What do you mean by "confidence level"? I can't tell what the numbers on this graph for "95% confidence level" and "99% confidence level" mean. Normally one would calculate a confidence interval, which has two numbers (a lower and upper bound). "Confidence level" usually (in my experience) is used to mean the same thing as alpha level, i.e., if some value is p=.03, someone might say it is "significant at the 95% confidence level but not the 99% confidence level). But I have no idea what it means to say, as this graph does, "the 95% confidence level is 0.34".

 @Stephen Politzer-Ahles , sir you are absolutely right. I also have the same experience about the confidence interval. If you know about any function for  finding the confidence interval of spearman rank correlation then please write for me. like  for 99% confidence interval of pearson correlation,i can use the function as:

[R,~,RL,RU] = corrcoef(a.',b.','alpha',0.01).

See for instance:

http://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1455&context=jmasm

http://stats.stackexchange.com/questions/18887/how-to-calculate-a-confidence-interval-for-spearmans-rank-correlation

http://onlinestatbook.com/2/estimation/correlation_ci.html

The trick is to transform the rank correlation score r into a normally distributed variable called z', introduced by Fisher. 

z' = 0.5 ln [(1+r)/(1-r)]

z' has standard error 1/sqrt(n-3)

where n is the number of pairs of scores. 

Thanks dear Jonas Nyman, one of your reference (http://stats.stackexchange.com/questions/18887/how-to-calculate-a-confidence-interval-for-spearmans-rank-correlation)  has the solution in Python and in the second reference (http://onlinestatbook.com/2/estimation/correlation_ci.html), there is no matlab function for calculating the confidence interval of spearman rank correlation.

The stackexchange reference shows a formula for calculating the confidence interval, it is very easy to write the formula using basic MATLAB code.

Abdur, there is no built in function for this in matlab. You will have to write it yourself. The formula you need have been provided in the links above. It should be easy to do.

@Stephen Politzer-Ahles , about the  numbers on the graph for "95% confidence level" and "99% confidence level" in my question, i am not sure what this means. Actually i came across this figure in one of  the research paper in the reference. .(https://www.researchgate.net/publication/29624675).

Also if possible then tell me how to insert the solid and dashed lines for 99% and 95% confidence levels shown in fig.4 of the reference paper.thanks

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 @Jonas Nyman, thanks for sharing your information. Here is the code for finding the confidence interval of spearman rank correlation:

RHO = corr(a.',b.','Type','Spearman');

n = numel(a);

STE = 1/sqrt(n-3);

% here the input is 95% confidence interval, for 99% use 0.99:

CI = norminv(0.95);

upper_bound = tanh(atanh(RHO)+CI*STE);

lower_bound = tanh(atanh(RHO)-CI*STE);

Dear Abdur

Please, read the file in the following link, I hope will be helpful for you.

http://faculty.washington.edu/gloftus/P317-318/Useful_Information/r_to_z/PearsonrCIs.pdf

Good Luck

Based on the paper you sent, it looks like this is not about finding confidence intervals. I skimmed the paper and the "confidence level" they are talking about is something different. I've never heard of it before and I haven't taken the time to look in depth at the references they provide (but this is something you must do if you want to use this statistic and understand what it means), but it appears to be some value such that if their correlation coefficient is above this value then they can conclude that it's significantly different than 0 at the stated confidence level. The formula they give in the paper is also extremely simple so it should be very easy for you to calculate these values from their data.

As for how to insert solid and dashed lines, this can be done with basic MATLAB code. If you can't figure it out then someone here can provide an example, but I suggest you search on Google a little, there are many examples and tutorials already.