Hi Javier, how are you?

In a two way anova you do post-hoc tests in two situations:

1. If you have an interaction between the two factors

2. If you have an overall effect and the group has more than 2 variables.

For example:

1. Treatment (A, B, C) versus sex (male, female):

If you have a treatment x sex interaction, you can follow with a post-hoc and compare whatever you want.

2. you dont have an interaction, but you have an overall sex effect: in this case you dont need a post hoc because you only have two groups and the anova is telling you that one sex is higher the the other.

3. you dont have an interaction, but you have a treatment effect: in this case you can do a posthoc to compare A, B, C. This will tell you that one or two treatments are higher than the other REGARDLESS of sex.

Good luck!

Hi Francisco. I´m not an expert in this topic. I hope that follow suggestion can help you. Apparently two way-Anova is suitable for the solution of this problem.

2 way-anova provides you the solution to the follow questions:

1. ¿Is factor 1 a source of variation in the concentration of metabolite?

2. ¿Is factor 2 a source of variation in the concentration of metabolite?

3. ¿Is factor 1 and 2 sources of variation in the concentration of metabolite?

In addition, post hoc test provides information about statistical differences between treatments of factor 1 or factor 2 (by separate) on the concentration of your metabolite. Exist some post hoc analyses that you can prove. I´m not sure, but, in example, Turkey´s post hoc test is only applicable for pairwise comparisons. This is helpful if you have a control group (for each factor of variation) on the concentration the metabolite.

I recommend you the software Graph Prism because is very didactic and easy.

http://cdn.graphpad.com/docs/prism/6/Prism-6-User-Guide.pdf

Hi Javier,

Theory says that it is only valid to perform post-hoc tests when there is an interaction that reachs significance. However, I always perform post-hoc tests because many times you obtained a non-significant interaction but post-hoc tests show that some comparisons reach significant levels. I think this happens because in basis science many times we employ a number of samples that are much lower than those recommended and in addition we suppose a lineality that perhaps is not met.

I recommend you to perform post-hoc tests although interaction is not significant and report any significant difference you might find in pairwise comparisons. 

Perhaps this cite could help you (Tybout et al. (2001). Analysis of Variance. J. Consum. Psychol., 10(1&2), 5-35. doi: 10.1207/S15327663JCP1001&2_03). In this paper it is discussed whether is valid to perform post-hoc test in the absence of interactions between factors.

You can request full text here: https://www.researchgate.net/publication/257474463_Analysis_of_Variance

Article Analysis of Variance

Hi Javier, how are you?

In a two way anova you do post-hoc tests in two situations:

1. If you have an interaction between the two factors

2. If you have an overall effect and the group has more than 2 variables.

For example:

1. Treatment (A, B, C) versus sex (male, female):

If you have a treatment x sex interaction, you can follow with a post-hoc and compare whatever you want.

2. you dont have an interaction, but you have an overall sex effect: in this case you dont need a post hoc because you only have two groups and the anova is telling you that one sex is higher the the other.

3. you dont have an interaction, but you have a treatment effect: in this case you can do a posthoc to compare A, B, C. This will tell you that one or two treatments are higher than the other REGARDLESS of sex.

Good luck!

Hi Javier,

I wanted to answer but Leandro already did beautifully

best

Hi Javier and Leandro,

My response only apllies when one of the factors has at least more than two levels. I assumed that that was the case you were discussing.

Thank you guys! Nice explanation Leandro, I was real really confused