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Confirmatory Factor Analysis (CFA) Online

Test whether your items load on the constructs you intended. Item groups are built automatically from names like TR1, TR2, TR3, and the output covers model fit, standardized loadings, reliability, convergent and discriminant validity.

Free · No sign-upReplaces AMOS · lavaanWorks with your data
Updated · By Bibin Xavier
Prefer to draw your model? CB-SEM Studio is a drag-and-drop builder: create constructs, set item directions, add or remove items, pick paths, mediators and moderators from drop-down lists, and get the same maximum likelihood results. Open the visual builder

Data 180 × 12

Paste from Excel, or drop a CSV, TSV or Excel file here.
Example data 180 rows, 12 variables. Data stays in this browser tab.
Respondenttext · 180 levelsTR1numeric · codedTR2numeric · codedTR3numeric · codedTR4numeric · codedSAT1numeric · codedSAT2numeric · codedSAT3numeric · codedSAT4numeric · codedLOY1numeric · codedLOY2numeric · codedLOY3numeric · coded
R00122123133423
R00254543434434
R00344341224231
R00412324444344
R00534233334322
R00654545544434
R00734443324133
R00833445455554

Variables and options

One line per construct, for example Trust =~ TR1 + TR2 + TR3. Add TR1 ~~ TR2 for a correlated error.
Results update automatically when you change an option.

Results

180 rows · example data
χ²(41)50.45p = .148
CFI.989
TLI.985
RMSEA.03690% CI [.000, .065]
SRMR.037
Table 1

Model fit

IndexValueThresholdVerdict
χ² / df1.23≤ 3 (≤ 5 acceptable)Good
CFI.989≥ .95 (≥ .90 acceptable)Good
TLI.985≥ .95 (≥ .90 acceptable)Good
RMSEA.036 [.000, .065]≤ .06 (≤ .08 acceptable)Good
SRMR.037≤ .08Good
p-close (RMSEA ≤ .05).755> .05Good
GFI.952≥ .90Good
AIC / BIC4986.9 / 5066.7lower is better (compare models)—

Note. Thresholds follow Hu and Bentler (1999). With small samples or many indicators, judge fit on several indices together.

Measurement model (standardized loadings and latent correlations)

.58.52.66TR[object Object].73[object Object].75[object Object].75[object Object].77SAT[object Object].72[object Object].77[object Object].77[object Object].64LOY[object Object].80[object Object].79[object Object].83
Table 2

Construct reliability and convergent validity

ConstructItemsCronbach’s αCR (ρc)McDonald’s ωAVE√AVEMSVVerdict
TR4.838.838.838.565.751.332Supported
SAT4.816.817.818.529.727.432Supported
LOY3.846.846.846.646.804.432Supported

Note. Thresholds (Hair et al., 2019; Fornell and Larcker, 1981): α, CR and ω ≥ .70 (≤ .95); AVE ≥ .50; MSV below AVE for discriminant validity. CR and AVE use standardized loadings; ω uses the unstandardized solution.

Table 3

Fornell–Larcker criterion

TRSATLOY
TR.751
SAT.576.727
LOY.516.657.804

Note. Diagonal: √AVE. Off-diagonal: latent correlations. Discriminant validity holds when each √AVE exceeds that construct’s correlations.

Table 4

Heterotrait–monotrait ratio (HTMT)

TRSATLOY
TR—
SAT.584—
LOY.510.648—

Note. HTMT below .85 (strict) or .90 (liberal) supports discriminant validity (Henseler, Ringle and Sarstedt, 2015). Computed from absolute item correlations.

Table 5

Measurement model (factor loadings)

ConstructIndicatorEstimateSEzpStandardized (λ)
TRTR11.000a———.730
TRTR21.0140.1119.17< .001.754
TRTR31.0710.1179.12< .001.749
TRTR41.0920.1179.35< .001.772
SATSAT11.000a———.723
SATSAT21.0650.1169.20< .001.771
SATSAT31.0540.1149.21< .001.772
SATSAT40.8620.1117.74< .001.636
LOYLOY11.000a———.795
LOYLOY21.0230.09710.55< .001.786
LOYLOY31.0980.10011.02< .001.830

Note. a Fixed to 1 to set the scale of the construct. Standardized loadings of .70 or more are ideal; below .50 suggests the item measures the construct poorly (Hair et al., 2019).

Table 6

Covariances

BetweenEstimateSEzpCorrelation
TR ↔ SAT0.3260.0655.01< .001.576
TR ↔ LOY0.3140.0654.82< .001.516
SAT ↔ LOY0.4110.0745.58< .001.657
Table 7

Explained variance (R²)

VariableR²
TR1.532
TR2.569
TR3.562
TR4.595
SAT1.523
SAT2.594
SAT3.595
SAT4.405
LOY1.632
LOY2.617
LOY3.689
Table 8

Variances and residual variances

VariableEstimateSEzpStandardized
TR10.4850.0647.53< .001.468
TR20.4300.0607.21< .001.431
TR30.4940.0687.28< .001.438
TR40.4480.0646.94< .001.405
SAT10.5300.0707.54< .001.477
SAT20.4510.0666.89< .001.406
SAT30.4400.0646.87< .001.405
SAT40.6360.0778.30< .001.595
LOY10.3900.0586.67< .001.368
LOY20.4360.0646.86< .001.383
LOY30.3650.0625.87< .001.311
TR0.5520.1045.29< .0011.000
SAT0.5820.1115.22< .0011.000
LOY0.6710.1125.99< .0011.000

Interpretation

The measurement model fits well (CFI = .989, RMSEA = .036). All standardized loadings are at least .50. All constructs show adequate reliability (CR ≥ .70) and convergent validity (AVE ≥ .50). HTMT values are all below .85, supporting discriminant validity.

A CFA showed acceptable fit, χ²(41) = 50.45, CFI = .989, TLI = .985, RMSEA = .036, SRMR = .037.

How to cite this tool

Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.

APA 7

Xavier, B. (2026). Confirmatory Factor Analysis (CFA) Online [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/confirmatory-factor-analysis/

BibTeX 

@software{xavier_cfa_2026,
  author = {Xavier, Bibin},
  title = {Confirmatory Factor Analysis (CFA) Online},
  publisher = {FreeStatisticalTools.com},
  year = {2026},
  url = {https://freestatisticaltools.com/confirmatory-factor-analysis/},
  note = {Web application}
}

Suggested sentence for your methods section: “The analysis was carried out with the free Confirmatory Factor Analysis (CFA) Online tool on FreeStatisticalTools.com (Xavier, 2026).”

What is confirmatory factor analysis?

Confirmatory factor analysis tests whether observed items load on the latent constructs you specified in advance. It is the standard way to establish the measurement model, reliability, convergent validity and discriminant validity of a questionnaire before testing hypotheses.

When to use confirmatory factor analysis

Use CFA to confirm a measurement model before testing structural hypotheses, to validate an adapted questionnaire, or to establish construct validity in a thesis.

Assumptions

  • Indicators are continuous or ordinal with five or more categories.
  • Approximately multivariate normal data and a reasonably large sample (200+).
  • Each construct has at least three indicators.

How to use this tool

  1. Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
  2. Choose the variables. Select the measurement model.
  3. Set the options. Fill in fix latent variances to 1.
  4. Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.

How to report confirmatory factor analysis in APA style

Report the fit indices, the standardized loadings, CR, AVE and the HTMT or Fornell–Larcker results in tables.

Frequently asked questions

What is the difference between EFA and CFA?

EFA discovers how many factors there are and which items belong to them. CFA tests a structure you specify in advance and gives fit indices to judge it.

What loading is acceptable in CFA?

Standardized loadings of .70 or more are ideal; loadings between .50 and .70 may be kept if CR and AVE are adequate; items below .40 are usually removed.

What sample size does CFA need?

Around 200 cases is a common minimum, and more for complex models; another rule of thumb is at least 10 cases per estimated parameter.

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