I think I agree with everything you've said here, but just want to note that while we absolutely should (where relevant) expect published code including automated tests, we should not typically consider reproduction that reuses that code to be "replication" per se. As I understand it, replication isn't merely a test for fraud (which rerunning should typically detect) and mistakes (which rerunning might sometimes detect) but also a test that the paper successfully communicates the ideas such that other human minds can work with them.
Sources of variance; Experimental Design, Hardware, Software, irrelevant environmental conditions/state, Data (Sample(s)), Analysis
Can you run the notebook again with the exact same data sample (input) and get the same charts and summary statistics (output)? Is there a way to test the stability of those outputs over time?
Can you run the same experiment (the same 'experimental design'), ceteris paribus (everything else being equal) and a different sample (input) and get a very similar output? Is it stable, differentiable, independent, nonlinear, reversible; Does it converge?
Now I have to go look up the definitions for Replication, Repeatability, Reproducibility
> Measures of reproducibility and repeatability: In chemistry, the terms reproducibility and repeatability are used with a specific quantitative meaning. [7] In inter-laboratory experiments, a concentration or other quantity of a chemical substance is measured repeatedly in different laboratories to assess the variability of the measurements. Then, the standard deviation of the difference between two values obtained within the same laboratory is called repeatability. The standard deviation for the difference between two measurement from different laboratories is called reproducibility. [8] These measures are related to the more general concept of variance components in metrology.
> In engineering, science, and statistics, replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated. ASTM, in standard E1847, defines replication as "... the repetition of the set of all the treatment combinations to be compared in an experiment. Each of the repetitions is called a replicate."
> Replication is not the same as repeated measurements of the same item: they are dealt with differently in statistical experimental design and data analysis.
> For proper sampling, a process or batch of products should be in reasonable statistical control; inherent random variation is present but variation due to assignable (special) causes is not. Evaluation or testing of a single item does not allow for item-to-item variation and may not represent the batch or process. Replication is needed to account for this variation among items and treatments.
> In simpler terms, given a statistical sample or set of data points from repeated measurements of the same quantity, the sample or set can be said to be accurate if their average is close to the true value of the quantity being measured, while the set can be said to be precise if their standard deviation is relatively small.
