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I want to test the correlation coefficient (i.e. |ρ|=1) that the relationship among variables is deterministic. If sample correlation coefficient ( r=0.93) can i test this value ( 1-r=1-0.93=0.07) using t-statistic ((r√(n-2))⁄√(1-r^2 )) with the statement that the relationship among variables is stochastic (i.e. ρ=0) or no relationship with 5% level of significance.

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Failure to reject a null hypothesis does not establish equivalence. You probably want to do an equivalent test of correlation coefficients. The paper below focuses on this exact issue.

http://onlinelibrary.wiley.com/doi/10.1111/bmsp.12045/abstract;jsessionid=279A5F4637E7DF195162EC836B860FB7.f04t03

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  • $\begingroup$ Wouldn't that require comparing correlations from two populations? $\endgroup$
    – dankernler
    Commented Jul 12, 2017 at 5:46
  • $\begingroup$ yes, not require comparing of two correlations @dankernler $\endgroup$
    – Aamir Khan
    Commented Jul 12, 2017 at 10:04

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