Significance testing for biserial correlation


I have run an analysis outlined below. It would be great if the group could tell me a) if this approach is appropriate and b) if the result is significant (to 95% or 99% level).

I have 20,000 survey responses to the question 'how likely are you to recommend my event to a friend / colleague', and the repeat behavior of those respondents (i.e. whether they did, or did not, repeat the event the following year).

I have run a Point-biserial correlation between the two variables, and have a value of 11%.

According to Wikipedia, using a transformation will result in a value equivalent to an unpaired t-test. With this high an 'n', an unpaired t-test would be highly significant.

Is this the correct way to interpret this result?



Super Moderator
Hi there, welcome.

A few hopefully helpful points:

1) A correlation is not a percentage. You can however square the correlation to get the percentage of variation in one variable that is explained by the other.

2) This correlation is significant, yes. But just about any correlation will be statistically significant given a sample of 20000 respondents. Remember that a low p value simply tells you that a correlation as large or larger than the correlation you observed in your sample would be very unlikely if the correlation in the population was exactly zero. It does not imply that the correlation is practically important - so think about how you will interpret the magnitude of the correlation. It might also be helpful to report a confidence interval for the correlation.