I have no normal data or data without homoscedasticity and I'm not very sure if this is suitable for a two way Anova analysis
A two-way ANOVA is usually based on a linear model of the following form:
y = mu + ax1 + bx2 + e
in which x1 and x2 are two qualitative explanatory variables (factors). Such a linear model is based on the usual assumptions of linearity, homoschedasticity, independence and normality of data.
You could do some of the following:
1) apply the linear model to the data as they are, relying on the "robustness" of the linear model
2) transform the data to make them more amenable to be treated under the assumptions of the linear model (e.g. box-cox transformation etc ...)
3) relax the assumptions of the linear model and try a generalised linear model (with the appropriate link function), or a thouroughlly non-linear model approach
Many thanks! My data is normal. I tried square root transformation and now my data has equal variances. Now I can perform two way ANOVA analysis.
Never rely on the "robustness" of the linear model.
Interestingly, simulations show that heteroscedasticity is the much bigger problem and often a by-product of non-normality. Transformation often does the job, as you discovered, as does a generalized linear model. I recommend familiarizing yourself with the latter because it's likely to become the norm in non-statistical fields over the next 10 years.
I forgot to specify that the objective of your work is also relevant in deciding which course of action to undertake.
If it's inference (e.g. biological inferences), Michael is right, a standard linear model would clearly be wrong if your data do not meet the assumptions (e.g. normality, homoschedasticity etc ...).
If you're in the field of predictions, a linear model may sometimes be surprisingly "robust" (i.e. give fair predictions) even when data are not normal, not homoschedastic etc ...
Cheers :-)
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA