Category: Correlation and Path

Phenotypic Correlation (rₚ) Calculator

(Plant Breeding / Statistics)

---

Input Instructions:

Enter paired observations of Trait 1 and Trait 2 separated by a comma, one pair per line.
Example: 45, 62

Calculate Phenotypic Correlation

---

Genotypic Correlation (r_g) Calculator

(Plant Breeding / Quantitative Genetics)

---

Formula Used:

r_g = Cov_g(X,Y) ÷ √(σ²_gX × σ²_gY)

---

Genotypic Covariance (Cov_g(X,Y)): Genotypic Variance of Trait X (σ²_gX): Genotypic Variance of Trait Y (σ²_gY): Calculate Genotypic Correlation

---

Genotypic Correlation (r_g) Calculator

(Plant Breeding / Quantitative Genetics)

---

Formula Used:

r_g = Cov_g(X,Y) ÷ √(σ²_gX × σ²_gY)

---

Genotypic Covariance (Cov_g(X,Y)): Genotypic Variance of Trait X (σ²_gX): Genotypic Variance of Trait Y (σ²_gY): Calculate Genotypic Correlation

---

Environmental Correlation (r_e) Calculator

(Plant Breeding / Quantitative Genetics)

---

Formula Used:

r_e = Cov_e(X,Y) ÷ √(σ²_eX × σ²_eY)

---

Environmental Covariance (Cov_e(X,Y)): Environmental Variance of Trait X (σ²_eX): Environmental Variance of Trait Y (σ²_eY): Calculate Environmental Correlation

---

Correlation Significance Tester

(t-test for Correlation Coefficient)

---

Formula Used:

t = r √(n − 2) ÷ √(1 − r²)

---

Correlation Coefficient (r): Number of Observations (n): Test Significance

---

Path Coefficient Calculator

(Correlation → Direct & Indirect Effects)

---

Formula Used:

P = r − Σ(r × P)
(Direct effect = Correlation − Indirect effects)

---

Correlation of Trait with Yield (rₓᵧ):

Indirect Effect via Trait 1

Correlation (rₓ₁): Path coefficient of Trait 1 (P₁):

Indirect Effect via Trait 2

Correlation (rₓ₂): Path coefficient of Trait 2 (P₂): Calculate Direct Effect (Path Coefficient)

---

Indirect Effect Estimator

(Path Coefficient Analysis)

---

Formula Used:

Indirect Effect = r × P

---

Indirect Path via Trait 1

Correlation (rₓ₁): Direct Effect of Trait 1 (P₁):

Indirect Path via Trait 2

Correlation (rₓ₂): Direct Effect of Trait 2 (P₂):

Indirect Path via Trait 3

Correlation (rₓ₃): Direct Effect of Trait 3 (P₃): Calculate Indirect Effects

---

Direct Effect Estimator

(Path Coefficient Analysis)

---

Formula Used:

P = rₓᵧ − Σ(r × P)

---

Total Correlation with Yield (rₓᵧ):

Indirect Effects

Trait 1: rₓ₁ and P₁ Trait 2: rₓ₂ and P₂ Trait 3: rₓ₃ and P₃ Calculate Direct Effect

---

Residual Effect Calculator

(Path Coefficient Analysis)

---

Formula Used:

Rₑ = √[1 − Σ(r × P)]

---

Trait 1

Correlation with Yield (r₁): Direct Effect (P₁):

Trait 2

Correlation with Yield (r₂): Direct Effect (P₂):

Trait 3

Correlation with Yield (r₃): Direct Effect (P₃): Calculate Residual Effect

---

Trait Importance Ranking Tool

(Based on Direct + Indirect Effects)

---

Trait 1

Direct Effect (P₁): Sum of Indirect Effects:

Trait 2

Direct Effect (P₂): Sum of Indirect Effects:

Trait 3

Direct Effect (P₃): Sum of Indirect Effects: Rank Traits

---