Calculate augmented row-column design capacity

Reports the plot counts, error degrees of freedom and feasibility of an augmented row-column layout with superimposed blocks (Piepho and Williams, 2016). Rows are grouped into row groups and columns into column groups; their intersections are the blocks. Groups can have equal sizes (rows_per_block, cols_per_block) or unequal sizes (rows_per_rowgroup, cols_per_colgroup), and blocks can hold any number of check plots (checks_per_block).

Usage

augmented_row_column_capacity(
  rows_in_field = NULL,
  cols_in_field = NULL,
  rows_per_block = NULL,
  cols_per_block = NULL,
  n_controls,
  rows_per_rowgroup = NULL,
  cols_per_colgroup = NULL,
  checks_per_block = NULL
)

Arguments

rows_in_field

Number of rows in the whole field.

cols_in_field

Number of columns in the whole field.

rows_per_block

Number of rows in each row group (equal groups).

cols_per_block

Number of columns in each column group (equal groups).

n_controls

Number of replicated checks/controls (vc).

rows_per_rowgroup

Optional vector with the number of rows of each row group (kb(i)), for unequal groups. Replaces rows_per_block.

cols_per_colgroup

Optional vector with the number of columns of each column group (sb(j)). Replaces cols_per_block.

checks_per_block

Optional number of check plots per block (pb(i, j)): a single number, a matrix with one row per row group and one column per column group, or a vector by row group. Defaults to n_controls (every block a complete block of checks). Smaller values give incomplete blocks; larger values give extra check replication.

Value

A one-row tibble with the field size, number of groups and blocks, check and entry plots, error_df, the error degrees of freedom of the row-column ANOVA, check_plots - n_controls - (rows - 1) - (cols - 1) - (row groups - 1)(column groups - 1) (a design is only analyzable when error_df > 0; Clarke and Stefanova (2011) recommend about 50), check_fraction, and the smallest slack of the row-group and column-group conditions of Piepho and Williams (2016), which must be non-negative for the row-group and column-group sub-designs to be estimable on their own.

References

Piepho, H.-P. and Williams, E. R. (2016). Augmented row-column designs for a small number of checks. Agronomy Journal 108, 2256-2262. doi:10.2134/agronj2016.06.0325

Examples

augmented_row_column_capacity(
  rows_in_field = 12,
  cols_in_field = 12,
  rows_per_block = 4,
  cols_per_block = 4,
  n_controls = 4
)
#> # A tibble: 1 × 17
#>   rows_in_field cols_in_field rows_per_block cols_per_block n_block_rows
#>           <int>         <int>          <int>          <int>        <int>
#> 1            12            12              4              4            3
#> # ℹ 12 more variables: n_block_cols <int>, n_blocks <int>, n_controls <int>,
#> #   total_plots <int>, check_plots <int>, entry_plots <int>, error_df <dbl>,
#> #   check_fraction <dbl>, min_rowgroup_slack <dbl>, min_colgroup_slack <dbl>,
#> #   every_row_has_check <lgl>, every_col_has_check <lgl>

# Example 3 of Piepho and Williams (2016): unequal groups and blocks.
augmented_row_column_capacity(
  n_controls = 4,
  rows_per_rowgroup = c(6, 5, 6, 5),
  cols_per_colgroup = c(3, 4, 3),
  checks_per_block = rbind(c(4, 5, 4), c(3, 5, 3), c(3, 5, 4), c(3, 5, 3))
)
#> # A tibble: 1 × 17
#>   rows_in_field cols_in_field rows_per_block cols_per_block n_block_rows
#>           <int>         <int>          <int>          <int>        <int>
#> 1            22            10             NA             NA            4
#> # ℹ 12 more variables: n_block_cols <int>, n_blocks <int>, n_controls <int>,
#> #   total_plots <int>, check_plots <int>, entry_plots <int>, error_df <dbl>,
#> #   check_fraction <dbl>, min_rowgroup_slack <dbl>, min_colgroup_slack <dbl>,
#> #   every_row_has_check <lgl>, every_col_has_check <lgl>