“My research is on cellular/molecular responses after hormones farmacological administration ”

What can be the unit of investigation here? I pretend that it is individual patients. What is measured as the response variable?

“I did my experiments once in june and then the same experiment in july.”

Did you take 48 patients in June and randomized them to the 16 treatments and then took 48 new patients and randomized them to 16 treatments? (Then it is a replicated experiment in two blocks.) Or did you measure the same patients again in July as in June?

Of course it is not just about the amount of numbers that you have (the 2*48). There is a difference if you had taken 16 patients, and measured them 3 times in June and then 3 times again in July. You would then have 2*48 numbers, but still just 16 experimental units. I believe that it is very common that researchers do that kind of pseudo replication. Of course the interpretation will be different with 16 experimental units as compared to 96.

By the way, did you formally randomize (with random numbers) to the 16 treatments? In my opinion, it is an experiment if you formally randomize. Otherwise it is just an observational study.

And, if you want to compare all the treatments with the control, then it is good to take an extra large sample in the control since everything is compared to that. The rule is (I hope I remember this correctly) to take the square rot of the number treatments, and that many times replicates in the control. So the square rot of 16 is 4, so you should have 4 times as many replicates in the control as you have in each of the treatment cells.

“But how can I compare the residuals?”

This is a good moment to study an elementary statistics book. The residual is the measured value minus the “predicted” value. In this case: residual = measured value – mean value(in that treatment group). Any statistical program can do that. Do the standard diagnostic checking that is mentioned in the books. (For example to look at the residuals if they are normally distributed. But skip the Kolmogorov-Smirnov test -that will just confuse you. Look at a histogram instead. Does it look normal? Then it is OK.)

Plot the June values (the 48) with the treatment group on the x-axes. Do they look strange? Is there any outlier? Generate 48 random numbers and plot them again, to get some feeling for how random numbers can work. Then do that again and again (say ten times) to experience randomness. I believe that a person with good common sense but limited statistical knowledge, should avoid many of the formal statistical tests, but instead do things like this that is obvious and makes sense to the person.

Maybe the result was different was different in June and July so that they are not comparable.

I would just present the result as means for each of the 16 group with a confidence interval. You could do bar charts with “error lines” for the confidence interval. (So I suggest you skip the Tukey HSD test. It just confuses you.)