Both slicing and consistency over time are particular examples of checking for reproducibility. If a phenomenon is important and meaningful, you should see it across different user populations and time. But verifying reproducibility means more than performing these two checks. If you are building models of the data, you want those models to be stable across small perturbations in the underlying data.
If a model is not reproducible, you are probably not capturing something fundamental about the underlying process that produced the data.
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