I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.

One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.

I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.

Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?

P.S.: my raw data are below:

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36 0.363 0.371 0.398 0.407 0.409 0.432 0.494 0.719

B: 0.11 0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19 1.233 1.505 1.897

C: 0.106 0.114 0.143 0.435 0.448 0.51 0.576 0.588 0.608 0.64 0.658 0.788 0.958