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.
Download Table
Click here to download the Excel workbook with the above table.
References
Ramsey, P. H. (1989) Critical values for Spearman’s rank-order correlation. Journal of Educational Statistics Fall 1989, Vol 14, No. 3, pp. 245-253
https://www.semanticscholar.org/paper/Critical-Values-for-Spearman%E2%80%99s-Rank-Order-Ramsey/6cf612d9e65dcfd73afab5da2283f67a2e2beb1d
Kanji, G. K. (2006) 100 Statistical tests. 3rd Ed. SAGE
https://uk.sagepub.com/en-gb/eur/100-statistical-tests/book229436
It’s a good corner, if you can insert the different types of languages.
Hi Charles,
I calculated the values of t, p and rho in excel by:
[cell: BA59]: t =(BA61-0)/WURZEL((1-BA61^2)/(ANZAHL2(BA$4:BA$18)-2))
[cell: BA60]: p =T.VERT.2S(ABS(BA59);ANZAHL2(BA$4:BA$18)-2)
[cell: BA61]: rho =PEARSON(BA$4:BA$18;$O$4:$O$18)
In BA$4:BA$18 the values of parameter #1 are found.
In $O$4:$O$18 the values of parameter #2 are found.
My p value results also (like ilse wrote before) differ from the results I get when I take the rho and compare it to the critical value in this table.
Is there a fault in my formula? (I tried to copy it from your implemented function. Maybe somethings wrong with it)
Thanks a lot and best wishes,
Daniel
Daniel,
What are the English equivalents to WURZEL and ANZAHL?
Charles
Dear Charles,
oh sorry, i forgot to edit this:
WURZEL = SQRT
ANZAHL2 = COUNTA
Best wishes,
Daniel
Daniel,
Since you are referring to a spreadsheet that I don’t have, can you send me an email with an Excel file containing your data and the formulas that you are referencing?
Charles
Dear Charles,
I sent you an example for Spearman via e-mail. So there SCORREL() is used instead of PEARSON().
In this case one paramter is normally distributed and the other one not. So I used Spearman.
Best wishes,
Daniel
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
I also found a table which is different from the above table. The table is like this Appendix: F
Values of Spearman’s Rank Correlation (r) for Combined Areas in both tails:
N 0.2 0.1 0.05 0.02 0.01
4 0.800 0.8000 ― ― ―
5 0.700 0.8000 0.9000 0.9000 ―
6 0,600 0.7714 0.8857 0.8857 0.9429
7 0.5357 0.6786 0.8571 0.8571 0.8929
8 0.500 0.6190 0.8095 0.8095 0.8571
9 0.4667 0.5833 0.7667 0.7667 0.8167
10 0.4424 0.5515 0.7333 0.7333 0.7818
11 0.4182 0.5273 0.7000 0.7000 0.7455
12 0.3986 0.4965 0.6713 0.6713 0.7273
13 0.3791 0.4780 0.6429 0.6429 0.6978
14 .03626 0.4593 0.6220 0.6220 0.6747
15 0.3500 0.4429 0.6000 0.6000 0.6536
16 0.3382 0.4265 0.5824 0.5824 0.6324
17 0.3262 0.4118 0.5637 0.5637 0.6152
18 0.3148 0.3994 0.5480 0.5480 0.5975
19 0.3070 0.3895 0.5333 0.5333 0.5825
20 0.2977 0.3789 0.5203 0.5203 0.5684
21 0.2909 0.3688 0.5078 0.5078 0.5545
22 0.2829 0.3597 0.4963 0.4963 0.5426
23 0.2767 0.3518 0.4852 0.4852 0.5306
24 0.2704 0.3435 0.4748 0.4748 0.5200
25 0.2646 0.3362 0.4654 0.4654 0.5100
26 0.2588 0.3299 0.4564 0.4564 0.5002
27 0.2540 0.3226 0.4481 0.4481 0.4915
28 0.2480 0.3175 0.4401 0.4401 0.4828
29 0.2443 0.3113 0.4320 0.4320 0.4744
30 0.2400 0.3059 0.4251 0.4251 0.4665
Reference: Wayne W, Daniel Chad L. Cross Biostatistics Basic concepts and Methodology for Health science (10th edition) P : A- 104
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:
https://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