Question

Can a test of significance show a statistically significant relationship while a measure of association shows a weak relationship between the variables? oh onshs Can a measure of association show a strong relationship while a test of significance shows that the results are not significant? If yes to either or both, present relevant examples illustrating how such situations might occur.

Answer 1

1) Strong Correlation/association but not significant

YES, it is possible

2) Significant but NOT Strong Correlation/association

YES, it is possible

3) Examples

1) generate X and Y variables with a correlation of 0.50 and sample size of 7

run a pairwise correlation and get p-value

* result r=0.5570, p=0.1940 - Significant

AND

2) Rerun this whole thing exactly the same way but use sample size of 100

* result r=0.50, p< 0.0001 - Not Significant

Basically it depends in the sample size. Sometimes you may have corr = 0.001 and sample size is say 100000 then in that case it is weak correlation but it will be significant due to sample size.