The table contains critical values for two-tail tests. For one-tail tests, multiply α by 2.

If the calculated Spearman’s rho is greater than the critical value from the table, then reject the null hypothesis that there is no correlation.

See Spearman’s Rho for details.

Hi,

Your website is helping me a lot with statistics, thanks!

I have a question about the values in the table on this page. I calulated the Spearman Rank correlation for a dataset with n=9 for alpha=0.05 two-tailed. I found in your table that the critical value I need to use is 0.700. My correlation is 0.6833, which means that it is not significant.

However, I also calculated the P-value, which is 0.042. This is less than alpha, so it is significant.

So both methods results in a different conclusion. Why is that, or am I doing something wrong?

Furthermore, I found another spearman rho table (http://users.sussex.ac.uk/~grahamh/RM1web/Spearmanstable2005.pdf) which ahs different critical values than the table on this website. There I find that rho_crit = 0.683, so my correlation is significant. Why is this table different?

I hope you can explain me!

Thanks a lot.

Ilse

Ilse,

I have also seen differences from one table of critical values to another. I can’t comment on the table you sent me since I don’t know how its values were calculated, but in general differences may be due to different assumptions or different simulation results

Where did the p-value = .042 come from? This value seems to be quite low compared to the .05 p-value at the critical value from the table you sent me

Charles

Thanks for this usefull table. However, I’m working with tables of thouthands of values. How could I find the Spearman’s Rho table for up to 70000 samples?

Thanks in advance for your help and advises

Aurélie

I don’t have a table for large values of n. Instead you can use the approach described on the following webpage:

http://www.real-statistics.com/correlation/spearmans-rank-correlation/spearmans-rank-correlation-detailed/

Charles

Thanks for the web, it is very insightful.

However, I have only looked at Spearman and Kendall, and I may be wrong, but I have the serious impression that when you say that to get the one-tailed test one should multiply alpha times 2, I think it should be actually the opposite, i.e., divide alpha by two.

Thanks,

B.

It really depends on how you look at it, but it any case the table is for the two-tailed test, and so if you want say the critical value for the one-tail test where alpha = .05, you need to find the value in the (two-tail) table where alpha is .1 (i.e. double).

Charles