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

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1. May 14, 2016

### tomizzo

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!

2. May 14, 2016

### Paul Colby

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,

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

3. May 14, 2016

### Paul Colby

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 $F_i(t_j)=\delta_{ij}$​