# Using interpolation to calculate p-values from t-table?

• I
Hi there,

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!

Paul Colby
Gold Member
Not knowing what a t or p table actually is, I'll jump right in. Say we have two measured values, ##p_1## and ##p_2## taken at ##t_1## and ##t_2##. Let us assume that ##t_1\lt t \lt t_2##. Then the linear interpolated value, ##p##, is given by,

##p=p_1+\frac{p_2-p_1}{t_2 - t_1}(t-t_1)##​

Paul Colby
Gold Member
Reading comprehension not my strong suit, I'll try again,

Let
##F_1(t)=\frac{(t-t_2)(t-t_3)}{(t_1-t_2)(t_1-t_3)}##
##F_2(t)=\frac{(t-t_1)(t-t_3)}{(t_2-t_1)(t_2-t_3)}##
##F_3(t)=\frac{(t-t_1)(t-t_2)}{(t_3-t_1)(t_3-t_2)}##

##p(t) = F_1(t)p_1+F(t)p_2+F(t)p_3##

##p(t)## is a quadratic interpolation. Note that ##F_i(t_j)=\delta_{ij}##​