Excel and the T-Distribution

Question

My stat book has an index of values relating to the t-distribution.

And Excel has a bunch of apparently related functions:

• T.DIST (x, deg_freedom, cumulative)
• T.DIST.2T (x, deg_freedom)
• T.DIST.RT (x, deg_freedom)
• T.INV (probability, deg_freedom)
• T.INV.2T (probability, deg_freedom)
• T.TEST (array1, array2, tails, type)

I cannot figure out the relationship between the values on the table and the values that Excel returns with these functions. Does one of these Excel functions return the table values?

Answer 1

For a given df and a given alpha, the value given in the table can be found either by

• T.INV(1-alpha,df) (for the one-sided value of alpha)
• T.INV.2T(alpha,df) (for the two-sided value of alpha)

I.e., for T.INV the table is based on the probability of the tail, while Excel is based on the CDF, hence 1-alpha. For T.INV.2T however the argument is alpha as in your table.

For instance:

=T.INV(0.75,5)     0.7267
=T.INV.2T(0.5,5)   0.7267
=T.INV(0.9,5)      1.476
=T.INV.2T(0.2,5)   1.476