STATISTICAL METHOD
Exploratory Factor Analysis (EFA)
Statistical Consulting for Scale Structure
We apply EFA to the structure of your items, choosing the extraction method for your data, deciding the number of factors by parallel analysis and defaulting to an oblique rotation, then reporting loadings, communalities and factor correlations in publication-ready form.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Exploratory Factor Analysis?
Exploratory factor analysis is a latent variable method that explains the correlations among observed items, such as questionnaire responses, through a smaller number of common factors, and estimates how strongly each item loads on each factor. It models the variance that items share and treats the rest as unique to each item, which separates it from principal component analysis. The number of factors, the extraction method and the rotation are analytic decisions, and the resulting structure is a hypothesis to be confirmed in separate data. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides EFA within your study design, with the relevant checks, estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is Factor Analysis of Items Appropriate?
EFA fits a question about how many dimensions a set of items forms and which items belong to each, and these are the research situations in which researchers most often ask us to apply or confirm it.
New Scale or Item Pool A questionnaire has been drafted for a construct with no settled structure, and the team needs to learn how many dimensions the items form and which items fit.
Weak or Cross-Loading Items Some items load weakly or on several factors, and the team must decide which to revise or remove, using content and wording as well as the size of the loadings.
Adapting an Existing Instrument An adapted scale has not reproduced its published structure in a confirmatory test, and the team needs to learn what structure the items form in the new population.
Reviewing a Completed Analysis Factors were kept by the eigenvalue rule with a default varimax rotation, and a reviewer has questioned both. Independent Statistical Review re-examines the choices.
ANALYTICAL APPROACH
How We Apply Factor Analysis to Your Items
Within the family of Multivariate, Scale & Reliability, EFA is applied once the items, sample and question show that a common factor model fits.
Suitability of the Data We review correlations, distributions, missing responses and sample size against the number of items. KMO and Bartlett's test are screening aids with limits, and sample size guidance is a rule of thumb.
Extraction and Item Type We use principal axis or maximum likelihood factoring for the common factor model. For ordinal items such as Likert ratings, we factor polychoric correlations, since Pearson correlations can distort loadings.
Deciding the Number of Factors Parallel analysis, the scree plot and interpretability decide the number, not the eigenvalue-greater-than-one rule, which tends to overextract. Fit indices from maximum likelihood add supporting evidence.
Rotation and Interpretation We default to an oblique rotation, oblimin or promax, because factors usually correlate, and read loadings, cross-loadings and communalities together. An orthogonal rotation needs a stated reason.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the factor solution is delivered with the estimates, checks and files needed to report and defend it.
Data & Variable Review Item coding and direction, response distributions, missing responses, outliers and the ratio of cases to items are reviewed, and the correlation type is chosen before any factor is extracted.
Method-Specific Checks Factorability, the parallel analysis, alternative factor numbers and the stability of the solution across factor extraction and rotation choices are examined, with item-level concerns flagged.
Statistical Results The pattern and structure matrices, communalities, variance explained, factor correlations and, with maximum likelihood, fit indices with their confidence intervals where available.
Publication-Ready Tables & Figures Loading tables, a parallel analysis plot and a factor correlation table, formatted to APA 7, COSMIN for health measurement instruments or the journal's requirements, ready to insert.
Interpretation Each factor is described from its loadings, with weak and cross-loading items discussed, and the structure presented as exploratory and in need of confirmation in a separate sample.
Reproducible Analysis Files R scripts using psych, SPSS FACTOR syntax, Stata do-files or Mplus input files are provided where applicable, so every loading can be traced and rerun if the data change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
We choose the method by what the analysis must answer. EFA explores structure, and these methods fit questions that are already specified, descriptive or about individual items.
01
Confirmatory Factor Analysis (CFA)
When theory or earlier work fixes the structure, CFA tests that model in separate data, and the model should not be fitted to the same sample used for exploration.
02
Principal Component Analysis (PCA)
When the aim is only to summarize many correlated variables in fewer scores, not to model latent constructs, components of total variance serve that purpose directly.
03
Item Response Theory (IRT)
For ordinal or binary items, IRT models each item's difficulty and discrimination along one trait and shows where on that trait the scale measures precisely.
04
Likert Scale Analysis
When a short, established scale is scored as designed, the question is usually item handling, scoring rules and reliability, not the discovery of a new factor structure.
CASE EXAMPLE
How We Work in Practice
An illustration of how an exploratory analysis of item structure moves from a plan to a reportable, defensible result.
ILLUSTRATIVE EXAMPLE · PSYCHOMETRIC TEST DEVELOPMENT · UNITED STATES
A testing organization drafted a 30-item workplace resilience questionnaire and needed to learn how many dimensions the items formed before refining the instrument.
The analysis plan, written before the pilot data were examined, specified five-point ordinal items, so we used polychoric correlations with principal axis factoring and an oblique rotation, because the dimensions were expected to correlate. Parallel analysis and interpretability set the number of factors, and the eigenvalue rule was reported only for comparison. Several items cross-loaded and two had low communalities, so they were reviewed for wording and content, not dropped on loadings alone. The structure was framed as a proposal for confirmatory factor analysis in a later, separate sample.
Outcome: The team received the loadings, communalities and factor correlations, the parallel analysis plot, a table of flagged items with wording notes, the scripts and a methods paragraph.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Factor Analysis
Factor analysis is run in the statistical software researchers already use, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Factor Analysis Across Research Fields
Questions about factor structure arise wherever questionnaires and scales are developed, each field bringing its own constructs, populations and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a researcher who needed to judge weak items and the suitability of the data for factor analysis, and received a concise analytical summary.
“We came to the team with a fairly technical Exploratory Factor Analysis (EFA) problem: the factor structure, weak items, and whether the data were suitable for factor analysis. They worked through the assumptions and reporting choices with us, then delivered a clean analytical summary rather than pages of software output. The final output was concise, clearly interpreted, and ready to use in our research reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your factor analysis, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your factor analysis, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The research question, the naming and meaning of each factor, interpretation and conclusions remain with you, and our statistical interpretation stays within what the loadings and the design support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Factor Analysis of Your Items
Short answers to what researchers ask before a factor analysis, from EFA versus PCA and the number of factors to confidentiality and the assessment process.
Should I use EFA or PCA for my questionnaire items?
EFA models the variance that items share and suits questions about latent constructs, whereas PCA summarizes total variance in components and does not model latent factors. The two can give different loadings, especially with few items or low communalities, so they are not interchangeable. For scale development we run EFA, and we use PCA when data reduction is the only aim.
How many factors should I keep after extraction?
Parallel analysis is generally the stronger guide, because it compares each eigenvalue with those from random data of the same size. We read it with the scree plot and with whether each factor is interpretable. The eigenvalue-greater-than-one rule often overextracts factors and is not used alone, and a factor supported by only one or two items is treated cautiously.
What sample size do I need for a factor analysis?
No single number applies, and figures such as 200 cases or ten per item are rules of thumb only. Adequacy depends on communalities, the number of items per factor and how clear the structure is, so a well-determined solution with high communalities needs fewer cases. We judge it from the data and report a small sample as a limitation.
Can you review an analysis that has already been completed?
Yes, we can review a completed factor analysis before submission or a response to reviewers. We check the extraction and rotation, how the number of factors was decided, how ordinal items were handled, the treatment of cross-loading items and the reporting, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With
Factor Analysis?
Share your research question, instrument and data. We assess whether an exploratory approach fits your items and confirm the method before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014