hi sadie.

i don't know which software package you use; i'll show this in R.

first generate some random data:

> set.seed(1)

> x y cor.test(x, y)

Pearson's product-moment correlation

data: x and y

t = -0.0098, df = 98, p-value = 0.9922

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

-0.1973739 0.1954620

sample estimates:

cor

-0.0009943199

spearman correlation is:

> cor.test(x, y, method="spearman")

Spearman's rank correlation rho

data: x and y

S = 160198, p-value = 0.7017

alternative hypothesis: true rho is not equal to 0

sample estimates:

rho

0.03871587

one way to compute a z-value and subsequently a 2-sided p-value is:

> r n z p cbind(r,z,p) # results same as above

r z p

[1,] 0.03871587 0.3705434 0.7109776

-abs(z) ensures that you get the correct area under the curve from the left side up to your value, regardless of the z-value's sign. to get the 2-sided p-value, just multiply it *2.

actually, spearman correlation is a pearson correlation of rank-transformed data, so you can use the rank() function on your variables and use cor.test() with the method "pearson" and it will return the same correlation and p-value as method = "spearman":

> cor.test(rank(x), rank(y), method="pearson")

Pearson's product-moment correlation

data: rank(x) and rank(y)

t = 0.3836, df = 98, p-value = 0.7021

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

-0.1589107 0.2333594

sample estimates:

cor

0.03871587

the t-value can be computed as (see [1]):

> (tval 2*pt(-abs(tval), n-2)

[1] 0.702139

hope this helps. kind regards, marco

reference:

[1] https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient#Determining_significance

https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient#Determining_significance

Thanks for taking the time to reply Marco. I should've said I'm using SPSS! You may know the equivalent functions? Thanks!

you're welcome.

i've kicked spss off my machines ages ago, so i can't tell whether this works or not, but i've found that under Transform > Rank Cases you can rank-transform your variables. i don't know how tied ranks are handled - in R, the "average rank" is assigned to equal values of a variable (there's a button called "ties" in the spss rank-window, maybe you have to set this there). once you have rank-transformed your variables, you can compute simple bivariate (pearson) correlations of your vars and get p-values.

however, if you have used some imputation method for your variables - don't you get a set of new variables with imputed values (don't know what spss does)? if so, you could compute spearman correlations right away (with p-values, etc.) and save yourself a lot of time point-and-clicking. ;)

I thought in SPSS it is calculated automatically, but it is ages since I've used it so I could be wrong

One approach to testing whether an observed value of ρ is significantly different from zero (r will always maintain −1 ≤ r ≤ 1) is to calculate the probability that it would be greater than or equal to the observed r, given the null hypothesis, by using a permutation test.  But it is difficult by hand.

Another approach parallels the use of the Fisher transformation

F(r)=0.5*ln((1+r)/(1-r)), then using normal statistic test  z=sqrt(9n-3)/1.06)*F(r).

Or  using t-test   t=r*sqrt( (n-2)/(1-r^2) )  with df=n-2.

Type 9n should be replaced by (n

F(r)=0.5*ln((1+r)/(1-r)), then using normal statistic test z=sqrt(9n-3)/1.06)*F(r).

one more notation,

r is the Spearman's rank correlations from the sample

Hi Li, do you know any good program to calculate significance level in IDL language?