ANIMAL GENETICS BREEDING Biometrical Techniques in Animal Breeding
ANIMAL GENETICS & BREEDING Biometrical Techniques in Animal Breeding Course No. AGB - 605 Lecture no. – 4 UNIT - III Correlation Dr K G Mandal Department of Animal Genetics & Breeding Bihar Veterinary College, Patna Bihar Animal Sciences University, Patna
Correlation: Association or relationship or interdependence between two or more variables. Variables: Continuous and discrete Attributes: qualitative traits Types of correlation 1. According to direction: (i) Positive (ii) Negative (iii) Zero
2. According to number of variables: (i) Simple (ii) Multiple (iii) partial 3. According to proportionate change between two variables: (i) Linear (ii) Non-linear
(A)According to direction: (i) Positive correlation – Both the variables move in the same direction. Example – height and weight (ii) Negative correlation – Both the variables move in the opposite direction. Example – Milk yield & fat percentage
(iii) Zero correlation – One variable increases or decreases but the other variable remains constant. Example: Variable X – 2, 5, 6, 8, 10, 12 Variable Y – 5, 5, 5, 5
(B) According to no. of variables: (i) Simple – only two variables are studied at a time. (ii) Multiple – three or more variables studied at a time. Example – feed quality, quantity given, feed conversion, body weight, etc. (iii) Partial correlation – studied three or more variables but find out correlation between two variables at a time while others kept constant.
(C ) According to proportionate change between variables: (i) Linear - Both the variables move at a constant ratio throughout. Example: X 5, 10, 15, 20, 25 Y 10, 20, 30, 40, 50 constant ratio ½. (ii) Non-linear – Variables do not follow a constant ratio throughout.
Coefficient of correlation: • Measures the degree of association or degree of relationship between two variables. • Denoted as ‘r’, i. e. , rxy so that, rxy = ryx • Concept given by Karl Pearson.
Methods to estimate coefficient of correlation: 1. Pearsonian method: rxy = Cov. xy / sdx. sdy Cov xy = [∑xy – (∑x)(∑y)/N] /(N-1) sdx = [[∑x 2 - (∑x)2 ] /N – 1 sdy = [[∑y 2 - (∑y)2 ] /N - 1
Properties of correlation coefficient: (i) Ranges from -1 to +1 (ii) Pure number (iii) No unit (iv) + 1 is perfect positive correlation (v) - 1 is perfect negative correlation (vi) when r = 0, it means no correlation (vii) rxy = ryx
Other methods to estimate Coefficient of Correlation: 2. Scatter diagram method 3. Graphic method 4. Rank correlation method 5. Least squares method
• Rank correlation: i)It measures the degree of association between the ranks of two variables. ii) Concept given by Spearman. iii) No unit iv) Ranges from -1 to + 1 6∑di 2 R = 1 - ------n(n 2 – 1)
Where, di = xi – yi xi = ith rank of x variable yi = ith rank of y variable n = pair number of observation ∑di = 0
• Example: AGB 605 Mid-term Rank (Xi) (x) Final (y) Rank (Yi) di = xi – yi di 2 A 60 6 58 6 0 0 B 70 4 68 5 -1 1 C 90 1 78 3 -2 4 D 65 5 88 1 4 16 E 75 3 84 2 1 1 F 85 2 72 4 -2 4 ∑di = 0 ∑di 2= 26 Total R = 1 - 6*26/6(36 – 1) = 1 – 26/35 = (35 – 26)/35 = 0. 25
v Standard Error (S. E. ) of r : S. E. of r = (1 - r 2)/ √N v Probable Error (P. E. ) of r : P. E. (r) = 0. 6745 (1 – r 2)/ √N v If r < PE, there is no correlation. v If r > 6 PE, the coefficient of correlation is said to be certain and significant.
Test of significance: v Coefficient of correlation is tested through t – test at N – 2 d. f. T- test: t (N-2) d. f. = (r√N – 2) / (√ 1 – r 2) Interpretation ?
Use of Correlation coefficient: i) For prediction of future performance on the basis of past record. y’ = Y – r. Sy/Sx(x – x) Where, y’ = predicted value of y y = mean of y r = correlation coefficient x = mean of x Sx & Sy = SD of x and y variable
2. The coefficient of correlation measures the degree of relationship between two characters. 3. The square of correlation coefficient between breeding value and phenotypic value (r 2 AP) measures the heritability. 4. It maintains relationship with regression. byx = rxy(6 y/6 x) & bxy = rxy(6 x/6 y)
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