We design a experiment with 2 factors. One factor is SR, which has 3 levels, RS, WS, and CS. Another factor is WFPS, which has 2 levels, 50% and 90%. The response variable is the concentration of nitrate, which will be measured at 0, 1, 2, ..., 7, 9, 11, ..., 31 days (totally, 20 times).
The experiment could be performed with 4 different scenarios:
(1) The complete random design. Each treatment have 3 replications. So, we have 3 * 2 * 3 (i.e., SR * WFPS * replications) experiment units. The response variable is measured from the sub-samples obtained from each unit at each sampling time.
(2) The same design as the above, but the number of experimental units will be 3 * 2 * 3 * 20 (i.e., SR* WFPS * replications * sampling times). At day 0, 3 * 2 * 3 units will be measured for the response variable, and then discarded. At day 1, another 3 * 2 * 3 units will be measured and discarded. And do the same thing until the experiment ends.
(3) The complete block design for the scenario (1). It means that there is no replication. Each replication is a block. In each block, there are 3 * 2 (i.e., SR * WFPS) units.
(4) The complete block design for the scenario (2). It also means that there is no replication. Each replication is a block. In each block, there are 3 * 2 *20 (i.e., SR * WFPS * sampling times) units.
A typical experimental results (only for WFPS = 50%) is listed following:
I have read some papers that are similar with our experiment. And (non-)linear mixed effect model are commonly used. However, I don't know whether this method is suitable in our situation, for the data is not varied in monotonic way.
Another question is when choosing the statistical method for the 4 scenarios, what I should paid more attention.
The third question is which book covered this kind of experiment.
Thank you very much for your consideration on this post. And any suggestions or comments will be really appreciated.