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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?

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  • $\begingroup$ 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". $\endgroup$
    – user10525
    Apr 18, 2012 at 13:27
  • $\begingroup$ 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. $\endgroup$
    – ET13
    Apr 18, 2012 at 13:37
  • $\begingroup$ 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. $\endgroup$
    – user10525
    Apr 18, 2012 at 13:41
  • $\begingroup$ 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? $\endgroup$
    – ET13
    Apr 18, 2012 at 13:57
  • $\begingroup$ 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. $\endgroup$
    – user10525
    Apr 18, 2012 at 14:17

2 Answers 2

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If you are concerned about sample size and significance, good concepts to start out with include effect size and power (while on the topic of CIs, you might want to include accuracy as well)

As noted previously, 95% CI refers not to probability but to confidence; it is not the likelihood that the current CI contains the population parameter, but that out of 100 CIs 95 CIs will succeed in capturing the population parameter. The true probability remains unknown (unless you take a Bayesian approach), see Explorations in statistics: confidence intervals.

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  • $\begingroup$ +1, this is a nice answer. Welcome to the site, I hope we'll see more like it in the future. $\endgroup$
    – gung - Reinstate Monica
    Apr 21, 2012 at 14:45
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The formulation of the null vs. alternative hypothesis has little to do with what you "want" to find. It's how scientists (at least scientists who have a need to use frequentist statistics) address their research question. Basically, all the null says is that the relationship between these two variables is either zero or unknown. The alternate hypothesis is your suggestion/assertion that there is a relationship.

You have a hypothesis and you are testing via significance testing of a correlation. Whatever your result, you have a piece of evidence that supports or doesn't support (or contradicts, if you use a two-tailed test) that hypothesis. If it doesn't, there are myriad reasons, including insufficient power, which could be the result of small samples, poor measurement, etc. The reason sample size matters is that greater samples provide greater information; greater information provides more confidence in what is observed.

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    $\begingroup$ I'd qualify here. "Either zero or unknown" is a false antithesis. In essence all parameter values are unknown; that is why we are estimating! A null hypothesis for Spearman correlation will usually be that the population correlation is zero. In principle, it could be that it is some other value; in practice that is hard to imagine here, unless one were using a value from some other study, in which case the problem might be better tackled in Bayesian form, as you seem to be hinting. $\endgroup$
    – Nick Cox
    Nov 3, 2015 at 19:54

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