When should you use a stable scientific library instead of writing a custom statistical implementation?

Short answer

Default to a maintained library such as SciPy or statsmodels whenever it implements the method you need, because it is tested against edge cases and documented. Write your own only when no library fits, and then validate it against a reference implementation or published values.

Why

A t-test fits in ten lines, which is why people write their own. The hard part is everything around the formula: small samples, ties, missing values, numerical stability and the conventions behind each default. Library defaults are themselves choices you must read. scipy.stats.ttest_ind assumes equal variances unless you pass equal_var=False for Welch's test, and nan_policy defaults to propagate, so one NaN returns NaN. numpy.std divides by N by default, while pandas Series.std divides by N - 1, so the same data gives two standard deviations depending on which call you made.

A custom function hides those choices where reviewers cannot see them, and a regulator or collaborator has to trust it without the years of bug reports a library has absorbed. A custom implementation is justified when the method is new, when the library cannot handle your data structure, or when you need a speed or memory profile it cannot give. In that case write tests that reproduce published worked examples, compare with an independent implementation on simulated data, and document the version of every assumption.

Pin the library version too, because defaults do occasionally change.

A strong answer covers

Libraries carry tested edge-case handling
Read and state library defaults explicitly
Example of differing defaults such as ddof or equal_var
Custom code justified only by a real gap
Validate custom code against references and simulations

Common mistakes

Trusting a library call without reading which variant of the method its defaults select
Writing a custom implementation and testing it only on the data it was written for

The interviewer might ask next

How would you validate a custom mixed-model fit when no library supports your exact design?