### Example :

Suppose we want to invest in a diversified emerging markets mutual fund. We narrow the field to 10 such funds, which are the largest in terms of total net assets. We are interested in whether the funds' most recent reported Sharpe ratios and expense ratios (the ratio of a fund's operating expenses to average net assets) as of mid-2013 are related. Our calculator shows the sample.

Because the expense ratios are bounded from above and below, and in practice there is at least a lower bound on alpha (as any return cannot be less than -100 percent), thus neither variable can be normally distributed and it is appropriate to conduct a test on the rank correlation coefficient.

Determine whether the null hypothesis \[ (H_0: ρ = 0) \]

is rejected in favor of alternative hypothesis \[ (H_a: ρ ≠ 0) \]

or not rejected at the 0.05 level of significance.

**The Spearman Rank Correlation Coefficient**

\[ α \]