I have to start with the standard disclaimer: without replication the strength of the experiment is limited. I know that that's an impractical bar for the hobby, but there's a reason that it is a basic part of research - because without it you have no way of knowing if your results are due to your dependent variable/s or if they are a result of error.
You seem to have forgotten that replication, in many cases when dealing with very complex systems, is dealt with by using a large value of n, having a good parameter control and then assessing the variance in the individual parameters. As I understand you here, you suggest looking at the covariance between the individual parameters as well, and if that is the case I can better understand your last remark regarding test methodology. I am not sure anyone really have looked at the covariance between all of the individual parameters in growth experiments, and if they have I can understand the need to reduce the number of parameters that is being used (feel free to educate me).
But I have a job, a family, other hobbies and frankly better things to do than run a minimum of 37 identical aquariums times the number of different setup methods to get something that would be worthy of a research grade experiment.
With that out of the way, these are some of my initial thoughts. I agree that adding mulm would be ideal when actually setting up an aquarium, but for the sake of the experiment I wouldn't as it seems like it would add a lot of variation. I would also not include hardscape or sand in the experiment for the same reason.
I strongly disagree with the use of old filter material (mulm) when setting up a new aquarium, why transfer algae spores, pathogens and potentially pests from an old setup? There are very good starter cultures to get the nitrogen cycle going that are based on aquatic strains, where you avoid any of those potential problems. But let us just for the sake of argument say that it was done that way it would be rather easy to make it consistent. All you would do was to take a given volume of mulm and dissolve it in a large volume of water. Ensure that the mix of mulm and water was sufficiently agitated, and kept agitated, and then take very small fraction of the volume out of the mix and transfer it to the individual aquariums. I would as a minimum use a total volume of mulm and water that was t x n^(1,5) x V, where t is the volume of water to be used for seeding each of the test aquariums (t << V), n is the number of aquariums to be seeded and V is the total fluid volume of the system (aquarium, lines and pump). Another constraint on the seeding would be that the volume of mulm used in the mix should be around t x n x V. I will grant you that this means that the seeding culture is more diluted at larger values of n, but this would have to be done to ensure the practicality of the experiment.
Some of the other details would depend on the other two methods you are testing, which aren't detailed here. For example, in the real world I wouldn't do a water change during a dark start, but I think you should keep the water change schedule uniform between treatments.
I am not sure how you do your research, but back in the day when I did do research at the university, we did not really discuss test methodology outside the research groups. This is not a research study, but I have not laid the old habits to rest, and that is why I have not gone into too many details on what I will be doing. I was looking for input as to how people do dark start, not looking to start a discussion on how to do the testing (although I now have started doing just that).
I think you need to think more deeply about your independent variables. Measuring dry matter makes sense as a measure of growth, but "pictures" is not really a metric. You could do a rating system, but you need to be more specific what you are rating.
As to pictures not being a metric is debatable and I could spam you with links to research articles within many different fields where pictures are used to describe differences and/or similarities . Some relating to comparing plant growth under different conditions, others within mathematics (knot theory springs to mind here) or for that matter cosmology and material physics, even taking an example close to home, Andreas Mogensen who used, yes pictures, taken as a part of the Thor-Davis experiment on the ISS. Yes, you could present the raw datasets but my experience tells me that there are not that many people that can look at a dataset and extract the relevant information from it in a glance, and yes I have tried to present large datasets containing tens of thousands of data points to people only to be told that they need it presented in a graphical form. It takes training and a fairly high level of base knowledge to identify the relevant anomalies in large datasets just by looking at it and most people as described above just give up. There is a reason why there is the saying: ‘A picture is worth a thousand words’, and when looking at which gives better results in a very visual hobby pictures are in my mind very relevant. Just look at the amount of threads where people are posting pictures just in this forum…
I would be very interested in knowing how you imagine measuring algae growth on hardscape and other hard surfaces in a test setup, while at the same time have it relevant for the average hobbyist starting a new aquarium? Just to take one parameter that matters too many people, or should I say many people like to eliminate. A picture of the setups prior to the weekly maintenance is a very easy way for people to relate to the scale of the ‘problem’.
Also, are you lumping all the plant species in the tank together or are you doing separate measurements for each species? Why species are you using and why? I am not being comprehensive here, these are just the first few things that came to mind.
Are you really suggesting that the trimmings should be sorted by type in a setup that is meant to look at how different start methods compare. That would only be practical in a Dutch setup or single plant setup and the relevance of the experiment would become very limited. As to what plants I will be using, that is something I have been discussing with relevant people, I am not going to have it in a plenum on the Internet, as that most like wouldn’t have been particularly productive.
You aren't going to be able to answer all your questions about this topic in one experiment, so you need to figure out which facet is the most important, focus on that, and try to keep everything else as uniform as possible. The more complicated you make it, the more difficult it will be to produce well supported conclusions.
Interesting take on test methodology… if I understand you right you are here saying that the more you test for the less you will be able to get clear results. Here I was under the impression that it is good test methodology to keep as many parameters fixed and have as few variables as possible in order to get reproducible results. Not sure how you do that without measuring as many things as practically possible. But I guess if you plan on looking at the covariance between different parameters then without knowing which data are significant and including the covariance between relevant data and insignificant data you end up with a situation where you just get a matrix of data that is overwhelming to most people. This brings us back to pictures and a reduced number of variables. I am not doing this in a vacuum of knowledge, and if I was this was not the right place to start.
Final remarks/questions: How many identical tests would you say was needed to draw any reliable conclusion’s (if you say 37, I would like you to post the method you used to get that number), do you apply that standard to all tests you read about within the hobby, and finally do you have any input on how you would do a dark start within the restraints defined in my original post? Not that your input on how you would do a dark start would matter, as the experiment already is running and I did not see your post in time (you must have posted just before me posting my last entry), but it would be nice if you actually did have something that was relevant to the original post.