when in two-way ANOVA transformation becomes hard and non-parametric tests unsuitable, can someone run one-way ANOVA for each factor separately such that if transformation doesn't work non-parametric test suitable for one-way ANOVA is employed?
Everything is allowed as long as you explain why and how you did so that other researchers can repeat your experiment exactly. However doing two ANOVAS instead of MANOVA may make you loose some interactions.
Kruskal-Wallis one-way analysis of variance works for independent k-sample case. Non-parametric tests are used when the sample size is less than 30 in Finland.
Hi
1.It is possible but you will loss your time and testing the multiple comparisons can not be done in one way ANOVA.
2. Please refer to:
. Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.
.Howitt, D. and Cramer, D.(2008). Introduction to SPSS.
Regards,
Zuhair
The answer is "yes". Resources and other factors must be considered due to the possibility that testing amy be prolonged if multiple comparisons are needed yet a one-way ANOVA used separately for each. You may also increase the chance of Type I and Type II errors. Bottomline: It depends on your resources and goals.
Hello Fisseha,
2way ANOVA is always preferable to doing 1way ANOVA because it makes better use of the information. For example, you can look at the interactive effect. And the tests have more power (larger df for the error term). There is nothing *wrong* with doing 1ways instead of the 2way, except you pay the price in loss of information and in power.
If the assumptions of normal and independent residuals are not met, one can still do a 2way ANOVA via randomization. See:
https://en.wikipedia.org/wiki/Resampling_(statistics)
b.t.w., did you know that the distribution of the data (taken as the response variable) is only a clue to which error distribution to use in analysis? It is not a prerequisite.
The assumptions for the general linear model (including regression, ANOVA, and ANCOVA) are that the errors (residuals) are normal and homogeneous (Eisenhart 1947, Seber 1966, Neter et al 1983 pp 31& 49, Quinn and Keough 2002 pp 110 & 280). Evaluation of assumptions in texts, where it occurs, often entails a residual versus fit plot (for homogeneity) and a normal score plot or Quantile-Quantile plot (for normality of the residuals). If you haven't already, I suggest you look at the residuals from your 2way ANOVA. And take it from there.
Good luck with your research,
David S
As has been said before, the problem with doing two one-way ANOVAS is that you lose information about the interaction. It might be possible to create an interaction comparison, by creating an independent variable that will do that comparison as a separate one-way ANOVA. For example, if each IV (say X1 and X2) has two levels, say -1 and +1, then the product X1X2 will create the interaction factor, comparing (High and High together with Low and Low) vs (High and Low together with Low and High). With more than two levels per factor, it becomes more complicated but I believe it would be doable.
If you don't want the interaction effect, you can do it separately. For example: you can run the glm using SAS software using appropriate synthax.
Hello Fisseha Asmelash,
Using both factors in ANOVA is always the best first model. It has more df (more power to detect effects). It allows you to quantify interactive effects. If the interactive effect is significant, you then run oneway ANOVA for each level of the other factor in the two way. In other words one way ANOVA on factor B, for each level of A. Your choice on how to split it, by A or by B.
In some situations the interactive effect is the research question focus. For example does a treatment effect depend on some other variable?
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