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# Two-way ANOVA for data with homogeneity of variance is violated

I'm currently doing a biomechanical tissue study and want to run a two-way ANOVA.

Here is how my data look like:

• Independent variable #1 : Treatment or Non-treatment
• Independent variable #2 : Different 3 conditions
• Dependent variable : Elasticity of tissues (n=23)

At first, my data showed not a normality, so I transformed to log10 and became good normal distribution. However, Levene's test showed that the data violated homogeneity of variance. The sample sizes in three different conditions are all the same. But in condition 3, the standard deviation is pretty large; assuming this makes data heterogeneous. To handle this, I also checked the ratio of largest to smallest variations, showing 5.45 which is higher than 3~4 which is a rule of thumb. In this case, what can I do more to run a two-way ANOVA ? or if I have to run alternative test (non-parametric), what options do I have ? Thanks!

ps. Following is the result from SPSS.

Treatment Group

• Condition / Average / SD / N
• 1 / -1.7416 / 0.11994 / 23
• 2 / -1.7766 / 0.10215 / 23
• 3 / -1.4389 / 0.21877 / 23
• Total: -1.6524 / 0.21642 / 69

Non-treatment Group

• Condition / Average / SD / N
• 1 / -1.6356 / 0.09080 / 23
• 2 / -1.6270 / 0.16576 / 23
• 3 / -1.3469 / 0.16575 / 23
• Total: -1.5362 / 0.19705 / 69

Levene's test : F 6.488 / df1 5 / df2 132 / p<0.000