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What are the differences between t.test() and When do you use these two functions?

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Due to the naming scheme of S3’s generic class, both functions are similar to one another. However, they are not related to each other.

t.test() performs t-test and is generic in nature. is called by the generic t() for transposing the input data.
As a result of S3 dispatch rules, t.test() along with t() would get called when the latter is applied to the class “test”