I tested the effect of pH on the delta 13C isotope change (beginning-end of experiment) in two species.
When I do a two-way ANOVA (two factors: pH and species, both with 2 levels), I get a non-significant interaction, and both pH and species have a significant effect (for pH, the p-value = 0.008).
When I take a subset however (only using species 2), with a one-way ANOVA for pH, pH does not have a significant effect (p-value=0.15).
How do I know which test is correct?
(I have added two barplots to illustrate this. One barplot with the full dataset and one barplot with the subset).
Both are "correct".
The p-value is a function of the sample size, and if you use only a part of your data, you will get larger p-values.
If you decide to ignore the interaction term, then you should still fit the two-factorial model, only without the interaction term. The model will then still use all the available data and you can directly interpret the two main-effects in this model.
PS: I am not very sure about your experimental design. If you analyzed the same observational units (subjects) "before and after" then you might consider a paired (repeated-measure) analysis (possibly a mixed model).
Thank you, Jochen!
The problem is that comparing the delta carbon isotope isn't very relevant (biological seen) between the two species, so I thought it might be better to fit the model on two subsets of data (for each species seperately). On the other hand, I learned during my statistics courses that it is always better to fit a model to the complete dataset.
Concerning the experimental design: you are right. I analysed the stable isotope values on day 1 and on day 8, for both species and both pH treatments. I have been reading about two-way repeated-measure ANOVAS or two-way mixed-ANOVAS. For as far I understood, the difference is that a repeated-measure ANOVA is appropriate when the same individuals undergo each treatments (in this case: pH treatment), while a mixed-ANOVA is appropriate if your individuals undergo different treatments. In this case, both species 1 and 2 had two pH treatments, but they were different individuals, so I think a mixed-ANOVA is more appriopriate?
I just saw that your plots show "difference in dC13 between day 1 and day 8". If these differences were determined from measurements at both days in the same individual, and if these differences were used in the model, then that this is already a "repeated measures analysis" and you don't need to consider it further.
Now, as I understood, did you do this for two levels of the factor "pH" and for two levels of the factor "species". Here you conclude that the interaction is "not significant". I am not sure if I would agree here, because the interaction plot (your 2nd figure) shows that the pH effect is larger (about twice!) in species 1 than in species 2. It is always "more difficult" to demonstrate an interaction that to demonstrate main effects, so your conclusion might simply be due to the fact that your sample size is not large enough.
When we do belive that the pH effect is different in the two species, then you sould analyze the effect in both species, ideally using the full factorial model (with interaction).
When we believe that the pH effect is independent if the species (i.e. we may assume the same pH effect in both species), then why should you estimate the pH effect only in one of the species? The specien information is then irrelevant and you should use all the data (irrespective of the species) to estimate the pH effect.
Like all quantitative research. The problem is not in the results that differ between the techniques, but, apply the correct technique in relation to the objectives or design PRE-SET, before performing the experiments (common error in experimental research, which is NOT DESIGN STATISTICALLY).
Only one of the analyzes is of correct READING, although both may be correct in CALCULATION, but only one responds to your goal.
In one way ANOVA the researcher takes only one factor while in the case of two way ANOVA the researcher investigates two factors concurrently. For a layman these two concepts of statistics are synonymous. However, there is a difference between one way and two way ANOVA.
Two-way ANOVA is often understood as an extended version of One way ANOVA. There are a number of advantages, due to which two way ANOVA is preferred over One way ANOVA, like with two-way ANOVa one can test the effects of two factors simultaneously.
The differences between one way and two way ANOVA can be drawn clearly on the following grounds:
Thank you all for these clear explanation! Much appreciated.
The "change between day 1 and day 8" is indeed caculated by using the difference per individual, so I will use the two way ANOVA on that full dataset.
Cheers,
Luna
Hi,
I would say both are correct. However, it gives you an hint that your data is well modeled pairwisely. Therefore, you will be modeled blocks rather than treatments. Hope this makes sense ...
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