Partial eta squared is not an independent measure: it follows from the <em>F</em> and its degrees of freedom through an exact identity. If it does not match, the error is in one of the three numbers.
Partial eta squared is the effect variance over the sum of effect and error variance: η²p = SSeffect / (SSeffect + SSerror). And F is the ratio of mean squares, which are those same sums divided by their degrees of freedom.
Rearranging gives η²p = (F · df₁) / (F · df₁ + df₂), with no added assumptions. It is not an approximation and it does not depend on the design: given F and its two degrees of freedom, partial eta is determined.
That makes a mismatch here more informative than one in a p value: there are no corrections, tails or conventions to explain it away.
It is eta squared, not partial. The commonest confusion. Plain eta squared divides by the total sum of squares, so it comes out SMALLER than partial whenever there is more than one factor. If your number is noticeably smaller than the recomputed one, you probably reported plain eta and called it partial.
It is omega squared. Omega corrects eta’s optimistic bias and always comes out slightly smaller. It is preferable, but it has to be called by its name.
They come from different models. The F from one table and the effect size from another, with different covariates. It happens in ANCOVA and it is what makes two tables in one paper contradict each other.
A property that trips people up: the partial eta squared values of the different effects in a model need not sum to 1, or even to less than 1, because each uses its own denominator.
Plain eta squared values do sum to at most 1, because they share the total denominator. A sum above one is not an error for partial etas; it is an error if they are presented as plain ones.
How to report both is in how to report partial eta squared in APA 7.
It works whenever the F and the two degrees of freedom belong to the same effect and the same error term. Mixed designs have several error terms, so each effect has to be paired with its own; mixing them produces a mismatch that is yours, not the paper’s.
Then this check does not apply directly: omega corrects the bias and always returns a slightly smaller value. Many methodologists prefer it for exactly that reason, but it has to be named as omega, not eta.
Not on its own: with a within-subjects factor and little error, values of .40 or higher are normal. What is suspicious is a value that does not follow from its F, or one compared against plain-eta benchmarks as if they were the same metric.
Yes, by rearranging: F = (η²p · df₂) / (df₁ · (1 − η²p)). It is useful for reconstructing an incomplete table from a paper you want to include in a meta-analysis.