CANE (version 0.1.1)

PooledLSD: Pooled Latin Square Design Analysis

Description

This function performs pooled analysis of variance (ANOVA) using the Latin square design for multiple locations or years. For more details see Montgomery (2017), Dean et al. (2017)<doi:10.1007/978-3-319-52250-0> and Ruíz et al. (2024)<doi:10.1007/978-3-031-65575-3>.

Usage

PooledLSD(
  data,
  Response,
  Location,
  Treatment,
  Row,
  Column,
  alpha,
  Mult_Comp_Test
)

Value

A list containing the following components:

• Individual_ANOVA: Summary of ANOVA results for each location or year.

• Location_wise: Multiple comparisons of treatments within each location or year.

• Bartlett_Test: Results of Bartlett's test for homogeneity of variances.

• Pooled_ANOVA: Combined (pooled) ANOVA table across all locations or years.

• Treatments_Comparison: Summary of pooled treatment comparisons using the selected multiple comparison test.

Arguments

data

A data frame containing the experimental data.

Response

A numeric variable representing the dependent variable (response).

Location

A factor indicating different locations or years.

Treatment

A factor indicating the different treatments applied.

Row

A factor indicating rows.

Column

A factor indicating columns.

alpha

A numeric value specifying the significance level for Bartlett’s test.

Mult_Comp_Test

An integer specifying the type of multiple comparison test:

• 1 = Tukey's honestly significant difference (Tukey's HSD) test

• 2 = Duncan's multiple range test (DMRT)

• 3 = least significant difference (LSD) test

References

Dean A, Voss D, Draguljic D (2017)<doi:10.1007/978-3-319-52250-0>.

Montgomery DC (2017). Design and Analysis of Experiments. John wiley & sons.

Ruíz JS, López OAM, Crossa J (2024)<doi:10.1007/978-3-031-65575-3>.

Examples

# Creating a sample dataset for Pooled Latin Square Design (LSD)
df <- data.frame(
  Location = factor(c(rep("Agra", 16), rep("Bihar", 16))),  # Locations
  Treatment = factor(c(4, 2, 3, 1, 3, 1, 4, 2, 1, 4, 2, 3, 2, 3, 1, 4,
  4, 2, 3, 1, 3, 1, 4, 2, 1, 4, 2, 3, 2, 3, 1, 4)),  # Treatments
  Row = factor(rep(1:4, each = 4, times = 2)),  # Row factor
  Column = factor(rep(1:4, times = 8)),  # Column factor
  Yield = c(29.1, 18.9, 29.4, 5.7, 16.4, 10.2, 21.2, 19.1, 5.4, 38.8, 24, 37, 
            24.9, 41.7, 9.5, 28.9, 13, 27, 7, 24, 10, 13, 41, 39, 42, 26, 19, 20, 
            20, 35, 8, 38)  # Yield values
)

# Running PooledLSD function on the dataset
out <- PooledLSD(df, "Yield", "Location", "Treatment", "Row", "Column", 0.05, 1)

# Print results
print(out)