what is the difference between type-I error & p-value in statistical inference?

Question

how can i convert r-correlation, F-statistics, t-statistics to p-value manually? i mean not by software/program or other automated process?

Answer 1

The p-value is the probability of type I, so they are related. Type I error is an occurence (reject H0 when it is in fact true), p-value represents the chance of that happening.

Many of these processes do not have "closed form" solutions, that means there is no algebraic solution. For instance, to find the area between z=1 and z=2 you have to integrate (calculus) functions like e^(-z^2/2) - there is no algebraic formula for its antiderivative so you can not solve this problem algebraically. At best you can approximate the integral - the most common ways are to use Taylor (or other) series on the integrand then integrate the terms or use area approximation like the trapezoidal rule, Simpson's rule or Netwon-Coates methods. The tables you find (in the back of textbooks) are a summary of this process: someone did this once and for all, then printed the results up in tables for everyone to use. These days technology has been programmed, either with the tables or with the process.

Answer 2

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