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

In summary, when using t-tables to find p-values, it is important to note that interpolation is necessary to get more precise values. Linear interpolation is a common method, but there are also alternative methods such as quadratic interpolation that can be used to extend the range of p-values.
  • #1
tomizzo
114
2
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!
 
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  • #2
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
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}##​
 

What is interpolation?

Interpolation is a mathematical method used to estimate values between known data points. It involves creating a curve or line that passes through the known data points and using this curve to estimate values at other points.

How is interpolation used to calculate p-values from t-table?

Interpolation can be used to estimate p-values from a t-table when the exact value is not listed in the table. This is done by finding the two closest values in the table and using the known p-values to calculate a new value that falls between them.

Why is interpolation necessary for calculating p-values?

In some cases, the t-table may not have the exact value needed to calculate a p-value. In these situations, interpolation is necessary to estimate the value and obtain a more accurate p-value.

What are the limitations of using interpolation to calculate p-values?

Interpolation relies on the assumption that the data follows a smooth curve or line, which may not always be the case. Additionally, interpolation can only provide an estimate and may not be as accurate as using the exact value from the t-table.

Are there other methods for calculating p-values besides interpolation?

Yes, there are other methods such as using statistical software or online calculators that can calculate p-values without the need for interpolation. However, these methods may also have their own limitations and it is important to choose the most appropriate method for the specific data and analysis.

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