# One way MANOVA or Two way MANOVA

I have done statistics many times at Uni at both Undergraduate and Postgraduate levels but as they say “if you don’t use it, you lose it” and that is certainly the case. I am trying to assist my daughter in her final year assignment by advising her on which statistical test to use but am getting confused between whether I need a two-way MANOVO and a one way MANOVA (or maybe neither if I am completely off track) and I am not finding any similar examples on the internet when I look to answer my dilemma.

Study aim: To investigate the effects of nitrogen on the growth of Salvinia Molesta

Outcome and explanatory variables

Growth is assessed as change in leaf size and leaf number = 2 dependent variables which are related as an increase in size in linearly related to an increase in leaf number

The effect of nitrogen is investigated by looking at two forms of nitrogen (nitrate and ammonium) and for each of these types of nitrogen there are several different concentrations of nitrogen and +/- salt in the growing environment(total conditions tested for each of the nitrogen types = 9 and each condition is tested on 5 plants).

I am not sure if there are 2 x IVs or just one. I think it is 2, one for each type of nitrogen being tested- each of which has several levels (concentration of nitrogen source and addition of salt) but if that is the case I cannot work out how to set up the spreadsheet and there will be empty cells. For each nitrogen/growing medium there was 5 samples.

Nitrate Ammonium Leaf size Leaf number N1C1T1 x x N1C1T2 x x N1C1T3 x x N1C1T4 x x N1C1T5 x x N2C1T1 x x N2C1T2 x x N2C1T3 x x N2C1T4 x x N2C1T5 x X Etc for each condition and trial

Where

Nitrate = results for nitrate environment Ammonium = results for ammonium environment C = condition – 1-8 different composition of growing environment T = trial number – 1-5

Which leads me to think there is only one IV - nitrogen, which has 2 types with each type having several levels but this is where it gets too complex for me to know if this is right as I can’t find an example that matches it. For this scenario I would set the spreadsheet up as follows:

Condition Leaf size Leaf number N1C1T1
N1C1T2
N1C1T3
N1C1T4
N1C1T5
N1C2T1
N1C2T2
N1C2T3
N1C2T4
N1C2T4
etc
etc

Where

N = nitrogen type – 1 or 2 C = condition – 1-8 different composition of growing environment T = trial number – 1-5

++ I am not sure if each individual trial result is recorded in the sheet or just the mean of the 5 trials

I hope you can provide some guidance. Specifically are you able to advise if MANOVA is the correct test and if so, is there one IV or two IVs and lastly do I record each trials result of only the mean for each condition (average of all 5 trials).

## 1 Answer

For MANOVA you need a balanced experiment, meaning each combinations of N and C has to be tested equal number of times. If that is the case, the 2 way MANOVA would seem adequate.

Since you are analyzing two sources of nitrogen, my feeling is that there should be an interacton term in your MANOVA, since the effect of a given dose of nitrogen of type 1 would likely not be the same under different doses of nitrogen of type 2 (to a certain extent, one might expect the two types of nitrogen to be sustitutive of each other).

• Thanks for your reply. To clarify - and this is where I am unsure if the 2-way MANOVA is correct is: Nitrate (nitrogen type 1) is tested under 8 conditions (different concentrations of nitrate and + or - salt) on 5 plants (5 trials for each condition). Ammonium (nitrogen type 2) is tested under exactly the same conditions i.e. concentrations as in experiment 1) and on 5 plants (5 trials for each condition). So given this I cannot work out how to set up the results. Are there 3 columns, the first with the nitrogen type and condition, the second leaf size and third leaf number? Apr 20, 2020 at 21:33
• I understood that a single plant was given nitrogen simultaneously of two types and different doses of each type, hence my recommendation of MANOVA 2-way. If you are giving nitrate or ammonuim (but not both) I think you can use a 1-way MANOVA with a single treatment and 16 levels, or a 2-way MANOVA with two crossed treatments (Ammonium, Nitrate) x (Dose1, ..., Dose 8). Or, still, multivariate regression, given that one treatment is cualitative (Ammonium, Nitrate) but the other is measured as a continuous value, even if it is discretized. Apr 21, 2020 at 9:51