How to run 3-way ANOVA on data with no equality of variance in R?

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How to run 3-way ANOVA on data with no equality of variance in R?

Timo
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Dear list members,

The plan was to run a simple THREE-WAY-ANOVA on my data to analyze the effects of 3 factors on 1 dependent variable.

I have 8 treatments in total, which results from 2 different manipulations of each factor.
The Shapiro-Wilk test showed, that I have a normal distribution, which should be fine.
The Problem comes up with the second requirement: The equality of variance. The levene-test sadly showed significance.

As you can see below, the biggest variance (group 5) is 2.9 times bigger than the lowest variance (group 1).

Is that ok enough, so that I can just use the "simple" ANOVA (Anova(aov(...), type=3), or is that not allowed?
If not, what else could I do?
I already read, that I could try: (Anova(aov(...), type=3), white.adjust=True).
What´s about that?

Thank you so much in advance!

Kind regards,
Timo



 Descriptive statistics by group
group: 1
   vars  n mean   sd median trimmed  mad min max range  skew kurtosis   se
X1    1 50 5.58 0.81    5.6    5.58 0.89   4   7     3 -0.03    -0.73 0.11
-------------------------------------------------------------------
group: 2
   vars  n mean   sd median trimmed  mad min max range  skew kurtosis   se
X1    1 43 5.59 0.84    5.6    5.62 0.89 3.8   7   3.2 -0.12    -0.66 0.13
-------------------------------------------------------------------
group: 3
   vars  n mean   sd median trimmed  mad min max range  skew kurtosis   se
X1    1 48 5.04 0.98      5    5.07 1.19 1.8   7   5.2 -0.53     0.73 0.14
-------------------------------------------------------------------
group: 4
   vars  n mean   sd median trimmed  mad min max range  skew kurtosis   se
X1    1 41 4.52 1.03    4.6    4.56 1.19 2.4 6.4     4 -0.25    -0.94 0.16
-------------------------------------------------------------------
group: 5
   vars  n mean   sd median trimmed  mad min max range skew kurtosis  se
X1    1 47 4.29 1.38    4.4    4.28 1.48 1.6 6.8   5.2 0.03    -0.95 0.2
-------------------------------------------------------------------
group: 6
   vars  n mean   sd median trimmed  mad min max range skew kurtosis   se
X1    1 40 3.53 1.18    3.6    3.47 1.33 1.6 6.4   4.8 0.39    -0.48 0.19
-------------------------------------------------------------------
group: 7
   vars  n mean   sd median trimmed  mad min max range  skew kurtosis   se
X1    1 40 4.25 1.13    4.1    4.26 1.19 1.6 6.2   4.6 -0.05    -0.89 0.18
-------------------------------------------------------------------
group: 8
   vars  n mean  sd median trimmed  mad min max range  skew kurtosis   se
X1    1 41 2.89 0.9    2.8     2.9 0.89   1 4.6   3.6 -0.09    -0.61 0.14