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I've started learning the concept of t-tables and have a question regarding methods to find p-values.

I realize that the t-table is limited in providing p-values for every possible t-score. Instead, we must rely on interpolation to attempt to get more precision on the p-value. I've read that linear interpolation is a common method for extending the range of p-values, but are there alternative interpolation methods?

The t-distribution is not exactly linear, thus there must be better interpolation methods/transformations available?

I'm having a difficult time with Google on this one, so I appreciate any help!