I got two groups of curves, with different treatment. One curve represent one sample, 3-4 curves in each group. Simulation of the graph is shown below (1 and 2 as group a, 3 and 4 as group b). Then I dont know what kind of analysis should be used to tell if there is significant difference between the two groups. Thanks.
Depends on what you are interested with.
From here and my experience your curve look like these two equations :
K*(1-exp(-t/tau))
or
K*(1/(1+a*exp(-rt))) -- Logistic function
The model depend on what your are measuring and what is your data...
Using the first one, you can evaluate (using 'fminsearch' on Matlab for example) the K (limit value) and the 'tau' (3*tau = time to get 0.95*K) for each curve and statistically compare your sample with these both variables.
Using the second one, it is quietly the same, as you can also obtained the limit value and the inflection point of the curve (=log(a)/r). And then compare them.
[Keep me inform if you need more help on the evaluation of your curve variables. Maybe someone would have other idea on the subject.]
Good Luck,
Cyril
Thanks Cyril, did you mean that first i need to fit the curve with a model, then see how much the sample deviates from the model, for comparison?
Yes, you could fit the curve with a model. Because you don't have curve yet but series of points. ;-)
You said you had 3-4 curve in each group. So for each of them you could fit a model and obtained variables (mean+sd) which are characteristic of your group.
Then you could statically compare your groups based on these variables :
- which one is higher -> difference in K
- which one is faster -> difference in tau or log(a)/r
Thanks to your advice, i found a way out, nonlinear regression by cumulative Gaussian distribution was used for curve fitting (through Graphpad). I got the mean of the best-fit value, but dont know if that is something similar to inflection point
Dear Yajie, Dear Eyas,
If you just compare the mean of curve or their 'Gaussian distribution', I think you'll miss something. Indeed as your curve is function of abscissa and ordinate, I see two main factors : the time and the ordinate value.
So when you do the 'Gaussian distribution' or the mean you do a mix of both factors (except if you compare variable of your Gaussian model).
Regards.
Hi Cyril, i agree. it is better to take into account the distribution factor of the data. In this case, the data fit well with cumulative normal distribution. Just that i need to find a way to extract the property of each curve for comparison. I wish i had learned Matlab.
Hi Cyril, you could build a curve combined with the data of groups one and two and another curve to the data in groups 3 and 4, then you compare both by traditional methods of comparing mean or median, for example.
You may consider using repeated measures analysis of variance with polynomial contrasts.
Hi
i have two curves plotting current distributiona w.r.t. same x-axis represent position
How to find difference of two curves and fit one w.r.t to teh another at the respective x-positions
If you are looking for an approach to model time series data, read the literature on growth curves. For comparing groups of curves, you may try the grofit package in R: https://cran.r-project.org/web/packages/grofit/grofit.pdf
A very interesting question and useful answers!
I would like to add an extra dimension to the discussion. For each set of point you will be able to fit one curve and from these curves you will obtain a series of obtained parameters which than can go through statistical analysis to find significant differences.
But I wonder if there is a way to do some kind of error propagation, because with the curve fitting you will have functions with a better fit to the measured values and it would be better if you can take this with you in the further analysis and make sure than somehow the obtained parameter values of better fits are given a higher weight to the final result. Any thoughts wheter such an analysis/function exists?
A second point; Is it sufficient to check significant differences between the obtained parameter values to say the curves are significantly different, and is it sensible to say that curves are significant different?
Hopely there will be some reactions to these follow-up question because I am having a comparable situation which I find difficult to assess how I should carry on statistically speaking.
No, maybe a little explanation of my data.
I am doing research on photosynthesis and a nice way to obtain photosynthetic characteristics is measuring the photosynthetic rate under different light intensities.
Typical you measure several leaves/trees for which you get one light-responsecurve (x=light, y=photosynthetic rate). Now we have obtained such curves for 15 trees three times. Once during drought, once 3 weeks after we rewatered them and once 16 weeks after rewatering.
Now I am curious whether it would be sensible to try and get signigicant differences between these three "treatments" and whether it is sensible to say that curves differ significantly from eachother?
I have obtained series of for instance maximal values or values under zero light and For these values I can say whether they differ significantly, but also then I don't really know how to take into account that some curve fits were far better than other ones and so some kind of error propagation technique would really be helpful.
Thanks for any advice.
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