I am plotting results which are not based on a Gaussian distribution. Is it possible to use the 95% confidence interval? Some literature stating your answer would be very helpful.
The Pearson correlation coefficient makes no normality assumptions, however, inferences using the coefficient typically require additional assumptions.
The usual 95% CI assumes bivariate normality - which effectively means that the residuals of a regression of X on Y or Y on X are sampled from a normal distribution (it doesn't require normality of X and Y).
However, you can relax these assumptions using other methods (e.g., bootstrapping with a BCa bootstrap).
Can you clarify your question? Do you mean a 95% confidence interval for a correlations coefficient?
Your question is not clear enough. If the distribution of the two variables is not Gaussian you should use Spearman's correlation coefficient. And you can use it's 95%CI with no problem. You can compute it easily in R or other statistical software.
As I recall for computing the CI of Pearson correlation coefficient both variables should be normally distributed - Doug Altman wrote in one his books - Practical Statistics for Medical Research (1992), but now I don't have access to the book - (edit - I found it and what I recalled was correct: "for the calculation of a valid confidence interval for r both veriables should have a normal distribution" page 279 - But as Thom S Baguley wrote and AK Singh, below, this is not necessary - the bivariate normality is necessary. In wikipedia and other sources it is also written that variables should have a bivariate normal distribution: "sample pairs are independent and identically distributed and follow a bivariate normal distribution"
The Pearson correlation coefficient makes no normality assumptions, however, inferences using the coefficient typically require additional assumptions.
The usual 95% CI assumes bivariate normality - which effectively means that the residuals of a regression of X on Y or Y on X are sampled from a normal distribution (it doesn't require normality of X and Y).
However, you can relax these assumptions using other methods (e.g., bootstrapping with a BCa bootstrap).
I agree with Thom, but would add that if (X,Y) has a bivariate normal distribution, the inference on the population Pearson correlation coefficient is still valid. For more information on this topic, take a look at
file:///C:/Users/AKS/Downloads/final_eTD.pdf
Thank you all. Yes, I meant the 95% confidence interval. I used the bootstrapping method and it worked.
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