What Is a Good Chi-Square / df Ratio?
A chi-square to df ratio of 2 or lower is treated as good and 3 or lower as acceptable, but this is a rough heuristic only, not a real cutoff. At large samples the chi-square test is almost always significant.
What the chi-square / df ratio is
The model chi-square (sometimes labeled CMIN) tests whether the model-implied covariance matrix matches the observed one; a non-significant chi-square means the model is not rejected. The normed chi-square divides that statistic by its degrees of freedom (χ²/df) to give a rough, sample-adjusted index.
Why chi-square alone misleads at large N
The chi-square test is sensitive to sample size: with hundreds of cases it is almost always significant even when the model fits well in practical terms. That is exactly why approximate fit indices like RMSEA, CFI, TLI and SRMR exist. Judge fit on the whole set of indices, not on chi-square alone.
Caveats: a heuristic, not a law
There is no consensus cutoff for χ²/df: thresholds of 2, 3 and even 5 all appear in the literature, so the ratio is at best a rough heuristic (Marsh, Hau & Wen, 2004). The 2 and 3 lines used here follow Schermelleh-Engel, Moosbrugger and Müller (2003, Table 1, p. 52) and Carmines and McIver (1981, p. 80). Report the chi-square value, its degrees of freedom and p-value for transparency, but base your fit conclusion on the approximate indices.
How to report it: report χ²(df) = value, p, e.g. χ²(120) = 198.4, p < .001, then the approximate indices. The fit index checker shows all of them.
Reference table
| χ²/df | Common label | Source |
|---|---|---|
| ≤ 2 | Good (heuristic) | Schermelleh-Engel et al. (2003) |
| ≤ 3 | Acceptable (heuristic) | Schermelleh-Engel et al. (2003); Carmines & McIver (1981) |
| > 5 | Often considered poor | Wheaton et al. (1977) |
Frequently asked questions
Is a chi-square / df ratio of 2.5 acceptable?
By the acceptable heuristic (≤ 3) it is acceptable, but the ratio is not a real cutoff. Base your fit decision on RMSEA, CFI, TLI and SRMR together.
Why is my chi-square significant even though fit looks good?
The chi-square test is sensitive to sample size and is almost always significant at large N. This is expected, which is why approximate fit indices are preferred for judging fit.
Should I still report chi-square?
Yes. Report the chi-square value, degrees of freedom and p-value for transparency, then present the approximate fit indices as the basis for your conclusion.
How to cite this page
If this page helped your research, you can cite it (APA 7):
Szymkowiak, A. (2026). Chi-Square / df Ratio: What Is a Good Value?. Explonia. https://explonia.com/thresholds/chi-square-df-ratio/
Last updated: October 2026
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