How to Report Levene's Test in APA 7

Levene's test is one of those procedures nearly everyone runs and nearly nobody reports properly. It reaches reviewers as “the assumption of homogeneity of variance was met”, with no numbers at all, or as an F missing one of its two degrees of freedom. The real trouble starts when it comes out significant, because a lot of people do not know what to do with that result and switch to a rank test that fixes nothing. Here is what the write-up needs, what to do when the assumption fails, and why a growing number of methodologists now recommend skipping Levene altogether. The wider map is in how to check statistical assumptions.

What the write-up has to contain

Levene's test is an ANOVA in disguise. It takes the absolute deviation of every score from the centre of its own group and runs a one-way ANOVA on those deviations. That is why the output is an F, and why it carries two degrees of freedom like any other F: the first is k − 1, where k is the number of groups, and the second is N − k. Two groups and 116 participants give F(1, 114); three groups and 138 give F(2, 135).

The full form is F(1, 114) = 9.62, p = .002. F and p are italicised, the degrees of freedom sit upright inside the brackets and hug the statistic. F can exceed 1, so it takes a leading zero when it needs one (F = 0.61); p never does. And do not write p = .000 even though that is what your output shows: that value is p < .001.

Levene needs no table of its own and no effect size. It belongs in a sentence in the Results section, immediately before the test it affects, or in the analysis plan if you prefer to group every assumption check there. What must not happen is the test appearing without its consequence: if you report Levene, the same sentence or the next one has to say which test you then ran on the strength of that result.

When it comes out non-significant, the honest sentence is not “variances were homogeneous” but “no significant difference between variances was detected”, F(1, 114) = 0.61, p = .436. A non-significant test does not establish the null, and with small groups Levene has so little power that it rarely detects anything at all. It is a wording detail, it costs four words, and a methods reviewer will notice.

The four Levene rows in SPSS, and which one to report

In the one-way ANOVA and Explore output, SPSS does not give you one Levene test, it gives you four rows: based on mean, based on median, based on median with adjusted df, and based on trimmed mean. They are not four competing tests but four ways of defining the centre of the group before the absolute deviations are calculated, and each returns a different F on identical data. The t test output, by contrast, prints only the mean-based row: to get the median version with two groups, ask for it through One-Way ANOVA or Explore.

The one to report by default is the median-based version, which is the Brown-Forsythe (1974) variant. Centring on the median makes the test far less sensitive to skew and to outliers, which is exactly the situation in which anyone in psychology starts worrying about homogeneity in the first place. The classic mean-centred version misbehaves with skewed data and flags heterogeneity where there is only asymmetry. In R, car::leveneTest() already centres on the median by default, so if your SPSS and R numbers disagree, that is usually why.

Whichever you use, name it. “Levene's test based on the median” is six words and it stops a reader trying to reproduce your F from the wrong definition. Choose before you look, too: picking whichever of the four rows gives the p value you were hoping for is p-hacking the assumption, and it is self-detecting, because all four values are printed in the same table you are reading.

Outside SPSS you will meet two relatives. Bartlett's test is more powerful when the distributions really are normal and collapses as soon as they are not, so it is rarely the right choice for psychological data. Box's M is the multivariate equivalent and turns up in MANOVA and discriminant analysis; it is so sensitive that many authors only interpret it below p = .001, and that convention has to be stated if you apply it.

When it is significant: Welch's t test

A significant Levene does not invalidate your data and does not push you towards a non-parametric test. It says only that Student's t, which pools the two variances into a single estimate of the standard error, is no longer the right tool. The replacement is Welch's t, which pools nothing: it estimates the standard error from each group's own variance and adjusts the degrees of freedom downwards to compensate.

You already have it. The SPSS t test output prints two rows — “Equal variances assumed” and “Equal variances not assumed” — and the second one IS Welch. In R, t.test() runs Welch by default and you have to ask for var.equal = TRUE to get Student's; in jamovi it is the Welch's checkbox. Its signature is fractional degrees of freedom: t(67.94) instead of t(114). That is not a rounding error and you must not truncate it; report it to two decimal places, because it is the visible evidence that you applied the correction. If a reviewer sees a whole-number df immediately after a significant Levene, they know you copied the row above without opening anything.

In the text it reads like this: “Participants in the intervention condition (n = 45, M = 22.10, SD = 10.40) reported lower perceived stress at follow-up than those in the waitlist control (n = 71, M = 26.30, SD = 6.80). Levene's test based on the median indicated unequal variances, F(1, 114) = 9.62, p = .002, so Welch's t test was used, t(67.94) = 2.40, p = .019, mean difference = 4.20, 95% CI [0.71, 7.69], d = 0.50.”

It is worth seeing what the uncorrected test would have said. On the same data, Student's t gives t(114) = 2.63, p = .010. Welch is the more conservative of the two here because the larger variance sits in the smaller group, which is the combination that inflates Student's Type I error most. When the larger variance sits in the larger group the bias runs the other way: Student becomes over-conservative and you lose power without ever seeing it happen. That asymmetry, not some magic threshold, is what the whole debate rests on.

Effect size is the awkward part. Cohen's d is defined on a pooled standard deviation, and pooling is precisely what you have just decided is inappropriate. Two honest options: report the pooled d while stating in the text that the variances differ, or use Glass's delta, which standardises on the control group's standard deviation (here 4.20 / 6.80 = 0.62). Either is defensible provided you say which. The rest of the t test format is in how to report a t test and a chi-square in APA 7.

When it is significant: Welch's ANOVA and Games-Howell

With three groups or more the replacement is Welch's ANOVA, which SPSS files under “Robust Tests of Equality of Means” alongside Brown-Forsythe, and which R gives you as oneway.test() with no extra arguments. The logic is unchanged: instead of pooling the variances, each group enters with its own weight — its size divided by its variance, so the noisier groups count for less — and the second degree of freedom is adjusted downwards.

The format is identical to an ordinary ANOVA apart from that fractional df: F(2, 71.35) = 5.26, p = .007. The first degree of freedom is still k − 1 and is still a whole number. The effect size is calculated from the sums of squares of the conventional ANOVA (η² = .09 on these data) and it is worth saying so in a note, because it does not come out of the Welch table and the reader should not have to guess where you found it. Remember that eta is a Greek letter: upright, and no leading zero.

The pairwise comparisons cannot be Tukey's. Tukey assumes equal variances, exactly like the ANOVA you have just discarded, so carrying it over contradicts you halfway through the paragraph. The standard choice is Games-Howell, which applies the Welch correction to every pair and sits in the same SPSS post hoc menu, in the “Equal Variances Not Assumed” block. For each comparison report the mean difference, its confidence interval and the adjusted p value.

A worked example: “Wellbeing scores differed across the three placement settings: inpatient (n = 34, M = 41.20, SD = 11.60), community (n = 58, M = 47.90, SD = 6.90) and primary care (n = 46, M = 45.10, SD = 8.40). Levene's test based on the median indicated unequal variances, F(2, 135) = 6.14, p = .003, so Welch's ANOVA was used, F(2, 71.35) = 5.26, p = .007, η² = .09. Games-Howell comparisons located the difference between inpatient and community placements (mean difference = 6.70, 95% CI [1.40, 12.00], p = .011); neither remaining comparison reached significance (inpatient vs. primary care, mean difference = 3.90, p = .247; community vs. primary care, mean difference = 2.80, p = .189).”

If what you are staring at is the SPSS trio of tables — Levene, robust tests, multiple comparisons — and you cannot tell which figure belongs where, paste the output into the interpreter and it returns the sentence in exactly this format. The rest of the ANOVA write-up is in how to report an ANOVA in APA 7.

Why many methodologists now use Welch by default

The sequence “run Levene, then pick a test depending on the result” is a conditional or two-stage procedure, and it has a problem no output will show you: the Type I error rate of the whole procedure is not the 5% you think it is. It is the error rate of a decision made from the same data you are about to test your hypothesis with. Zimmerman (2004) showed that this kind of preliminary test can make error control worse rather than better, and Rasch, Kubinger and Moder (2011) reached the same conclusion for the two-sample t test.

The second problem is that Levene's power runs in the wrong direction. With small groups — 20 or 25 per condition, the usual size across a good deal of psychological research — it barely detects variance differences that genuinely do damage. With large samples it detects tiny differences that affect nothing. It is the same pathology that makes Shapiro-Wilk so widely misread: an assumption test whose sensitivity tracks sample size rather than the severity of the problem.

The third is that the correction is close to free. When the variances really are equal and the groups are balanced, Welch gives up a negligible amount of power relative to Student; when they are not equal, it holds the nominal error rate where Student inflates it. Delacre, Lakens and Leys (2017) put the argument in a title that leaves little room: psychologists should use Welch's test by default. Student's t is a special case that only wins anything under a condition you cannot verify reliably.

If you adopt that policy, state it once in the analysis plan and never revisit it: “All between-group comparisons used Welch's t test and Welch's ANOVA, without a preliminary test of homogeneity of variance, following Delacre et al. (2017).” One sentence. It covers every comparison in the paper and removes the reviewer's line about a forgotten assumption check.

That said, plenty of journals, examiners and supervisors still expect to see Levene printed, and this is not a battle worth fighting in a response letter. Report it and use Welch anyway. “Levene's test indicated unequal variances, F(1, 114) = 9.62, p = .002; in any case, all comparisons used the Welch correction” satisfies both camps and costs you nothing.

What reviewers flag

An F with only one degree of freedom. “F = 9.62, p = .002” lets nobody recompute anything. Levene always carries two, and the automated statistics checkers several publishers now run will try and flag it as incomplete.

“The assumption of homogeneity was met.” A non-significant test does not establish equality of variances, least of all with small groups. The defensible wording is “no significant difference between variances was detected”, with the F and the p beside it.

Reporting a significant Levene and then reporting Student's t. This happens more than you would expect, because the Student row is the first line of the table and the eye goes straight to it. A whole-number df on your t after a significant Levene means you copied the wrong row.

Switching to Mann-Whitney because Levene was significant. It is the instinctive escape and it solves nothing: the Mann-Whitney U test also assumes the groups share a distributional shape if you want to read it as a comparison of medians, and with markedly different variances that assumption fails too. Heteroscedasticity is handled with Welch, not by moving to ranks.

Using Levene on repeated measures. If your “groups” are time points from the same participants, the assumption in play is sphericity, the test is Mauchly's W and the correction is Greenhouse-Geisser or Huynh-Feldt. Levene compares independent groups and has nothing to say there.

Letting the assumption redesign the study. A significant Levene changes the test, not the research question and not the design. If your result stops being significant once the correction is applied, that is information about your study and it belongs in the discussion; it is not a reason to go back to the row that still gave you p < .05.

Frequently asked questions

How do you report Levene's test in APA 7?

With the F statistic, both degrees of freedom and the p value: F(1, 114) = 9.62, p = .002. The first degree of freedom is the number of groups minus one and the second is N minus the number of groups. It goes in a sentence in the Results section, with no table of its own and no effect size, and it is always followed by a statement of which test you ran on the strength of that result.

What do I do if Levene's test is significant?

You change the test, not the data. With two groups, use Welch's t test, which is the “Equal variances not assumed” row in SPSS and what t.test() does by default in R. With three or more, use Welch's ANOVA with Games-Howell pairwise comparisons instead of Tukey. The degrees of freedom will come out fractional, and that is correct: report them as they are, to two decimal places.

How many degrees of freedom does Levene's test have?

Two, because Levene's test is an ANOVA on the absolute deviations from each group's centre. The first is k − 1, where k is the number of groups, and the second is N − k. Two groups and 116 participants give F(1, 114); three groups and 138 give F(2, 135). A Levene F with only one degree of freedom is incomplete and nobody can recompute the p value from it.

Which version of Levene's test should I report, mean or median?

The median-based version, which is the Brown-Forsythe variant and the row SPSS labels “Based on Median”. Centring on the median makes the test far less sensitive to skew and outliers, and it is what car::leveneTest() in R uses by default. Whichever you use, name it in the text: the four SPSS rows return four different values on the same data.

Do I always have to run Levene's test before a t test?

Fewer and fewer methodologists think so. Choosing your test from a preliminary test on the same data leaves the real Type I error rate uncontrolled, and Levene has least power exactly in the small samples where unequal variances do most damage. The alternative recommended by Zimmerman (2004) and Delacre et al. (2017) is to use Welch by default and declare it in one sentence of the analysis plan.

Does Levene's test apply to repeated measures?

No. Levene compares variances across independent groups. In a repeated measures ANOVA the equivalent assumption is sphericity, tested with Mauchly's W and corrected with Greenhouse-Geisser or Huynh-Feldt. In mixed designs you will see both in the same output, one for the between-subjects factor and one for the within-subjects factor, and they are reported separately.

With the F, both degrees of freedom, the p value and one sentence saying which test you ran next, your Levene report meets APA 7. And if you decide to skip it and use Welch by default, that meets it too, provided you declare the policy before the results. When the design gets harder — badly unbalanced groups, covariates, variances that shift over time — we can work through it together in my statistical consulting.