I need mathematical/ statistical methods used to examine the impact of soil erosion on agricultural production based the data collected from local community .
What is "survey based data"? How was the data obtained, if it is opinion survey, no it cannot be used. Soil analysis need actual physical data, not perception or opinion. If your use of the word "survey" was meant "sampled" then look into whether the sample collected was representative of the land area under study. If there is no sampling or selection problem, then do pre and post test for soil condition.
WHAT TO TEST FOR? Looking for changes in NPK level may be a start. Other soil conditions may follow and could be tested. See literature on soil condition studies. What is erosion? The loss of surface or top soil. How does this loss affect plantatiin, etc. You might need to test fir levdls of nutrients in the soil.
Statisticaly the impact measure by using regression analysis by considere the data from soil as independent variables and amount of prodicts of agriculture as dependnt variable
Not many communities are going to have the soil, nutrient, erosion and other data sufficient to address productivity changes. Best to collaborate with experienced or research soil scientist, and pick study areas with or initially had similar soils, rainfall, etc. Differences in slope and farming practices can affect erosion, productivity, organics to provide nutrients and water holding capacity. Some crops are known to deplete nutrients. Soils and conditions being basically equal, some farmers may use better methods..
In such studies you need real data from sampled soil and landscape to study or model this. I think you may mean you need published data (observational studies based on sampling) correlated the erosion with the productivity, but survey data (questionaries) is not measuring this.
