What statistical test its appropriate for my experimental design? i need some help with my research. I dont know if its possible to use a statistic test in my design.
To exemplify, following the design:
1 - I fertilize and distribute 100 embryos in each well (W1, W2, W3);
2- After the determined time, 20 minutes after fertilization per example, i do the fixation of the embryos and count 100 embryos, distributing him in 6 categories. If the embryo have 2 cells, i add one to 2C categorie, at the end i had a total of 100 embryos.
3- I do the same count in each well individually, per time;
4 - At the end i have the count of a total of 100 embryos distributed in 6 categories, for each time (20 or 30 minutes), with 3 wells per time.
5- In the days 2 and 3, i repeat the same design, only 20 minutes and
30 minutes after fertilization.
Day 1 ---- 20 minutes
--- well 1 = Count 100 embryos (distributing in 6 categories);
---well 2 = Count 100 embryos (distributing in 6 categories); Count well 3 = 100 embryos (distributing in 6 categories)

The dataframe that i got its something like this:

I create a graphic for exemplify the final result to the count in 20 minutes:

Initially the data was only exploratory, but some people asked to me for statistical differences between the means.
I want to know if it's possible to test the difference between the means of distribution of embryos for each time individually. Looking for the graphical figure, its possible to test if the mean of embryos in 2C its statisticaly different from the other groups in 20 minutes after fertilization (2C x F, 2C x 4C, 2C x 8C, 2C x M, 2C x B) ?
 A: The key is to understand the kind of data you have, how it relates to your study design, and how it fits with potential inferential tests.
Textbooks on applying statistics in your discipline probably have a decision tree to help choose statistical tests depending on the type of data and study design.  Similar guidance can also be found online, such as how to choose the right statistical test.
Your study involves categorical data (six categories), and you have counts rather than values measured along a continuous scale.
Also, if an egg is classified as, say, 2C then it is not classified as 4C.  There are a fixed number of eggs, and the more of them that go into one category, the fewer of them are available for other categories.  So the number of eggs in 2C is not independent of the number of eggs in 4C, and so forth.
Is Kruskal-Wallis an appropriate test?

a non-parametric method


used for comparing two or more independent samples

You would like to compare six samples, which is consistent with a test for "two or more".  However, your six categories are not independent, so Kruskal-Wallis is inappropriate for your study.
Also, Kruskal-Wallis is most appropriate for numerical data measured along some continuous scale.  Your data is count data, so is not "numerical" in the relevant sense.  This is another reason to consider whether a more appropriate test can be identified.
What kind of test is appropriate?
When we have k possible mutually exclusive outcomes, n independent trials, and we count the number of times each outcome occurs, the counts follow a multinomial distribution.
We can probably find a multinomial test.  That source notes that we could use a chi-square (goodness of fit) test.
When you look at your results, one bar in the graph is much higher than the rest and of course we would like to know whether that apparent difference is real or whether it's just a bit of random variation among probabilistic outcomes.  However, before doing a whole set of pairwise comparisons it would be prudent to start with a single omnibus test.
A useful null hypothesis might be

*

*H0: The six outcomes are all equally likely.

If a multinomial test of the null hypothesis has a small p-value, that would suggest that some outcomes might really be more likely than others, so the statistics would be backing up what your eyes are telling you when you look at the chart.
For an exploratory study, that might be sufficient.  You could potentially proceed to look at pairwise differences, using an appropriate test, but then you might have to make adjustments to account for family-wise error.
Family-wise error is also relevant if you do a separate multivariate test for each well at each time period and each day.  If you roll a pair of dice enough times you will occasionally come up with two sixes, and that does not necessarily suggest that the dice are loaded.  You can make adjustments to your statistical analysis to take account of how many times you roll the dice, or how many multivariate tests you are performing.
