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I’m trying to find the best method to fill gaps in precipitation dataset – which aren’t normally distributed – comparing several methods, from basic methods (simple averages) to complex ones (ANN). I’m using over 300 stations in a simple process: create artificial missing records, impute data and compute performance metrics (MAE, RMSE, r2, index of agreement, percent bias, RMSE/SD, and so on…). But I’m stuck computing significance between methods to determine if they are actually different.

I’m not sure if an ANOVA test over some metric is enough to determine difference between methods or if I need to use raw data used to compute metrics to test significance along methods. Any hint?

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Imputation is essentially prediction. Since you are leaving out known data to impute, what you are looking for is whether differences in predictive accuracy are statistically significant or could be due to chance.

One standard test in such a situation is the test. Diebold (2015, Journal of Business & Economic Statistics) gives a nice overview.

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