Skip to contents

Analyse a robustness screening experiment

Source: R/robustness.R
msa_robustness.Rd

Estimates the main effect of every factor in a Plackett-Burman (or any two-level orthogonal) design on a response such as accuracy, agreement with the reference, or the mean parsed value, and judges which effects are active with Lenth's pseudo standard error, which needs no replicate runs. Effects beyond the margin of error (ME) are flagged as active; effects beyond the simultaneous margin (SME) are flagged as simultaneously active. Lenth's ME and SME are conservative: with normal noise and all effects zero, actual false alarm rates per effect (ME) and per experiment (SME) are below the nominal alpha.

Usage

msa_robustness(
  design,
  response,
  factors = NULL,
  alpha = 0.05,
  transform = "none"
)

Arguments

design

A pb_design (or a data.frame with coded -1/+1 columns named in factors).

response

Numeric response, one value per run, in the row order of design.

factors

Factor columns to analyse; default: all coded columns.

alpha

Nominal significance level for ME and SME.

transform

Either "none" (default) or "logit". The latter requires a real numeric vector of finite proportions strictly between 0 and 1 and applies log(p / (1 - p)) before estimating effects. No boundary correction is applied. Proportions of exactly 0 or 1 require a prior correction, such as computing an empirical logit and passing those logits with transform = "none".

Value

An object of class msa_robustness: a data.frame of effects (effect = mean at high level minus mean at low level, t_lenth = effect / PSE, active flag) with attributes pse, me, sme, plus the response summary. With transform = "logit", effects, PSE, ME, SME and the attributes response_mean and response_sd are on the logit scale. If design carries a seed attribute it is copied unchanged to the result for reporting. Otherwise no seed provenance is claimed.

References

Lenth, R. V. (1989). Quick and easy analysis of unreplicated factorials. Technometrics 31, 469-473.

Daniel, C. (1959). Use of half-normal plots in interpreting factorial two-level experiments. Technometrics 1, 311-341.

Examples

d <- pb_design(list(format = c("plain", "sci"), units = c("nM", "ng/mL"),
                    typos = c(0, 2), context = c("none", "extra"),
                    system = c("A", "B"), temp = c(0, 0.7)), seed = 1)
set.seed(7)
acc <- 0.9 - 0.08 * (d$typos > 0) - 0.05 * (d$temp > 0) + rnorm(nrow(d), 0, 0.01)
msa_robustness(d, acc)
#> Robustness screening: 8 runs, 6 factors; response mean 0.8334 (sd 0.0532)
#>   Lenth PSE 0.0100, ME 0.0432, SME 0.1081 (alpha = 0.05)
#>   factor  effect t_lenth active active_simultaneous
#>    typos -0.0770   -7.67   TRUE               FALSE
#>     temp -0.0602   -6.00   TRUE               FALSE
#>    units  0.0158    1.57  FALSE               FALSE
#>   format  0.0076    0.76  FALSE               FALSE
#>  context -0.0058   -0.58  FALSE               FALSE
#>   system  0.0034    0.34  FALSE               FALSE
#>   active factors (|effect| > ME): typos (above ME only), temp (above ME only)