I am often faced with analyzing data that follow a pattern as shown in a mock example in the image below. Key data characteristics:
for any value of the predictor (e.g. temperature), the most frequently observed outcome is always Zero. If I were to calculate the median for example at any predictor value, I would get zero. Thus the outcome (e.g. crack area) is highly skewed toward zero or exponentially distributed.
often I have many more observations available in a certain predictor range.
My interest here is not so much Prediction as finding associations between effects and outcomes.
I have read on this forum (for example here) about the dangers of turning continuous variables into discrete variables.
My question: in a case such as this, would it be acceptable to classify the predictor and outcome and then analyze the observed frequencies in a Contingency Table using the Chi-Square statistic. For example, in my view there is a clear conceptual difference between "No Cracks" and "Some Cracks" or "High Cracks".
If this approach (Contingency tables) is not appropriate, can you please suggest other approaches to analyze this type of data, bearing in mind I am primarily interested to find associations between variables, and secondly only in predictive modelling. My analysis outcomes need to be explained to non-statisticians.