You cannot expect helpful advice when you don't explain what precisely your response variable is (what you are measuring/counting/observing). This will help to identify a sensible statistical distribution to model expectations about your values.

Further: have you a series of different treatments on the same biological replicate (specimen)? Did you perform treatments in parallel (e.g. growing cells in a 12-well plate, then treating each well differently, then repeat the whole thing a couple of times)? Or did you apply each treatment on a separate plate with cells from the same or different individuals?

You need to explain your experimental design in much more detail, so that we can understand what the replication structure is and what sources of common variance exist. Otherwise it is not possible to provide good advice on how to "normalize" your data or how an appropriate hierarchical model might look like to account correctly for these different sources of common variance.

Jochen Wilhelm ive added the info your requested, let me know if you can help.

If you grow the cells in 3 wells in parallel, then the 3 wells can be considered three parts of a larger well, so to say. Count the numbers of cells in these three wells and sum them up. Do not calculate proportions from the counts. It's better to use the counts. Do not average these numbers. Use the sums of the counts in the 3 wells as your read-out and use a binomial model.

Since you know the number of cells in each well, you can divide the measured cytokine conc in each well by the number of cells in that well to get the concentration per cell. These concentrations per cell can be averaged over the 3 wells.

This is done for each condition.

As I understood, you have a 2x2x2 design, with the experimental factors:

(i) inflammatory stimulus (no/yes)

(ii) treatment with hormone A (no/yes)

(iii) treatment with hormone B (no/yes)

And as I understand further, the scientifically interesting questions are supposedly if the hormone treatments alter the reaction to the inflammatory stimulus, and, possibly, if the combined treatment effect is different to the sum of the individual treatment effects (that is, there is a synergistic or antagonistic effect of the two hormones). Simple effects may be only interesting to demonstrate or check that the inflammation worked as expected and that the experiment was good enough to see that.

These questions can be addressed in a 2- or 3-factorial statistical model looking for the 2-way and 3-way interactions.

For the cell numbers, these models should be binomial models. If this doesn't work for you, you can calculate the proportions by hand and use the logit-transformed proportions in a normal model. For the cytokine concentration, these models should be gamma, quasi-Poisson or log-normal models (that is: use the log-transformed concentrations in a normal model).

Now what I did not understand is if you used cells from "the same flask" also across different treatments. If so, then you should include the "flask ID" as another factor in your model to account for differences between flasks. It does not matter for your purpose if you model this as a fixed or a random intercept term.

Notably, the only "family of tests" you may consider for multiple testing are the two tests of the 2-way hormone x inflammation interactions. Here a simple Bonferroni-adjustment will do (either double the two p-values or test at a test-wise alpha/2).

If you have no idea what I was trying to tell you here, I strongly suggest consulting a local statistician. You may give her/him this text to get a quick overview of your experiment and a possible analysis strategy.

Good luck

Great thank you I appreciate the effort, I do not understand most of what you said but equally I am doing a bsc and my deadline is in less than a week so consulting a statisician is probably beyond what is expected of me or what I can achieve.

It seems from what you are saying you are giving me methods to investigate the interaction of the number of cells vs the inflammation to esnure that the inflammatory effect is not due to increase in number of cells instead of a hormone effect, while this sounds interesting I think that is the source of the complexity that I can not and likely will not understand in 5 days.

the number of cells placed into the wells was kept constant across conditions and replicates both biological and tehcnical, while it would be interesting to see their interplay thats not what I meant. the experimental design is exactly right plus hormone B has 2 concentrations each seperatly done but yes essentially

If i am trreating each as an indepedent experiment one studying inflammation and one studying proliferation with no interaction I am just interested in the effects of the hormones on each seperately.

In that case would I be okay using a 3 way anova using hormnone A, hormone B and inflammatiory stimulus as my indepednet variables and each time using a different dependent variable being inflammatory cyotkine production /proliferation by prolfierative markers ?

My initial qualms were with the use of multiple comparisons should this be based on each hypothesis or for the overall experiment meaning using proliferation as the outcome

for the effect of hormone A vs hormone B i would compare the condition of hormone A without inflammatory stimulus vs hormone B without inflammatory stimulus, then also compare hormone A with inflammatory compared to hormone B with inflammatory. because i dont see the point in comparing hormone A withotu inflammatory Vs hormone B with inflammatory because the effect of the second would be difficult to discern what is affecting the prolfieration.

Further, within this field they often use percentage change from control, control being no treatment at all just continoius growth. Now since some of the changes would be positive and some negative and all relative to 0 being the control can I still run an ANOVA on this data.

what I have done so far is just a one way ANOVA using the conditions as the independent variable and not specifying the breakdown of the hormones. then doing multiple comparisons once without adjustment and once with, the ones with correction were insigificiant I am concerned this is due to having 12 conditions and therefore 66 comparisosn which would make sigifigance viritually impossible so i suspect I am doing things wrong with the correction and questioning if i should be subsetting my data as explained above to do the multiple comapriosn correction based on each hypothesis e.g. inflammatory stimulus (not cytokine production but the one that was administered) increases prolfieration so that would be comparing the condition without inflammation with the same hormone to every condition with inflammation with that same hormone.

thanks for helping, if i dont make sense i think it should be fine within the deadline I am just really conufsed as to when and how to correct for multiple comparisons. Also I will try to do the 3 way anova with what i have and see what comes out maybe thats the issue with what I am doing.