What is the relationship between sample size and correlation. Can someone help me understand this:
A decrease in the sample size will lead to an increase in the magnitude of the correlation needed to reject the null hypothesis.
Hi,
The statement is based on this formula to calculate the t-statistic that is then compared against the critical t-value to determine if the correlation is significantly different than 0 or not:
t-statistic: (r√(n-2))/√(1-r²)
As you can see from the above formula, if n decreases, then r needs to increase for the t-statistic to be larger and thus have a better chance at having a correlation that is significantly different from 0 (rejecting the null hypothesis).
If you have three data points and the sample correlation is +0.5, that could be a fluke; the population correlation might really be zero.
If you have 10,000 data points and the sample correlation is +0.05, it’s probably not a fluke; the population correlation probably isn’t zero.
wow… how to write equations in AF??
I write them in Word and paste them. You can get all sorts of math symbols, Greek letters, superscript numerals (well, 1, 2, and 3, anyway), and so on.