p-values for T-test are not accurate enough

[estebanz01]

I found while building the paired t-test that the p-values (1 - P(x <= X)) calculated using the Student's T distribution are behind of the expected value. A couple of test shows a difference of two decimal values from the expected one:

• In https://www.statsdirect.com/help/parametric_methods/paired_t.htm we have p-value of 0.0006 and 0.0012 but the gem returns p-values of 0.0004 and 0.0008.
• In http://www.unm.edu/~marcusj/Paired2Sample.pdf we have a p-value of 0.026 and I got a p-value of 0.024.

I traced this back to the way how ruby handles the decimal points. The calculated ones by minitab or R are different than the ones calculated by Ruby itself.

I'm logging this as a bug, but it's not related to the code itself (😅). I'm logging it for future references.

[estebanz01]

Due to a monkeypatch made by the descriptive_statistics gem, I was seeing a stacktrace pointing to ruby classes instead of the real issue. I tried to do more detailed debugging process and I found out that the problem is in the variance calculation (see: thirtysixthspan/descriptive_statistics#43) So, this bug can be fixed! 😃 🎉

[estebanz01]

Fixed in #19