You have one dependent with three states: 0=organic, 1=conventional, 2=integrated.

You should take as many measurements as possible regarding erosion. Soil type, moisture, pH, particle size, and so forth. I would also take measures of biotic diversity, especially botanical, as that will influence the presence of roots in the soil. Given that you will have 30 to 90 variables it is nearly certain that one of them will show a significant difference, even if such differences between cultural methods do not exist. You may also enjoy a bountiful harvest of significant outcomes, such that most of the variables show a significant difference. However, this apparent wealth is partly an illusion because there is certainly some correlation between a few of your independent variables. A multivariate analysis will help sort this out to give a more balanced perspective. However, none of this is possible if you do not have a sufficient sample size. Therein lies the catch: it take too long to process all the samples and there are not enough cooperators in each group (organic/conventional/integrated). So you need to find balance between trying to measure all the important variables, limits to the number of field sites you can manage, and what you expect from your analysis. Your best bet is to talk to a statistician at your university/company and come up with a good experimental design that addresses these factors within the limitations of your time and budget.

 I'm not familiar with your field, but it looks like you have one dependent and 3 independent variables and you want to discover their relationship. Maybe you have to try first Pearson Correlation between the pairs of the dependent and the other three independent variables. If you find strong correlation you can put the independent variables into a multiple regression model . After the choice of the model do all the necessary statistical tests but first check if your model make sense (Search your literature regarding the  model or models that are often used by other researchers).

Best

Π 

according to  your question it sounds look like the multinomial logistic regression, because the dependent variable has 3 categories, which has no order involve in these categories, so the best option is to use Multinomial logistic regression.  

Soil erosion as well as farming practices can have many variables to consider.  How you face this statistical design may depend if this is a short term exercise or example as for a class project, longer term dissertation or decades within a professional career.  It is good to evaluate your statistical approach first, and the suggestion to use a statistician is a wise one.  You have many other potential decisions on your study as to soil type, slope, farming practices representative of your categories that would be useful to test, etc.  But time, interest level and funding may be critical drivers on how you set this up.  You may want to consider a model such as Universal Soil Loss Equation as a first step to help understand the factors involved with soil erosion.  If I might suggest, small well designed catchment studies, with measured sediment delivery for control (forested or grassland) and the three farming practices.  The study we documented on sediment from a small ephemeral gully in SC, USA may have some methods if you want to capture sediment delivered from uniform catchments within farming operations and soils of your choosing, for a comparative study of practices.  Consultation with a soil scientist, agronomist and area farmer or farmer cooperative may help also may a practical design that is useful to your intended readers of your research, and may help with some funding or voluntary assistance.  

William

ok lets say that i need more depended variables, as the ones you mentioned , taking them as inputs to my study will provide a multivariate analysis about either the relationship or the difference between them but.. this is not what i meant. i need to show the relationship between pairs of variables like a multi bivariate analysis that could be used to consider the competition on the farm level of a number of pairs of variables and so identify which is the most stronger. any thoughts over this issue? i dont want to consider any more depended variables as these are intended to be measured when we want to consider the interaction between all of the variables available which i did not had in mind..if i correlate between integration and sustainable maagement the outcomes will be perhaps invalid or so

in any case, thank you for your feedback

alex

Actually, I think you can assume to have only one independent variable (soil erosion decrease) and only one dependent variable, which can take three possible values (organic, conventional and integrated). Then, if your data are normally distributed, you can apply an Anova test, otherwise a Kruskall-Wallis test.

Hi Alex, I think your approach is correct as an initial approach. I too would analyze a pearson or spearman correlations (does ordering between variables matter?) between all independent/dependent variables. If you are trying to perform a regression, and pearson correlations are high, then I would apply a multiple linear regression model. You can set a threshold to determine which features are  allowed into the model, but since you only have 3 independent variables I would recommend an exhaustive approach. Moreover, if you applied MLR then you could analyze betas of the resulting model. Small beta values correspond to neglectable features, which can be safely removed from the model without degrading performance. Best regards. G

Marianna

i have scores from the variables (organic, integrated  and conventional) (like 0.3% organic) and so i cannot consider a depended variable (organic, conventional or integrated) as one variable that correlates with an independed variable like "soil erosion decrease". Along with that you cannot  consider multivariate analysis with many outcome variables as the latter gives invalid results. so i believe that it may mean that my initial approach was valid i think 

best wishes alex 

Apologies, it is difficult for me to know your three independent categories as different farming practices or intensities common to your area.  On your x axis, you would have your three practices, each with its own combination and intensity of soil disturbance,  cultivation, weeding, harvesting, etc.  Each category on the x axis would have its resultant plot of soil erosion.  By comparing the results, you might easily show which category of farming produces more or less sediment.  The soil erosion values would plot on the dependent y axis in units applicable to your area.  

Some of my points relative to detail can be reduced if your farming categories are located on the same soils, slopes, rainfall, etc., so the differences are not associated to the site differences, but do to the farming category differences.  

I have to admit, I have some difficulty in the term soil erosion decrease, as farming land generally causes a soil erosion increase in comparison to stable forested land.  However, I guess if you were starting out with barren, eroded soils, the farming practices putting vegetation and other treatments on the land to produce a crop and also help control erosion may result in reduction in soil erosion.  The idea of using uniform small catchments of maybe a hectare or two in size, and capturing, measuring all sediment over various time intervals such as every year and possibly after any extreme event(s).  If you locate your study areas on different soils, slopes or circumstances, then the results you may find would not be comparible.  You may want to measure supportive information with this type study such as % ground cover or % soil disturbed by cultivation at various times as a comparison as to help describe why soil erosion is different between the treatments.  The three category of treatments you are using conventional, etc. should be farming categories recognizable to farming interests as reasonable approaches.  You can keep it simple, and sometimes that is the best if you have limited time, but in the end you will probably want to compare categories of farming and describe something about why they are different.  

@William (small digression from topic) I would think that any climax ecosystem would be relatively resistant to erosion. This includes shortgrass prairie, tundra, sage brush, savannah, and so forth, not just stable forests. If this were not true then I don't see how large grasslands maintain soil for six million years or so (https://www.nsf.gov/news/news_summ.jsp?cntn_id=121029), or however long the American plains have been around.

@Alix

Now this sounds like a mixture design or a response surface. So a farm can be described as 20% organic + 70% conventional + 10% integrated? In this case you could rescale to get a few farms that are 100% organic, a few that are 100% integrated, and 100% conventional. Then there would be farms that are some blend of these three traits such that %organic+%conventional+%integrated = 100%. Design Expert (https://www.statease.com/dx10.html) is a good software package for this, though others will also work. I used this approach for modeling pesticide activity as a dependent variable.

William hey,

I red your comment and i wanted to tell you in relevance  that i am  looking for agricultural management approaches in a rural region where farming is being proliferated and i am trying to connect soil erosion decrease with type of management adopted while measurements will be realized for all variables mentioned above in terms of cover for farming and in terms of soil erosion for climate change incidences. so i do not know if  i need to have same soil, slope etc. but   instead i am looking for answers about the two variables in the same region were we determine and assume that all site elements stay at optimum levels or at least at above threshold levels in order to make the measurement valid. that is growth depends from the variable that is minimized  while all other variables stay the same in terms of safe ecological limits

So do i have to consider something more or this approach is valid? i hope you can help me with  your comment

I agree. Find the Pearson correlation between each independent variable and the dependent variable first and then proceed to use Multiple Linear regression

You can try GBM analysis (Gradient boost Machine) analysis to see the relative influence of the three parameters to the one dependent variable.