser-Meyer-Olkin (KMO) measure and Bartlett’s Test of Sphericity in SPSS, and what each is actually checking; how to interpret factor loadings to establish construct validity; the practical difference between construct, convergent, and discriminant validity, and how each is tested; and how to report validity results correctly alongside your reliability analysis in Chapter Three or Four.
1. Validity vs. Reliability: Two Different Questions
Students frequently run a reliability test, get a Cronbach’s Alpha above 0.70, and assume the instrument has now been “tested” and is ready for the main analysis. This is a common and consequential misunderstanding. Reliability and validity are answering two entirely different questions, and a thesis that only reports one is, in the eyes of most examiners, only half-finished on this front.
Reliability asks: are these items internally consistent — do they hang together? Validity asks a harder, more important question: are these items actually measuring the construct they claim to measure, and are they measuring it as a coherent underlying dimension rather than several unrelated things bundled together? A set of items can be highly reliable (respondents answer them consistently) while still not validly capturing the concept the researcher intended — for instance, if the items were unintentionally tapping into a related but distinct construct.
The order matters in reporting, not necessarily in execution. Most methodology chapters present validity testing (via factor analysis) before or alongside reliability testing, since factor analysis is often used to confirm which items genuinely belong together as a scale — before that finalised scale’s internal consistency is then checked with Cronbach’s Alpha.
2. What KMO and Bartlett’s Test Actually Check
Before you can run a factor analysis to establish construct validity, SPSS needs to check whether your data is even suitable for that kind of analysis in the first place. This is exactly what the KMO measure and Bartlett’s Test of Sphericity do — they are not tests of validity themselves, but a gatekeeping step that tells you whether proceeding to factor analysis is statistically justified.
| Test |
What It Checks |
What a Good Result Looks Like |
| Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy |
Whether your sample size and the pattern of correlations among items are adequate for factor analysis to produce reliable, meaningful factors |
KMO value of 0.60 or above is generally considered acceptable; 0.80+ is considered meritorious to excellent |
| Bartlett’s Test of Sphericity |
Whether your items are correlated with each other at all — if they were completely uncorrelated (an “identity matrix”), factor analysis would be meaningless |
A statistically significant result (p < 0.05) — this is the outcome you want, since it means meaningful correlation exists |
A common point of confusion: for Bartlett’s Test, a significant p-value (below 0.05) is the desired, “good” result — the opposite of how significance is usually interpreted in hypothesis testing elsewhere in a thesis. A non-significant Bartlett’s result means your items are not correlated enough to justify factor analysis at all.
3. How to Run KMO and Bartlett’s Test in SPSS: Step-by-Step
- Open the Factor Analysis dialog. Go to Analyze → Dimension Reduction → Factor (in older SPSS versions this may appear as Analyze → Data Reduction → Factor).
- Move your items into the Variables box. Select all items belonging to the construct you are validating and move them into the “Variables” field.
- Open the Descriptives sub-dialog. Click “Descriptives,” and under “Correlation Matrix,” tick KMO and Bartlett’s test of sphericity. Click Continue.
- Open the Extraction sub-dialog. Click “Extraction.” Leave the method as Principal Components (the standard default for most thesis-level construct validity checks) and ensure “Eigenvalues over 1” is selected under “Extract.” Click Continue.
- Open the Rotation sub-dialog. Click “Rotation” and select Varimax — the most commonly used rotation method in applied social science research, which produces a clearer, more interpretable factor structure. Tick “Rotated solution.” Click Continue.
- Set the loading display threshold (optional but recommended). Under “Options,” tick Sort by size and Suppress small coefficients, setting the absolute value to 0.30 or 0.40 — this makes the rotated factor matrix far easier to read by hiding weak, irrelevant loadings.
- Click OK. SPSS will generate the KMO/Bartlett’s output along with the Communalities table and the Rotated Component Matrix.
4. Reading the Output: KMO Value, Bartlett’s Significance, and Factor Loadings
≥ 0.60
minimum acceptable KMO value to proceed with factor analysis
Kaiser, 1974
p < 0.05
the significance level Bartlett’s Test should reach — confirming sufficient correlation among items
Bartlett, 1954
≥ 0.40
the commonly used minimum factor loading for an item to be considered a meaningful part of that factor
Hair et al., 2010
The KMO and Bartlett’s Test table appears first in your output — this is the checkpoint result, reported as a single line in your methodology section. The more analytically important table for establishing construct validity is the Rotated Component Matrix, which shows how strongly each item “loads” onto each extracted factor. An item with a high loading (typically 0.40 and above) on the factor it was designed to measure — and low loadings on other factors — is behaving exactly as construct validity requires.
Output Element
Reading the Rotated Component Matrix
Each row is an item; each column is an extracted factor/component. Look across each row for the highest loading value — that tells you which factor the item “belongs to.” An item that loads reasonably strongly on more than one factor (a “cross-loading,” commonly flagged above roughly 0.30–0.40 on a second factor) is a candidate for review, since it is not cleanly distinguishing between the constructs being measured.
5. Construct Validity: What It Means and How Factor Analysis Establishes It
Construct validity is the broad umbrella question of whether your instrument genuinely measures the theoretical concept it claims to measure, rather than something else entirely. Exploratory Factor Analysis (the KMO/Bartlett’s/rotated matrix process described above) is the most common way applied researchers establish this in a thesis, because it provides empirical evidence — not just researcher assertion — that items intended to measure the same construct do, in fact, statistically cluster together as a single, distinct factor.
In practice, construct validity is demonstrated when: the number of factors extracted matches the number of constructs the researcher theoretically expected, and each item loads strongly onto its intended factor rather than scattering across multiple factors or failing to load meaningfully anywhere.
6. Convergent and Discriminant Validity Explained
Construct validity is often broken down into two more specific sub-types, both of which examiners increasingly expect to see addressed explicitly, particularly in Masters and PhD research using multi-item scales.
Convergent Validity
- Checks whether items that are supposed to measure the same construct actually correlate strongly with one another
- In SPSS-based factor analysis, evidenced by items loading strongly (≥0.40, ideally ≥0.50) onto their intended factor
- In more advanced approaches (e.g., using AMOS for Confirmatory Factor Analysis), assessed via Average Variance Extracted (AVE), with AVE ≥ 0.50 commonly cited as adequate
Discriminant Validity
- Checks whether constructs that are supposed to be conceptually distinct actually behave as statistically distinct in the data
- In SPSS-based exploratory factor analysis, evidenced by items not cross-loading heavily onto factors they weren’t designed to measure
- In more advanced approaches, assessed by comparing the square root of each construct’s AVE against its correlations with other constructs (the Fornell-Larcker criterion)
A scope note for most thesis-level work: full convergent/discriminant validity testing via AVE and the Fornell-Larcker criterion typically requires Confirmatory Factor Analysis in a structural equation modelling tool (such as AMOS or R’s lavaan package), which goes beyond what basic SPSS factor analysis provides. For most undergraduate and Masters-level theses, demonstrating strong, clean loadings and minimal cross-loading in an SPSS-based Exploratory Factor Analysis is considered sufficient evidence of convergent and discriminant validity — but check your specific university and supervisor’s expectations, as some PhD programmes require the more advanced AMOS-based approach.
7. What to Do When KMO Is Low or Bartlett’s Test Fails
A KMO value below 0.60, or a Bartlett’s Test that is not statistically significant, means your data is not currently suitable for factor analysis — proceeding anyway and reporting the factor loadings regardless is one of the more serious methodological errors an examiner will catch quickly.
Diagnostic Step
Where to Look First
Check your sample size relative to the number of items — factor analysis is sensitive to small samples, and a common rule of thumb calls for at least 5–10 respondents per item, with 100+ total respondents as a practical minimum for most applied studies. Also check the Anti-Image Correlation Matrix (available under the same Descriptives sub-dialog) for individual items with low measures of sampling adequacy on the diagonal — these specific items are often the ones dragging the overall KMO down and may need to be removed before re-running the analysis.
8. How to Report Validity Results in Your Thesis
📋 Example of Adequate Reporting
“Construct validity of the [construct name] scale was assessed using Exploratory Factor Analysis with Principal Components extraction and Varimax rotation. The Kaiser-Meyer-Olkin measure of sampling adequacy was 0.81, exceeding the recommended threshold of 0.60 (Kaiser, 1974), and Bartlett’s Test of Sphericity was statistically significant (χ² = 412.6, df = 45, p < 0.001), confirming the data was suitable for factor analysis. All items loaded strongly (≥0.52) onto their intended factor with no significant cross-loadings, providing evidence of both convergent and discriminant validity.”
Minimum Reporting Checklist
What Your Validity Section Should State
The extraction and rotation method used; the KMO value and a citation for the threshold applied; the Bartlett’s Test result (chi-square, degrees of freedom, and significance level); a summary of the factor loadings obtained (or reference to a table presenting them in full); and an explicit statement on whether the results support convergent and discriminant validity.
9. Common Mistakes That Get Flagged at Defense
Reporting only Cronbach’s Alpha and calling it “reliability and validity” — this is by far the most common gap examiners flag. Alpha alone establishes internal consistency, not validity; the two need to be reported and interpreted separately.
Proceeding to interpret factor loadings without first checking KMO and Bartlett’s Test, or checking them but not reporting the actual values obtained — an examiner will typically ask for these numbers directly if they are missing.
Using a factor loading cut-off inconsistently, such as citing a 0.40 threshold in the text but including items with loadings below that in the final scale without explanation.
10. How Tobit Research Consulting Can Help
Tobit Research Consulting supports Masters and PhD students across Kenyan universities — including the University of Nairobi, Kenyatta University, JKUAT, Mount Kenya University, CUEA, and Strathmore — through the validity and reliability testing stage of Chapter Three and Chapter Four, where methodological rigor matters most to examiners.
SPSS Validity & Factor Analysis Support — Nairobi, Kenya
Whether you need to learn to run this yourself or want your dataset analysed by our team, we offer:
- One-on-one SPSS training covering KMO, Bartlett’s Test, and factor analysis interpretation
- Professional construct, convergent, and discriminant validity testing on your dataset
- Clear, APA-formatted output tables ready to insert into Chapter Three or Four
- Interpretation guidance so you can defend your validity results with confidence
We work with students across all Kenyan universities and can typically turn around a standard dataset within 3–5 days.
Request SPSS Support →
📍 Bruce House, 4th Floor, Nairobi CBD, Kenya | Tel: +254 728 430 728 | tobitresearchconsulting.com
References: Kaiser, H. F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31–36. Bartlett, M. S. (1954). A note on the multiplying factors for various χ² approximations. Journal of the Royal Statistical Society, 16(2), 296–298. Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate Data Analysis (7th ed.). Pearson.
