Hello, I performed experiments with two way ANOVA.
One factor is 'species'(ex: 1,2,3)
and another factor is 'treatment' (ex: +,-)
When I carried out the two way ANOVA, only the main factor 'treatment' showed a significant difference, and there was no statistical significance in another main factor 'species' and their interaction (species * treatment) as well.
But I still want to evaluate the effect of 'treatment' within the 'species'.
For example, the difference between species 1 with and without treatment (1+ vs 1-).
So in this case, is it ok to perform an independent t-test with (1+ vs 1-)?
or do I need to do post-hoc tests within the species?
Thank you in advance.
If the ANOVA analysis is correct, this is what we are looking for! The significant interaction doesn't appear in all analysis! It happens only when the response of a level of variable differs than others. Regards.
I agree with Medhat: the experiment seems to be conducted to find out if the treatment-effect differs between species. The non-significant test of the treatment x species interaction tells you that your data are not sufficient to say anything about such differential treament effects. It's actually recommended to stop here and re-think the research.
Nevertheless, there might be other things to check, e.g. if the treatment was effective at all. The corresponding hypotheses to test would be about simple effects. And if variance homogeneity can be assumed, post-hoc tests are the better choice because they have more power and and more robust (because the standard errors are estimated from all the data, not just from the groups being actually compared).
Among other things, you should examine the response variable and conduct the correspondent residual analysis. If assumptions are not met, then perhaps you might need to make a variable transformation (eg., if your variable is in percentages). Maybe with a model in which the response variable is transformed and a model that meets the assumptions (normality, variable homogeneity, independent residuals) you could get a significant result for your interaction. You could also examine the sample size and the power of your model.
If you have a reasonably good model, it can be that there is not an interaction between the factors you could proceed to examine the simple effects. Simple effects where significant differences were detected can be examined with a suitable posthoc test.
regards
Just adding to the other good comments made, I would interpret your results as treatment is significant regardless the level of species (1, 2, 3 etc), i.e., treatment response is the same across all species. That means that your predictor (the Y axis) 'behaves' the same for all the levels of species under a given treatment.
However, to better visualize and interpret an interaction, I think the most useful thing to do is to plot line graphs for the interactions. Hypothesis testing for the interaction can be flawed for many reasons, just like any other hypothesis testing. Ideally, we shouldn't rely solely on p-values. So, plot the line graphs and check whether the lines go to the same or different directions. In your scenario, plot your predictor on the Y axis, species on X axis and separate lines for each treatment. Which trajectories the lines follow? Are there two parallel lines with similar slopes? Do the lines cross? Do one line go a certain direction for one level of X and then change to the next level? Different lines likely mean an interaction is present. Should you have an interaction, you would follow them up with simple effects analysis.
Hope that helps. Best of luck!
From my own opinion, post doc is not required if the research or an experiment is not significant.
And it not everytime that your treatment will be significant. It is either the test is the same or differ.
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