Assuming a twotailed test with 005 how large a correlation

Assuming a two-tailed test with = 0.05, how large a correlation is needed to be statistically significant for each of the following samples? a) A sample of n = 8. b) A sample of n = 18. c) A sample of n = 28.

Solution

1) The numerical value of the Pearson correlation indicates the strength of association between the two variables

x and y.

A correlation coefficient of 1 Þ a perfect correlation between x and y. A zero coefficient Þ no correlation. Higher the numerical value of r, stronger is the correlation between x and y.

(2) Refer to this table: http://archive.bio.ed.ac.uk/jdeacon/statistics/table6.html

= 0.05

(a) n = 8, Df = n - 2 = 6, Critical correlation coefficient = 0.707

(b) n = 18, Df = n - 2 = 16, Critical correlation coefficient = 0.468

(c) n = 28, Df = n - 2 = 26, Critical correlation coefficient = 0.381