Statistical Methods I

• Sewall Wright's Path Analysis and Degrees of Determination:
• In a causal chain system where variable $C$ acts on effect $X$ indirectly through intervening variable $A$ ($C \to A \to X$):
• Multiplicative Determination: The degree of determination of $X$ by indirect cause $C$ is the product of the direct degrees of determination: $d_{XC} = d_{XA} \cdot d_{AC}$. (True)
• Compound Path Coefficient: The compound path coefficient along the chain is the product of the component path coefficients: $p_{XC} = p_{XA} \cdot p_{AC}$. (True)
• Degrees of determination along a linear causal chain are multiplicative, not additive ($d_{XC} \ne d_{XA} + d_{AC}$). (False)
• Additive Determination by Independent Causes: Since $A = C + D$ where $C$ and $D$ are uncorrelated independent causes, the total determination of $X$ by $A$ equals the sum of determinations by $C$ and $D$: $d_{XA} = d_{XC} + d_{XD}$. (True)
• Conclusion: Statements (A), (B) and (C) only / (A), (B) and (D) (Option 2).

Correct option: (2) (A), (B) and (C) only.

• Hardy-Weinberg Equilibrium Genotype Frequencies:
• For a diallelic gene with allele frequencies $p$ (allele $A$) and $q$ (allele $a$) such that $p + q = 1$:
• Heterozygote frequency: $f(Aa) = 2pq$
• Recessive homozygote frequency: $f(aa) = q^2$
• Given condition: The heterozygous genotype is twice as frequent as the homozygous recessive genotype:

• Dividing both sides by $2q$ (for $q \neq 0$):

• Since $p + q = 1$ and $p = q$:

• Conclusion: The required allelic frequencies are p = 0.5; q = 0.5 (Option 4).

Correct option: (4) p=05;q=05