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How should I transform non-negative data including zeros?

I want to log-transform some of my data because the Levene's homogeneity of variances test rejected the null hypothesis for those sets, before performing a two-way balanced ANOVA.

Now, some of the data I collected have null values, because they are related to my plants' tillers, and some of them didn't have any.

So for my log-transformation, should I simply use the formula =LOG(x+1) (in LibreOffice Calc) so those null values go back to 0? Or the value of the constant I add depends on how the datasets look? For example, I have weights that range from 0 to 12 grams, other weight that range from 0 to 1.5 grams, and leaf area ranging from 0 to 565 cm². Would =LOG(x+1) be ok for data ranging from 0 to 565, but not for data ranging from 0 to 1.5?

Here are some histograms to show how my data is distributed:

enter image description here

What do you think? Thanks in advance!

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    $\begingroup$ This question may be relevant: stats.stackexchange.com/questions/1444/… $\endgroup$
    – mogron
    Jul 5, 2012 at 8:37
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    $\begingroup$ as well as: stats.stackexchange.com/questions/30728/… $\endgroup$
    – Stéphane Laurent
    Jul 5, 2012 at 8:53
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    $\begingroup$ specially this part stats.stackexchange.com/a/1630/603 $\endgroup$
    – user603
    Jul 5, 2012 at 11:18
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    $\begingroup$ These discussion go into issues of adjusting 0 when tranforming to the log. But the log transformation is generally done to adjust for skewness. The square root transformation seems to be a more common choice for variance stabilization. In this case the histograms look skewed probably because of the truncation to 0. I don't think doing a log transformation is a good idea in this type of situaation. $\endgroup$
    – Michael R. Chernick
    Jul 5, 2012 at 11:26

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