I'm afraid I'm not familiar with densitographic profiles, so I can only make a suggestion with respect to "curves" in general. If your curves are summaries of individual curves fit to individual data, then one approach is to target a relevant parameter, say, a "slope," and do a traditional t-test, or an ANOVA, on the slope data (best fit to each case). You are then testing the hypothesis that each experimental condition is reflecting the same underlying process. Regardless of which approach you take, there needs to be clear, methodological reasons for your comparison. Maybe the magnitude or latency of a particular "peak" is important; but it must be more focused than, "how to compare these four curves?" In other words, what is it in the curve data that will answer your particular research question?

Hello,

Just a note! Why not go back to the original data which used in the drawing of the curves!

please share a snapshot please!

Hi Lilia,

if this is only about the question whether two distributions differ or not (no matter how), then a classical test is the Kolmogorov–Smirnov test.

But if there is a specific characteristic (e.g., location of a peak in density) then you need to come up with an adequate function that approximates the density profile (e.g., double exponential, gaussian etc). If there is a curve possible for each replication, you then can use these to estimate parameters of interest (e.g., for an estimated peak) for each replication in each condition, and then can use further statistical methods (e.g. t.tests, ANOVA etc; as Stefano said) to test for differences between conditions. The drawback of this method is, that you need very sound reasons to use a specific function to estimate a density peak (if it is not the empirical mode value), because the difference is a "hypothetical" difference (assuming that the use of a function is adequate...).

Another, more sophisticated, solution would be to use a Bayesian model selection approach (e.g., testing whether one Gaussian distribution (Hypothesis 1) for all treatments is more likely than a single Gaussian distribution (Hypothesis 2) for each single treatment (i.e., with independently estimated means and standard deviations). This could be done in R (jags, or Stan) quite easily.

Hope this helps,

Best René