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Calculate Relative Efficiency of Experimental Design (Blocking and Split-Plot)

Source: R/calc_design_efficiency.R
calc_design_efficiency.Rd

Computes the empirical Relative Efficiency (RE) of a Randomized Complete Block Design (RCBD) or Split-Plot design compared to a theoretical Completely Randomized Design (CRD / DCA), evaluating whether blocking or whole-plot restriction successfully reduced experimental error and calculating the equivalent number of replications saved.

Usage

calc_design_efficiency(fit)

Arguments

fit

An object of class `"agri_fitted_model"` returned by fit_experiment.

Value

An S3 object of class `"agri_design_efficiency"` containing:

design_type

Canonical experimental design evaluated.

relative_efficiency_pct

Relative efficiency expressed as a percentage (%). Values > 100% indicate precision gain.

reps_saved_pct

Percentage of additional replications a CRD would have required to achieve the same precision.

mse_actual

Mean square error of the actual design.

mse_crd_theoretical

Estimated mean square error if the experiment had been conducted as a CRD.

interpretation

Plain-language agronomic interpretation of blocking efficiency.

Details

The relative efficiency for an RCBD relative to a CRD is computed using the classical Kempthorne (1952) and Cochran & Cox (1957) formula with degrees of freedom correction factor: $$MSE_{\text{CRD}} = \frac{df_b \cdot MSB + (df_t + df_e) \cdot MSE}{df_b + df_t + df_e}$$ $$k = \frac{(df_e + 1)(df_{\text{CRD}} + 3)}{(df_e + 3)(df_{\text{CRD}} + 1)}$$ $$RE = \frac{MSE_{\text{CRD}}}{MSE_{\text{RCBD}}} \times k \times 100\%$$

Examples

data(wheat_splitplot, package = "agriDesignR")
fit <- fit_experiment(
  data = wheat_splitplot,
  response = "grain_yield",
  main_plot = "temperature",
  sub_plot = "genotype",
  block = "block"
)
eff <- calc_design_efficiency(fit)
print(eff)
#> 
#> ======================================================================
#>   agriDesignR: Relative Design Efficiency (RE)
#> ======================================================================
#>   Design Evaluated: Split-Plot Design (Parcelas Divididas)
#>   Blocking Factor : block
#>   Relative Effic. : 208.23 %
#> 
#> 
#> Variance Comparison (Actual Design vs. Theoretical CRD)
#> ----------------------------------------------------------------------
#>   - Actual Error Variance (MSE)       : 8.527 (df = 27)
#>   - Theoretical CRD Variance (MSE_crd): 17.872 (df = 30)
#>   - Replications Gain/Saved           : +108.23 %
#> 
#> 
#> Agronomic / Biological Assessment
#> ----------------------------------------------------------------------
#>   [OK] Highly Effective Blocking: The blocking factor 'block' increased experimental precision by 108.23% compared to an unblocked DCA (CRD). A CRD would have required 2.08x more replications per treatment to detect the same effect size.
#> 
#> ======================================================================
#>