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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
 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
 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

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

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?

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

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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