You need to do a test, such as ANOVA, that incorporates all variables and tests all interactions. Multiple t tests do not test for interactions between variables and increases the chance of Type 1 errors. You can only use ANOVA if the distribution is normal, otherwise use PERMANOVA. And you only test for interactions if the overall p value is < 0.05. :)

My first question would be how you define "safeguarding cardiovascular properties" in terms of the variables you are measuring, and if taking values every 10 min is required for that. If the course over time is relevant, then I'd expect some time-course analysis, that is, some kind of regression models, not ANOVAs or t-tests.

If you say you like to compare values before and after the surgery, then your main goal is to estimate the "difference in difference", corresponding to the interaction term in the 2-way ANOVA (with time and group as factors). You will have paired data (before/after measurements taken from the same animal), so it's possibly simpler to calculate these differences per animal and then compare the two groups of differences with a t-test (the alternative would be to include a factor for "animal ID" in the ANOVA-model to fit individual intercepts per animal).

You should take care that the ANOVA assumptions are reasonable for your variables. For instance, variables like protein concentrations should be assumed log-normal distributed and would require a log-transformation.

My second question would be if the study has a high chance to provide some conclusive results. That means: how many animals would be required, given the assumed effects and variances? (keyword: power analysis; power should be > 0.8). And is the number of animals you can measure large enough?

Jochen Wilhelm wrote: If the course over time is relevant, then I'd expect some time-course analysis, that is, some kind of regression models, not ANOVAs or t-tests.

I agree. In that case, I think you would want a multilevel model, with horses as level 2 variables and occasions of measurement at level 1 (i.e., clustered within horses). Here are a couple of places where you might find some helpful resources:

• https://www.bristol.ac.uk/cmm/
• https://www.pilesofvariance.com/

Q. How many cardiovascular features will be recorded? And are they all considered equally important? Or do you have a small number of primary outcomes (1 or 2) with the others being considered secondary?

What I am getting at with that question is the so-called multiplicity problem that arises when you have multiple outcomes. Two of my favourite articles on multiplicity are these 2005 Lancet articles by Schulz & Grimes:

Article Schulz K, Grimes DMultiplicity in randomised trials I: endpo...

Article Multiplicity in randomised trials II: Subgroup and interim analyses

Finally, your situation reminds me of the attached excerpt from Frank Harrell's well-known book on regression models. He described a two-group clinical trial with several DVs measured on just one occasion. And in that scenario, he suggested binary logistic regression with group (treatment vs control) as the outcome variable and the multiple DVs (as originally conceived) as the explanatory variables. In your case, given the repeated measurements every 10 minutes, you would have to use a multilevel logistic regression model to account for the clustering of the repeated observations within horses.

Please bear in mind that I have only been thinking about this for 10 minutes, and I never heard Harrell or anyone else extend his suggestion to this multilevel scenario. But on the face of it, it makes sense to me. ;-)

Regarding the multiplicity problem Bruce Weaver mentioned:

This is a problem only if you screen for a variable that might be a "marker". If your variables are all known to be indicative for the same "cardiovascular property", then this is not a screening for which you would need to correct for multiple testing but each test would rather add information. I woudln't go farther than that, but acually, in such a case, the p-values might even be combined using Fisher's method to evaluate that "combined evidence". This can be conceptually tricky (as data from different variables are not independent within animals) and I would not consider this in a student's project. Just don't tap into the trap of "multiple testing corrections" if your task is not a screening.

Jochen Wilhelm Regarding your questions:

- We are expecting one premediction protocol to induce some level of negative side effects on the carpdiopulmonary system (reduced heart rate, reduced cardiac output, and possibly hypotension). The aim of this project would be to design another premedication protocol that would overcome these side effect and maintain horses under acceptable cardiovascular values. Because these effects are only seen during the suregy, as these effects will be abolished by using a reversal agent, we are relying on the monitoring values taking throughout the suregy in order to assess the efficacy of the new premedication protocol (that should overcome the CV side effects).

- Unfortunately I am not in charge of perfomring the power analysis for this project, one of my fellow student has come up with the final animal number for this study based on her litterature review. We are expecting to perform a power analysis as this exercise is not going into that much details regarding patients recruitement. The main goal of this exercise was to design an anaesthetic protocol. However, we are expecting to predict what statistical test would be most appropriate for this, hence my presence on here to gather some precious feedback :)

Bruce Weaver We ended up choosing 3 variables, heart rate, mean arterial blood pressure and end tidal CO2. However we are not entirely set and might reconsider following a read of your suggesting material :)

Dear Laura.

You are at a good time to do the right thing, which is to set up the experimental design correctly, this will ensure that the variations in the dependent variable are the product of the independent variables or causes that enter the design.

I assume that there are several dependent variables, but I only see a single independent variable (protocol).

What is the effect of the premedication protocol on the cardiovascular properties of the enrolled animals?

a single VI (protocol)

in the case of a 2-way anova, the question or problem could be.

what is the effect of the premedication protocol on the cardiovascular properties of the enrolled animals, independent of the age group to which the animal belongs?

2 VI, protocol, age block design

what is the effect of the premedication protocol and in which age group does the animal have the best cardiovascular response?

2 VI, protocol, age interaction design.

once you are clear on this you can look up the appropriate statistical procedure, it will also tell you what is the minimum sample size per cell, (number of replicates per treatment).