# Spearman's rank correlation for a beginner: Sample size and Interpretation

I am a computer scientist performing research, which includes calculating the Spearman rank correlation of two lists, one ranked by a human, another by a computer program.

I have the following questions:

1. I was reading this post and have become concerned with how large my sample size has to be to have a significant confidence level.
2. Also if I have understand correctly the Fisher transform gives you a confidence level after you have gotten the Spearman rank correlation. If possible I would like to know the ideal sample size before I start the experimen
3. On interpreting the value given to you by the Spearman rank correlation: I have read about the null hypothesis

The general form of a null hypothesis for a Spearman correlation is: H0: There is no association between the two variables [in the population].

However what I want to prove is the opposite ie: that there is a very close association between the two variables. How is this done?

• Well, if you calculate a confidence interval for this coefficient and the value $0$ is not included, this indicate a possible association between the variables. I guess you would also reject H0 which would indicate evidence against "no association". – user10525 Apr 18 '12 at 13:27
• I'm sorry, what does"the value $0$ is not included" mean please? Any by rejecting H0 I have shown there is some association but it would be helpful for me to know how "good" this association is. – ET13 Apr 18 '12 at 13:37
• Spearman's rank correlation coefficient takes values in $[-1,1]$. $0$ means no correlation (in this sense, of course), positive values of this coefficient indicate positive association and similarly for negative values. Say you calculate a confidence interval for this coefficient and you get $I=(0.7,0.9)$. This suggests strong positive association between the variables and also $0$ is not included in the interval. – user10525 Apr 18 '12 at 13:41
• The confidence interval tells me how reliable the correlation is (from wiki:en.wikipedia.org/wiki/Confidence_intervals). Am I correct in saying that it is the Spearman correlation which gives me the association and the correlation is just how likely this correlation is correct given the sample? – ET13 Apr 18 '12 at 13:57
• A confidence interval (CI) actually tells you how reliable the 'estimation' is: "is used to indicate the reliability of an estimate". The interpretation of a 95% CI is "the probability that this interval contains the true value of the parameter is 95%". Spearman's coefficient is a measure of dependence (there are others) and it actually measures the correlation, see the definition. Therefore, a 95% CI can be used to assess the degree of association by analysing the values it contains. – user10525 Apr 18 '12 at 14:17