Hello Noa,

Did you use the original Levene's test (based on deviations from the group average) or did you use the Modified Levene's Test (based on deviations from the group median)?

Have you tried using transformations to take care of the unequal variances?

Fisrtly,use another homogenity of variance test such as hartley Fmax to see results also true. In some analysis small variance differences may be result a significant levene result. Levene uses difference scores in each group and perform a ANOVA, So Levene results may be significant If groups size drastically differ or ıf some groups in your data extreme scores. According to Howell (2013, page 234) the results of variance analysis more likely to be  valid when the ratio of largest variance to smallest variance  was four or below among the groups.

Secondly, continue your analysis and use  post hoc Games-Howell. and report homogenity of variance violated so I used games-howell

Third, perform a bootsrap analysis, ıt is no requirement for assumptions.

Fourth, you can also perform a Bayesian mixed anova design

Howell, D. C. (2013).Statistical Methods for Psychology. Belmont, CA: Wadsworth Cengage Learning.

Best.

It is well known that Hartley's Test is sensitive to unequal sample sizes, while the Brown & Forythe Test does not have such a limitation.

If you have a total sample size greater than 30 and equal sub-sample sizes, ANOVA is robust to violations of homogeneity of variance. Noa Magal

Arash has reason, additionally a common way for variance stabilization is the transformation of responses. If your responses in any experiment “i” are “y_i” common transformation “yt_i” for variance stabilization are,

yt_i=log(y_i)

yt_i=ln(y_i)

yt_i=y_i^(-n)