It's a 3x3 factorial design. The conditional distribution of log root weight, log shoot weight and log length should be approximately normal.

You need to give information about your dependent variable(s) as this determines a lot about your model. Best, D. Booth

Thanks. My dependent variables are root and shoot weight as well as length among many other parameters.

It's a 3x3 factorial design. The conditional distribution of log root weight, log shoot weight and log length should be approximately normal.

Jochen Wilhelm I would be applying ANOVA 2 way right? and then for the post hoc would I be using Tukey's HSD or LSD?

No, it's a 3-way ANOVA. Tukey's HSD and LSD does not apply to multiway-ANOVAs. If you want to compare group means it might be best to recode the model to have 9 groups and then do the comparisons you want. In case you use R you can do these comparisons with glht (package multcomp).

Hi. You might find this attachment on factorial designs to be helpful with Jochen's

excellent comments. Best, David

Jochen Wilhelm what is the third independent variable here? the doses of heavy metals?

Also, can you please elaborate on what you mean by recoding the model to get 9 groups, is this an application available in R only? Since I am using SPSS/Statistix 8.1. Thank you.

David Eugene Booth Thank you so much, I will study this thoroughly.

according to the new information, it is expected to know the impact on the length, weight of the outbreak and others, you should use a MANOVA ?, but Fahkria, is interested in obtaining a response for each dependent variable or jointly ?

I assume each heavy metal is analysed independently, because different biological uptake mecanisms will be involved. So you actually have an experiment to check the lead uptake, and another to check cadmium uptake. The experiments have three experimental factors:

Factor #1: "treatment" (treated, control)

Factor #2: "biochar" (a,b,c)

Factor #3: "heavy metal dose" (0, 50, 100 mg)

Jochen Wilhelm Yes you are right. The treatment column will consist of whether or not heavy metal is present?

Carlos Jimenez-Gallardo I am checking the effect on dependent variables separately sir.

No, as I understood you have a treament, but you did not mention what this is. If you meant with "treatment" that heavy metal is given, then there are only two factors:

Factor #1: "heavy metal dose" (0, 50, 100 mg) Factor #2: "biochar" (a,b,c)

The presence/absence of heavy metal is in factor #1, as "being absent" is a dose of 0.

Jochen Wilhelm I have 2 heavy metals with 2 doses of each and then 3 organic amendments with a single dose. So that makes it 2 factors right? I have 8 controls in my factorial design as mentioned above.

In this case I would be using 2 way ANOVA right? and as a post hoc test would I be using HSD or LSD?

Not quite... you have 2 heavy metals with 3 doses each (0 is also a dose!). It's important to understand that this is part of that experimental factor. If you call these dose=0-samples "controls" does not make that different.

If I understood you correctly now, you have a 3 (doses) x 3 (biochar) - design. This allows you to investigate the interaction of dose and biochar. This is an actual ANOVA, as you would compare models with and without interaction terms.

I don't quite understand what post-hoc tests you want to do. If you want to compare any combination of dose & biochar, you might better fit a one-factorial model, where each group is one possible combi (=9 groups). There you could do Tukey's HSD, but the more interesting question is likely for the interaction of dose and biochar, what can be analyzed only in the two-factorial model.

This way, there are 12 groups because there is also also a group where no biochar is present. So there would be 2 doses of biochar as well i.e. 0 and 10 g/kg.

As for the post hoc test, I want to check whether heavy metal stress has been alleviated by the presence of biochar so I wouyld be comparing the different groups with control with neither heavy metal nor any biochar. So can't Tukey's HSD be applied after 2 way ANOVA?