UGC NET COMMERCE SOLVED PAPERS 2017-19 - UGC NET COMMERCE December 2018

54. The probable error of the coefficient of correlation (r) is calculated by which one of the following formulae?

  • Option : D
  • Explanation : Probable Error and Standard Error of Coefficient of Correlation
    The probable error (PE) of coefficient of correlation indicates extent to which its value depends on the condition of random sampling. If r is the calculated value of correlation coefficient in a sample of n pairs of observations, then the standard error SEr of the correlation coefficient r is given by

    The probable error of the coefficient of correlation is calculated by the expression:

    Thus with the help of PEr we can determine the range within which population coefficient of correlation is expected to fall using following formula:

    where ρ (rho) represents population coefficient of correlation.
    Remarks
    1. If r < PEr then the value of r is not significant, that is, there is no relationship between two variables of interest.
    2. If r > 6PEr then value of r is significant, that is, there exists a relationship between two variables.
    Illustration: If r = 0.8 and n = 25, then PEr is

    Thus the limits within which population correlation coefficient (ρr) should fall are
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