You can first do an omnibus ANOVA and then do three planned comparisons if the omnibus ANOVA comes out significant. Or you can do regression with Group dummy-coded with control as the baseline, and then if the group variable is significant in a model comparison F-test then you can look at the three individual dummy coefficients to get the three planned comparisons. In fact these approaches are formally equivalent I think, they look different on the surface but they both come from a general linear model.

You can do ANOVA with that. But how many variables are you working with, so that you may proceed and do multiple comparisons analysis

Thank you for your answers!

Fausto: I don't have any data yet. We studied the literature, made a hypothesis, designed the study and did preliminary tests. We will soon do our experiments but we like to have worked out the best ways prior to our study.

Stephen: Can you explain what you mean by "three planned comparisons"? Do you mean post-hoc analysis with Dunnett / Tukey / ...?

Olalekan: If I am right, I work with one variable, namely the added cell type:

• - control group: no added cell type (only cardiomyocytes)
• - experimental group 1: we add fibroblasts
• - experimental group 2: we add peripheral-blood mononuclear cells
• - experimental group 3: we add mesenchymal stem cells

If I were in your situation I would plan on ANOVA.

You're right that it will spit out a p-value stating if you have significance overall among your groups. I suppose you're also right that EG1 and EG2 theoretically can raise that p-value if they sit in between control and EG3. BUT I also think that's not really what you care about. It seems that you primarily care about the multiple pairwise comparisons.

After you use a post-hoc correction (e.g. Tukey's but there are many), you can simply use the p-values for pairwise comparisons you care about. This is more conservative than a bunch of t-tests. And in all but the rarest cases, those pairwise outcomes will fall on the same side of your critical p-values as would the corresponding t-tests, anyway.

There are assumptions inherent in every test, and in ANOVA one major one is normality of residuals. If your residuals are non-normal, you can use Kruskal-Wallis as a fallback. I'm not as familiar with the implementation but there are post-hocs for that as well.

The previous answers are true. However, sometimes a different approach may make the response easier to understand. Dr Galetto states that these methods depend on the (nature of) the data. If your recordings are measured with equal distance between the units, for example mm, grams or litres, “parametric” statistical tests are usually appropriate. Such data are called metric data.

If, on the other hand, your data are such that what you record are observations like big, bigger biggest or very tender, tender, not so tender, tough, very tough, a “non-parametric” approach is appropriate. Such data are called ranging data. Then you must use so-called non-parametric tests.

If you want to test the null-hypothesis that none of the groups are significantly different from each other, and the data are parametric, ANOVA is appropriate. If you have ranging data you have to use a non-parametric test: Kruskal-Wallis. The above principle statements are rather sweeping, which are usually, but not always true. Their appropriate usage implies the satisfaction of certain conditions, which is outside the scope of this discussion.

In your particular case, I assume that you have parametric data. Then, as stated above, ANOVA is appropriate. This test answers only one, but essential question: Is there a significant difference between the mean values of your 4 groups. If the answer is negative, this means that there are no significant difference between the groups, and further analyses are meaningless.

Only if the answer is positive, you may test each variable against each of the other variables, which in your case amounts to 6 permutations (1-2, 1-3, 1-4, 2-3, 2-4, 3-4). If you do all these tests, you have to adjust your alpha-level, because otherwise you increase the risk of a type I error. One way of doing so (but not the only one) is the use of “Bonferroni” correction, which in your case means that you divide your chosen alpha-level by the number of tests performed (0.05/6 = 0.008). So, in order to reject your null-hypothesis, p < 0.008.

The three planned tests mentioned by dr. Stephen Politzer-Ahles, are those that you yourself mentioned in your message:

- does EG1 give a better result than control?

- does EG2 give a better result than control?

- does EG3 give a better result than control?

Two final points: If you only need answer to the above three questions, then only three tests are required, and the Bonferroni correction would be 0.05/3 = 0.017, which means that your null-hypothesis would be more easily rejected.

If, as you say, you have reason to believe that EG1 > EG2 > EG3 > CG (preferably if your supposition can be justified by clinical observations or convincing deductions), you may use on-tailed tests, which are more powerful than to-tailed ones.

Good luck with your Research!

Dear Linus,

You have four experimental groups and haven't any control. Infact, you transplant in four conditions. So, you have four independent  groups that you must test equality of their means by ANOVA. If it is significant you test EG1>EG and if it is significant then you test EG2>EG1 and finally, if it is significant then you test EG3>EG2 (All by t-test approuch).

Thank you very kindly for all these insights. I have been studying the difference between the Tukey test and Dunnett test, and depending on my research question, they seem appropriate for my study:

• Do I want to compare each experimental group to the control (3 pairwise comparisons)? --> Dunnett
• Do I want to compare each group to each other group (6 pairwise comparisons)? --> Tukey

If I decide before my study starts that I will use one of these tests, do I need ANOVA? Is an ANOVA result with p

Yes of course, before you want to do pairewaise compairisons, you need to do ANOVA and result that is significant.

     Analysis of variance is used when you want to determine whether there were differences between several arithmetic mean. 

     Conditions for computing variance analysis are: a). each of the populations must be normally distributed, b). variance of these populations (S2) must be the same and c). selection of respondents should be random and independent. 

     The basic idea contained in this analysis of variance: must be demonstrated that the variability between the groups is greater than the variability within the groups. If the variability between groups significantly higher than the variability within the groups then it is really a groups that does not belong to the same population. However, if the variability between the groups is less than the variability within the groups, then these groups does belong to the same population.

     From this point on, it can be seen that the variance analysis actually consists in the fact that the variability of all obtained results is divided into the parts of which it is composed, that is, the internal variability within each group of results, and the variability between the individual groups. From the relationship of these two variables it can be concluded whether groups are different (ie not belonging to the same population), or their differences are only random, so all (groups) actually come from the same "mother" population.

     When the calculation determines that the variability between groups is greater than the variability within the groups, it is necessary to determine whether the variability between groups sufficiently greater than the variability within the groups, to be able to declare that the groups actually significantly different. With the help of Snedecorovih F tables can be set up, how many times must a minimum variability between groups be greater than the variability within the groups, to make a difference between both variability was statistically significant. With the help of degrees of freedom is calculated F limit at the level of 5% or 1%, and if our F higher, it means that our groups does not belong to the same population (p

ONE WAY ANOVA will be OK,  but your choice of post Hoc test is a function of the accepted hypothesis.  If the alternative hypothesis is accepted based on your alpha level,  then you can go ahead with pay Hoc test. 

Although I do not know the kind of numerical data and the expected variances among the groups, I believe that ANOVA is a good method to compare the differences among the different experimental groups. My understanding of the research groups though, is that all groups including the CG seem to be experimental groups to me. A control groups should be one that is not being treated at all. All of your groups are just experimental groups subjected to different levels of the treatment. If it is possible to have a control with no treatment, then a one-way ANOVA coupled with Tukey's HSD will give the best if the data meats the assumptions of ANOVA: Randomization, Sample representation, Normality of the residuals, Uniformity of variance of the groups. If there is a way to include a better control, Dunnett's mean comparison with the control may be used in stead of the Tukey's HSD.

Also if there are possible co-variances or nuisance factors, the design should be made to take care of them so that variability emanating from these factors can be treated statistically. Good luck!

You can use One-way Anova. You can then separate the means based on your p-value of the hypothesis

I would recommend ANOVA followed by post-hoc Tukey's or Duncan's multiple range tests.