Dear all,
I am currently analyzing new data (ie; the area of an object, for three different conditions, see below for a graph example) and now comes the question of statistics.
I wish to only compare Condition 1 vs Condition 2 ; and Condition 2 vs Condition 3. In this situation, I usually do an ANOVA (or the non-parametric version if assumptions of normality and/or equality of variance are not met) with Post-hoc (I compare the mean of every condition against every other condition), and just take the comparison that I need.
My knowledge of statistics is very limited, so the following question might sound trivial... But I am wondering if I am right by doing like that, because I often see similar graphs in published articles that instead use two student's t tests. What is the most objective/correct way of doing statistics in this case? And if I wish to only compare Condition 1 vs Condition 2 ; and Condition 1 vs Condition 3 ; is the approach similar?
Thank you very much for your help,
Kind regards,
Quentin
You are correct in doing ANOVA with a global F test first in a situation like yours with > 2 groups/conditions. The ANOVA posthoc tests after a significant F statistic are more powerful than the conventional independent samples t tests because they use the sample size from the entire design (all three groups/conditions) to derive the standard error of the mean difference rather than just the two group sizes. The ANOVA posthoc tests also have more degrees of freedom when there are > 2 groups, providing greater statistical power.
I'd like to add something to Christian's correct answer:
As he said, the post hoc tests (= tests you can do after having all the data - not only the data of the groups you actually compare) use the information of all the data to get better estimates of the standard error. This pooled standard error can be easily obtained from an interim result of an ANOVA, this is why most software offer such post-hoc tests in conjunction with ANOVA.
Another point is that you might want to control the type-I error rate for your global hypothesis" all of these groups are from populations with the same mean object area". This can be done in many different ways. The simplest approach is Fisher's least significant difference appoach. This method works when you have exaktly 3 groups (as you do). It starts with actually doing the ANOVA and checking the significance at the desired level (usually 0.05). If this is not significant, then you are done with the result that your data are not conclusive about any difference. Only of the ANOVA is considered significant, then you can do all three possible post-hoc tests (including the two you aim to do) at the same level of significance. Given the significant ANOVA this will make sure that the desired global type-I error rate is kept.
And finally: doing ANOVA or t-tests (which here are done using the pooled standard error) assume that the variable has a normal distribution. The object area can not be negative, so theoretically the normal distribution is not a good assumption in your case. But the values you measured are all relatively far away from zero (relative to the scattering of the values), and there is no drastic difference visible in the distribution beween the groups, so that the assumption is practically reasonable in your case.
If you were interested, look at the link below.
It has interesting answers for you.
https://www.researchgate.net/post/Three-means-comparison-by-t-test-or-ANOVA
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