Chi Square Test: p-value

Hello there, I have a simple question, yet I don't find the right answers on the MATLAB Documentation Center.

p-value of the test, returned as a scalar value in the range [0,1]. p is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. Small values of p cast doubt on the validity of the null hypothesis.

How is the p-value defined? MATLAB seems to have a different definition than the current definitions I know/find on the internet. Thank you so much for any tips! Tanja

Answer 1

[Star Strider]

The explanation I give for the p value is that it is the probability that the data are explained by a random process rather than your experimental design. The lower the p value, the lower the probability that a random process explains your data.

(A somewhat more precise definition is that the p value is the probability of accepting a false-positive result. It is known as the ‘alpha’ probability, or the probability of a a Type I error.)

[Tanja]

Thank you so much for your answer. I found that explanation as well when I searched for the solution-my problem is: doesn't this explanation conflict with the MATLAB explanation

Small values of p cast doubt on the validity of the null hypothesis.

I'm sorry, maybe I just don't understand this statement the right way. Thank you so much for your time! Tanja

[Star Strider]

My pleasure!

MATLAB’s answer is simply a different way of expressing the probability of a Type I error. The null hypothesis is that there is no difference between the two groups under consideration.

To restate the MATLAB interpretation, small p values (alpha probabilities) cast doubt on the validity of the assumption that there is no difference between the two groups under consideration. So small p values indicate that there is a small probability that the two groups are the same.

[Tanja]

Thank you so much! That actually helps a lot. Do you know where I can get the mathematical description of the p-value? Thanks again in advance.

[Star Strider]

My pleasure!

I would start with the Wikipedia article on the p-value. Every statistics book has detailed discussions on it. I also recommend the article on Type I and type II errors to put the p-value in context.

The classic statistics textbook is Snedecor and Cochran, Statistical Methods, that I highly recommend.