if and , then ).Second, compare with the value for the statistic calculated in Step 3.Reject your if your calculated value is greater than or equal to the Critical value; (significant result).Accept your if your calculated value is less than the Critical value; (non-significant result).For example, if and then reject the Null Hypothesis.Table of Critical Values for Critical Significance Levels () of 0.1, 0.05 and 0.01 for the rS statistic where degrees of freedom () is the number of pairs of data points minus two for a Spearman correlation. Critical values of the Spearman rank-order correlation coefficient, rS, based on Zar (1999) and sources therein.
It is important to realize that statistical significance does not indicate the strength of Spearman's correlation. In fact, the statistical significance testing of the Spearman correlation does not provide you with any information about the strength of the relationship. Thus, achieving a value of p = 0.001, for example, does not mean that the relationship is stronger than if you achieved a value of p = 0.04. This is because the significance test is investigating whether you can reject or fail to reject the null hypothesis. If you set α = 0.05, achieving a statistically significant Spearman rank-order correlation means that you can be sure that there is less than a 5% chance that the strength of the relationship you found (your ρ coefficient) happened by chance if the null hypothesis were true.
Thus we reject the null hypothesis that there is no (Spearman) correlation between age and Brozek percent fat (r = 0.27, p-value = 1.07e-05). As age increases so does percent body fat.