COEFFICIENT OF CORRELATION “r” Among quantities X i and Y i, both of them affected by the respective standard errors  Xi and  Yi. X Y  Xi  Yi ii.

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Presentation transcript:

COEFFICIENT OF CORRELATION “r” Among quantities X i and Y i, both of them affected by the respective standard errors  Xi and  Yi. X Y  Xi  Yi ii X - Variance Y - Variance XY – Co-variance

Is r not equal to zero (statistically significant)? t TEST (N-2) degrees of freedom

RATIO OF CORRELATION “  ” X Y n 1 = 3 elements n 2 = 3 elements n 3 = 4 elements k = 3 groups

Is  2 not equal to zero (statistically significant)? t TEST (N-2) degrees of freedom

ARE “r” and “  2 ” statistically equal or not? F TEST 1 = (N-2); 2 = (N – k) degrees of freedom

LINEAR CORRELATION r = t r (22) =  = t  (22) = F(6, 16) = 1.36 m = q = 1.547

UN CORRELATION r = t r (22) = 0.65  = t  (22) = 2.23 F(6, 16) = m = 0.1 q = 20.1

NOT LINEAR CORRELATION r = t r (22) = 12.1  = t  (22) = 26.9 F(6, 16) = 9.15 m = 1.59 q = 1.1

REFERENCES 1.Amandola G., Terreni, V. Analisi Chimica Strumentale e Tecnica. V Ed., Masson Italia Editori, Milano 1986, pag. 587 – 596.