Question

In a random sample of size 50, Pearson’s r is -0.4.

What is the probability of getting a sample with this correlation, if no correlation existed in the population?

Answer 1

Given that no correlation existed in the population, as a correlation value of 0 is less than 0.4 in absolute sense, therefore the distribution of the sample pearson correlation coefficient could be approximated by a normal distribution here given as:

Now the probability of getting a correlation of -0.4 is computed here as:

P( r < -0.4)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.0031 is the required probability here.