Well, I think Rabin Thapa is right. First the design should be finalised which can be Split split plot or Strip split plot of Factorial RBD. Then the analysis can be done as per the drsign used to conduct the experiment.

Dear Mohd Ikmal Asmuni, as a chemist I'm not an expert in this field, but to me the problem seems rather specialized. Why don't you discuss this experiment with your supervisor?

It looks like some kind of ANOVA model will be suitable. Here are some resources that may help.

• http://drs.icar.gov.in/Electronic-Book/index.htm
• http://drs.icar.gov.in/ebook/EBADAT/index.htm
• http://drs.icar.gov.in/
• https://online.stat.psu.edu/stat502/

You have several Dependent Variables (DV), namely growth performance, and three factors (with different levels) that can affect the relationship between dependent variables instead of influencing a single dependent variable.

Therefore, I would prefer Multivariate ANOVA (MANOVA).

I think , Robin Thapahas given good answer and quite in tune with wth yoru requirement , please consider any one ,out of the two very good options....however latter gives better results because of the interaction effect of the two fctors..

I didn't notice that there are multiple DVs. Thank you, Roberto Molteni, for pointing that out. Even so, MANOVA is not always a given. It depends on whether one has a multivariate question or a series of univariate questions. See the classic article by Huberty & Morris (1989), for example. HTH.

Article Multivariate Analysis Versus Multiple Univariate Analyses

Well, I think Rabin Thapa is right. First the design should be finalised which can be Split split plot or Strip split plot of Factorial RBD. Then the analysis can be done as per the drsign used to conduct the experiment.

Thank you, Bruce Weaver , I have also other doubts.

I guess that there are strong interrelationships among the outcome variables, therefore I would still prefer MANOVA; however, I have other doubts that I briefly summarize.

A problem is the complexity of the experiments and the difficult interpretation of the statistical analysis. I think that factor Light intensity and Nutrient were enough to have a huge experiment.

Even so, dear Mohd Ikmal Asmuni , you need a sufficient quantity of data to run a reliable statistical analysis, especially MANOVA.

Anyway, you should have the data and before whatever statistical analysis, the Assumptions for the statistical analysis should be verified.

Well, I think Rabin Thapa is right. First the design should be finalised which can be Split split plot or Strip split plot of Factorial RBD. Then the analysis can be done as per the drsign used to conduct the experiment.

With so many variables, I would use regression models to assess differences between treatments and their significance in relation to growth.

Nice discussion

1. Three factorial experiment

2. Split-split-split plot design experiment

You can use the split split plot design experiment

It seems to me that you have a 3X3X2 experiment, and you could analyse the data by means of an ANOVA for each Response variable (DV) and with 3 factors, also include interactions between the factors. A General Linear Model (GLM) program may be used, with Light Intensity, Nutrients and Media as the factors. If you are brave, you may do a MANOVA which will include all the DVs and the three factors in one model.

Dear Prof. Francois E Steffens

I still would like suggest to start with MANOVA, if there are the assumptions to do it, because there should be strong interrelationships among Dependent Variables mentioned by Mohd Ikmal Asmuni

A multiple ANOVA could lead to a distorted view of those interrelationships.

dear Francois E Steffens and Roberto Molteni yes, there should be strong interrelationships among DV such as the photosynthesis rate, chlorophyll content...I think i will go for ANOVA then look at the results then try to go for MANOVA.. what do you think?

Dear Mohd Ikmal Asmuni ,

If there are assumptions for run a MANOVA, I would prefer it first.

Do not take literally the example but it is like to run post-hoc test and then ANOVA

MANOVA is still the best analysis for experimental research.

Interesting research. You can go for analysis as a three factorial experiment, as a split split plot design experiment or strip split plot design experiment.

MANOVA can either be used.

But still more I hope there is replication unless which you will be blocked.

You can also use a generalized linear mixed effect regression and proceed to independant variables selection for better result accuracy.

Make sure linear model assumptions are respected.

Traditionally, ANOVA is it, but I think that would only tel part of the story. since you data re also temporal I'd suggest some cross correlation investigations to see how the various variables take effect with time. But then you can analyze things to death..

ANOVA is preferable.

Debe tener presente los objetivos de la investigación, y el papel que tiene cada uno de ellos sobre la variable respuesta, si el interés es el efecto de todos ellos sobre la respuesta un diseño factorial sería adecuado, debe establecer los tratamientos como la combinación de los niveles de los factores de interés. Pero si alguno de ellos opera como factor de bloqueo hay que tener en cuenta esto también, ahora debe contemplar el número de replicas también a realizar.

You have a good amount of data you can perform ANOVA/ PCA/ clusters/ and other analesis too

Dear Jules, I see that the data was generated from a complete factorial complete design, if you had repetition, the ANOVA under mixed linear model seems appropriate.