Nonlinear fit to median instead of mean values?

Hey,

my question might be more theoretical. The datasets I currently analyse are not normally distributed (according to shapiro-wilk and kolgomorov-smirnov @ p = 0.05). Therefore, I prefer plotting them as boxplots. However, I would actually like to fit a nonlinear model (in that case a hill equation) to the (non-existing) mean in order to extract some parameters.

So, is there any way and is it allowed to fit my function to the median instead of the mean values? I haven't found publications where this is done and I assume that this is for a good reason. I just don't know why and what else to do with my data.

Thanks for your help!

Philipp

[Sindar]

I'm not an expert, but I don't think it's accurate to describe standard fitting as fitting to the mean.

Regardless, can you share an image of your data and discuss what you think a median-fit would look like? There may be some method of optimization that can replicate your goal (standard fitting minimizes summed-squares distance. Maybe you want summed-abs to suppress the importance of outliers?)