When not to look at p-value I am trying to indentify correlations between the columns of a dataset I have. I am using the pearson correlation index, and am looking at the p-value I get from the "correlation test" of R. I know that, in theory, the p-value is the probability of the correlation being due to chance. Now, what I wanted to know, can I always look at this value to have a good metric of how certain the relation between the variables is, or are there any assumptions that have to be statisfied?
EDIT
I'll add some context in order to better explain the question
I am actually studying the relationship between some variables I extracted from a tv series (eg number of character, number of cuts, IMDB rating etc.) and wanted to see if there is any kind of relation between them. In order to do this, I thought correlation might be a nice idea. Some variables have got interesting correlations, with very little p-values, and reading online it seemed like a good idea looking at this value.
After the comments I am not sure I really understood what this value means, but reading online I found this:
"The p-value is the probability that the null hypothesis is true. In our case, it represents the probability that the correlation between x and y in the sample data occurred by chance" (source).

It sounds like you might want to do exploratory data analysis instead of a deep dive into the meaning of p-values. Basically, make plots, lots of them, to understand the patterns in your data.
It might help to keep in mind to following advice from [1]:
Quick tips to improve your [regression] modeling

*

*Think about variation and replication (ie., patterns you observe in one dataset won't necessarily replicate in another dataset about the same phenomenon)

*Forget about statistical significance and p-values

*Graph the relevant and not the irrelevant; make many graphs

There are 7 more steps (see below) but the first 3 steps are most relevant to you since you seem to be at the start of your investigation.
Notes

*

*The Pearson's correlation coefficient measures strength and direction of a linear relationship. So by choosing Pearson's correlation out of hand you've implicitly decided to see if there is a linear relationship between the variables. Again, plotting the data might turn out to be more informative than computing correlations.

*You plan to run multiple statistical tests with the goal of discovering interesting hypotheses. It's important to correct for doing all those tests because each test has a probability of making a false discovery (type I error). The probability of making false discoveries grows quickly with multiple testing. This is an advanced topic. You can learn more about it here.


Quick tips to improve your [regression] modeling, continued


*Interpret regression coefficients as comparisons

*Understand statistical methods using simulations

*Fit many models

*Set up a computational workflow

*Use transformations

*Do causal inference in a targeted way, not as a byproduct of a large regression

*Learn methods through live examples

[1] A. Gelman, J. Hill, and A. Vehtari. Regression and Other Stories. Cambridge University Press, 2020.
