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ANOVA in scipy can produce NaN (Not a Number) as output when there is missing data (i.e., NaN values) present in the input data or when the sum of squares is negative. NaN values can propagate through calculations and lead to NaN values in the result. This can happen when there are missing values in the data, and the analysis requires complete data, or when there are extreme outliers in the data that cause the sum of squares to be negative. In such cases, it is necessary to preprocess the data to remove the NaN values or handle them appropriately to avoid NaN values in the result.