Imagine that you predicted a moderate correlation between people's scores on a measure of anxiety and the degree to which they report having insomnia.
You administered measures of anxiety and insomnia to a sample of 30 participants, and obtained a correlation coefficient of .28. Because this correlation is not statistically significant (the critical value is .30), you must treat it as if it were zero.
Yet you still think that anxiety and insomnia are correlated. If you were going to conduct the study again, what could you do to provide a more powerful test of your hypothesis?