The conditional probability distribution

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Suppose n = 5 and we observe the data (X₁, Y₁) = (3.7, 9.2),(X₂, Y₂) = (4.3, 9.4),(X₃, Y₃) = (5.0, 9.2),(X₄, Y₄) = (6.2, 10.4), and X₅, Y₅) = (5.3, 9.2). What is the conditional probability distribution of r_s under H₀ (8.1) when average ranks are used to break ties among the Y's? How extreme is the observed value of r_s in this conditional null distribution? Compare this fact with that obtained by taking the observed value of r_sto the (incorrect) unconditional null distribution of r_s. (See also Problem 48.)

Problem 48

For the case of n = 5 untied bivariate (X, Y) observations, obtain the form of the exact null (H₀) distribution of r_s. (See Comment 41)

Reference no: EM131108496

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The conditional probability distribution : Suppose n = 5 and we observe the data (X1, Y1) = (3.7, 9.2),(X2, Y2) = (4.3, 9.4),(X3, Y3) = (5.0, 9.2),(X4, Y4) = (6.2, 10.4), and X5, Y5) = (5.3, 9.2). What is the conditional probability distribution of rs under H0 (8.1) when average ranks are use..

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