Hello Fabienne. First of all, congratulations on the kinetic growth study experiments with 4 different mediums! And 60 hours too! Good job!

Regarding statistical analysis, I assume that you have about 120 pairs of numbers, so you could use a parametric test (eg. ANOVA paired t-test). However if the numbers are not normally distributed, you will have to go for a non-parametric test (especially the Wilcoxon matched-pairs signed-rank test). I would recommend GraphPad Prism software to you since I find it to be very easy to use for statistical analyses of my experiments. All the best!

Thanks a lot for your answer Nurul!

I was thinking about performing an ANOVA as well but I hesitated. 

Maybe I am mixing things up but isn't there a problem performing an anova if the datapoints are not independent from each other?

Let me explain: as you assumed correctly I have 120 datapoints (times 3 due to the replicates) for each medium. But the absorption that I measured at timepoint 1h (for example) is directly dependent/influenced by the absorption measured on the previous measurement, in this case at 0.5h. 

Furthermore, my model is definitely not linear. Doesn't an ANOVA only work for linear models?

So I was thinking about fitting and defining a best fit curve for each medium an then somehow comparing that. But I have no idea how to do so. 

I usually work with the software R. But thanks for the hint, I will check out GraphPad Prism software!

A statistical comparison is sensible only when you have som particular growth model in mind. This could be an exponential model or a logistic model, or some biphasic model... this depends on your assay and the underlying biology.

If you do have such a model, you can use your observed data to estimate the values of the coefficients in this model. These coefficients will have particular meanings, and you may then infer the differences in the media w.r.t. these coefficients. For instance (very simple!) you fit a simple exponential model like y = exp(b*x) with a different "b" for each medium. This coefficient refers to the growth rate, so you would actually compare the growth rates obtained in the different media. If, for instance, you observe some logistic growth and fit a logistic model, you will fit coefficients for the time of the inflection point, the slope in the inflection point, and the maximum value. It may be that reaching different maxima is relevant for your problem, or that half the maximum is reached at different times, or that the grow rate at that time is different...

If your measurements over time are taken from the same culture ("repeated measures") you may consider a mixed model using the cluture-IDs as a random factor in the model to account for the intra-culture correlation of the observations (a culture that "accidentally" grows slower will give you generally lower values).

I recommend the book "Data Analysis Using Regression and Multilevel Hierarchical Models" from Gelman and Hill to learn these things.

Several methods have been proposed for analyzing growth curves. Much of the literature and some PCA-Based methods are discussed in the following papers.

Snee, R. D. (1972) "On the Analysis of Response Curve Data", Technometrics, V14, No.1, 47-62.

Snee, R. D. (1979) "A Useful Method for the Analysis of Growth Curves", Biometrics, v35, No. 4, 835-848.

Y. Wnag, R. D. Snee, G. Keyvan and F. J. Muzzio (2015) “Statistical Comparison of Dissolution Profiles”, Drug Development and Industrial Pharmacy,  Online, August 2015.

I suggest that you carefully consider the modified principal component approach. It very nicely identifies differences in curve shape and level.

Yo may have a look at growthcurver, an R package specifically designed to analyze microbial growth curves. It is particularly well suited for the statistical and graphical analysis of growth curves performed in a plate reader. A standard form of the logistic equation is fitted to the data, estimating parameters like doubling time, carrying capacity, and growth rate. The paper describing the R package is freely available here: Article Growthcurver: An R package for obtaining interpretable metri...

The package vignette can be found here:

https://cran.r-project.org/web/packages/growthcurver/vignettes/Growthcurver-vignette.html

Pablo Vinuesa, does 'Growthcurver' handle replicates or direct comparison of mediums?

Here is a website that will perform a permutation tests:

http://bioinf.wehi.edu.au/software/compareCurves/

https://cran.r-project.org/web/packages/statmod/statmod.pdf

this link is useful

aem.asm.org/content/61/12/4389.full.pdf

regards

Before any statistical analysis, I think you should ask yourself: Why do you want to compare the growth curves? Do you have some hypotheses? Do you want to compare or rank? What is the characteristic of interest (parameter)? The next step is to make a descriptive and structural analysis of the data ....

It is not an easy question.

I would suggest to try to adjust a mathematical curve in one of the data sets, for instance, using regression. First visualizing the curves to try to guess the nature of the model to be fitted (you may realize you need non-linear regression method). If the 4 sets seem to be similar in shape from the graphical analysis, then fit a regression model in one of them. Use the same model for all the curves and compute the residuals. Then, visualize the shape of the residuals, if they look quite normal (bell shape), perform a test for equal variances, and ANOVA test for the means. If using the same model, you do not see significant differences on the residuals, in shape, variance and mean, then you can conclude that you have not detected significant differences among the 4 curves. Maybe, only visualizing the raw data (not the residuals) you may realize they are significantly different. Sometimes just simple graphical analyses can make the difference.

Try this link also

https://genome.cshlp.org/content/early/2016/11/18/gr.210286.116.full.pdf

To simply show whether one medium supports better growth, I wonder if you can simply compare the concentrations/ODs at a particular time point with an ANOVA, so long as the cultures have not reached saturation . To do this, you could average your replicates for each type of medium for a single time point to get four means, and then perform ANOVA. If this is allowable statistically, I imagine this approach would not be as fancy as fitting mathematical models to your growth curves, but it may be a simpler way to show significantly different growth if that is all you are trying to say.