# Sample Size for Bivariate Correlation, Pearson Correlation, and Pearson Product Moment Correlation

Posted December 30, 2008

To satisfy some of the requests of my blog readers, I am covering sample size calculation for a bivariate correlation or the Pearson correlation. This test might also be called the Pearson product-moment correlation.

I am going to assume that you know what a Pearson correlation is and its function, if not check out this blog entry on dissertation statistics help featuring bivariate correlation. In a nutshell we are testing for a significant relationship between two variables. Please keep reading, but if you are just looking for someone to help you calculate the sample size for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation using bivariate correlation, Pearson correlation, or Pearson product-moment correlation, or to justify the sample you already have, click here.

Sample Size for Bivariate Correlation or Pearson Correlation

There are some things we have to understand prior to calculating the sample size of our bivariate correlation or Pearson correlation. We have to first understand why we are calculating the sample size. If you are looking for some more information on these things, check out this blog entry.

Significance

Sample size is calculated for the bivariate correlation or the Pearson correlation so we know how many people we have to survey, poll, or sample to find the test significant at the level of significance we have set. This is the probability of committing a Type I error. Usually the level of significance is set at 0.05. This means there is a 5% probability that our results are due to chance. Get help with determining the correct level of significance for your bivariate correlation, Pearson correlation, or Pearson product-moment correlation.

Power

Power is the opposite of significance and is probability of falsely accepting the null hypothesis or… in plain English… the probability that we missed something and the test we ran was significant even though the result was not significant. This is the probability of committing a Type II error. Usually this is set at 0.80, making the probability 20% or four times as likely as committing a Type I error (measured by our level of significance). Get help with determining the correct power for your bivariate correlation, Pearson correlation, or Pearson product-moment correlation.

Effect Size

This circumstance is slightly different than other tests, in that there is no causality or direction in a sense. Effect size in this case is measured as *r *and represents the strength of the relationship. These *r *effect sizes for the bivariate correlation and the Pearson correlation are 0.10 for a small effect size, 0.30 for a medium effect size, and 0.50 for a large effect size. Just to make sure credit is given where credit is due, these effect sizes are courtesy of Jacob Cohen and his fantastically helpful article *A Power Primer.* For this example we will use a medium effect size. Get help with determining the correct effect size for your bivariate correlation, Pearson correlation, or Pearson product-moment correlation.

Now that we have determined these factors – and these numbers are the numbers that will be used 98% of the time in a Master's thesis, Master's dissertation, Ph.D. thesis, and Ph.D. dissertation – the rest of the sample size calculation for the bivariate correlation or the Pearson correlation is easy. For this we will refer again to *A Power Primer *by Jacob Cohen. If you are looking for this journal article you will find it here.

What is the sample size needed for a significant bivariate correlation or a significant Pearson correlation (Pearson product-moment correlation)?

Here it is…. 85. For a significant Pearson product-moment correlation at a 0.05 level of significance, a power of 0.80, and a medium effect size, we need 85 people. This number will fluctuate with changes in any of those measures, including power, which is sometimes set at 0.90. To have me calculate the sample size needed for your bivariate correlation, Pearson correlation, Pearson product-moment correlation, or for that matter any correlation or test, click here.