Question

Suppose you believe the strength of the linear association between weight (lbs) and sleep (average per night), r1=-0.2 is significantly different than the association between weight and exercise (hours per week), r2=-.25.

What is the required sample size required to assess whether the two correlations are significantly different? Assume alpha = 0.05 and beta = 0.1.    

Answer 1

The standard normal deviate for = Z_α = 1.960

The standard normal deviate for = Z_β = 1.282

C = 0.5 * ln [(1+r)/(1-r)] = 0.203

Total sample size = N = [(Z_α+Z_β)/C]² + 3

                                  = [(1.960 + 1.282) / 0.203]² + 3

                                  = 259

The standard normal deviate for = Z_α = 1.960

The standard normal deviate for = Z_β = 1.282

C = 0.5 * ln[(1+r)/(1-r)] = 0.255

Total sample size = N = [(Z_α+Z_β)/C]² + 3

                                  = [(1.960 + 1.282) / 0.255]² + 3

                                  = 164