That is true. My study was funded from my own pocket so I could not have ideal conditions (even though I made an enormous effort to do everything by the book). Thank you for accepting my design.

Implants look like cylinders and they were rotated to a certain extent at each trial - only their position remained the same.Now I think your question is that "are your results valid"? I haven't read them yet, but I think why not? If you have used the correct test, and the assumptions of the test are met, why not? OK exerting 11 x 3 forces at a single point of each implant might be somehow limiting. If possible, I would rotate the implant at each trial, so that each new force would be exerted to a new point (of course if the implant design was symmetric, which I think it was). But even in your current design, as far as those forces did not bend the implant, or did not change the shape of the loading area (I mean the geometry of the small area at which the force is applied), it could be OK to load the same point frequently. I am not concerned with the former as you already told us that forces up to 120 N do not bend the implant permanently (to the plastic point) (even at microscopical level). But I am not sure whether titanium alloy is malleable or not under the forces up to 120 N.

The changes were within the method sensitivity error, so I believe that I could use the average values.You can use a repeated-measures ANOVA and its posthoc, or at least a paired t-test for this purpose. Put the results of all the implants in rows and differentiate them according to the number of the force application rounds (a table of 5 x 11 = 55 rows and 3 columns). Then using a t-test, check if there is a significant trend in the values in the first round compared to the second, and between the second and third rounds. If there were no significant changes between the three rounds of force application, it means that OK the error introduced into your design by ultra-microscopic deformations at each trial is not affecting your results (of course if your test power was sufficient [which I guess it would be, given the good sample size of yours]).

My supervisor advised me to use the average values the other day. If I use the average values, then I suppose that Greta's advice on performing ANOVA remains valid and that I can use the ANOVA tables obtained using Greta's code?However, you could still tend to use them and take the averages of the three trials of each Force-Brand. Using the second and third trials would of course introduce some measuring bias into your results (if there was a significant decrease in your deformations in the second and third trials). In particular, your Mean values would become affected (the mean would reduce or increase a little bit of course). But the correlations between the independent and dependent variables might still be valid. Although I do not recommend this option (even though I think the changes in the mean value would be really small, if detectable).

I most certainly will inform you about everything that I am doing with this study. Thank you.I suggest you to report as well the results of the statistical assessment of the validity of the second and third trials in your thesis (and later, article) [and also here, if you wished].