Define a sparse relative cell-mean pattern

Creates a sparse mean-shape specification for the balanced simulation functions. End each cell definition with value. Unlisted cells have raw value zero, and factors in the tested term that are omitted from every row are broadcast when the pattern is resolved against a design.

Usage

means_pattern(...)

Arguments

...: Repeated named sparse-cell definitions. Each definition must use the same factor names in the same order and end in a finite numeric scalar named value. Factor levels may be supplied as one-based integer indices (for example, time = 3) or as the generated balanced-design names (for example, time = "time3"). The two forms are equivalent after the pattern is resolved against a design.

Value

An object of class anovapowersim_means_pattern, retaining the sparse definitions until a balanced simulation function resolves them against its design and tested term.

Details

Pattern values describe relative shape, not effect magnitude. The selected power function projects the raw values onto the requested ANOVA term, normalizes that component, and rescales it uniformly to reach target_pes. Multiplying all values by one positive constant, adding an intercept or a lower-order component, or reversing every sign therefore leaves the same target-term direction (up to sign). Under nonsphericity, different directions within a multi-df term can nevertheless produce different simulated power.

This differs from cell_design(), where each m is a literal population mean whose magnitude directly determines the simulated effect.

Default direction

When no pattern is supplied, balanced simulations use centered scores in generated level order, i - (L + 1) / 2 for levels i = 1, ..., L, normalized to unit length. Interactions use the Kronecker product of their factors' normalized score vectors, followed by one final normalization after broadcasting. This is an ordered, reproducible convention rather than a neutral scientific assumption; an explicit pattern is recommended whenever the expected shape is known.

Examples