Description Usage Arguments Details Value Built-in methods Author(s) References Examples

Computes a pseudo standard error using any of a variety of built-in methods, or a user-supplied one.

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`effects` |
Numeric vector of effects or contrasts to be explored. |

`method` |
Character value. The name of the method to be used. See Details. |

`verbose` |
Logical value. If |

`alpha` |
Numeric significance level, between 0 and 1. |

`...` |
Additional arguments passed to |

The `PSE`

function implements methods of estimating the standard error of effects estimates from unreplicated designs. The underlying assumption is that the effects all have the same variance, and that “effect sparsity” assumption applies, whereby the majority of the effects are inactive and only a handful are active. The method may be any “directed” method (as described in Hamada and Balakrishnan (1998).
A number of built-in methods are available; see the list below.

Users may easily write their own method. The method `"foo"`

would be implemented by writing a function `foo_pse <- function(effects) { ... }`

and saving it where it can be found in the search path. An example can be found by listing `unrepx:::Lenth_pse`

.

If the user-supplied function needs to use weights, coefficients, or other parameters that depend on `length(effects)`

that would be cumbersome in simulations (e.g., in `ref.dist`

), the user may instead provide a function `foo_pse <- function(effects, parm) { ... }`

, along with `attr(foo_pse, "setup") <- function(n.effects) { ... }`

which returns the `parm`

argument (say, a `list`

) to be used when `length(effects) = n.effects`

. The setup function is called automatically if the `"setup"`

attribute exists, and if so, the function is expected to have the second argument. See a listing of `unrepx:::Zahn_pse`

for an example.

`PSE`

returns a single numeric value, named in the style `method_PSE`

.
`ME`

returns a named numeric vector of length 2, containing the margin of error `ME`

and the simultaneous margin of error `SME`

.

- Daniel
The 68.3rd quantile of the absolute effects. See Daniel (1959).

- Dong
The RMS method, applied after excluding all effects that exceed

`2.5 * PSE(effects, "SMedian")`

in absolute value. See Dong (19??).- JuanPena
An iterated median method whereby we repeatedly calculate the median of the absolute effects that don't exceed 3.5 times the previous median, until it stabilizes. The estimate is the final median, divided by .6578. See Juan and Pena (1992).

- Lenth
The SMedian method, applied after excluding all effects that exceed

`2.5 * PSE(effects, "SMedian")`

in absolute value. See Lenth (1989).- RMS
Square root of the mean of the squared effects. This is not a good PSE in the presence of active effects, but it is provided for sake of comparisons.

- SMedian
1.5 times the median of the absolute effects.

- Zahn, WZahn
The Zahn method is the slope of the least-squares line fitted to the first

*m*points of`hnplot(effects, horiz = FALSE)`

, where`m = floor(.683 * length(effects))`

. (This line is fitted through the origin.) The WZahn method is an experimental version of Zahn's method, based on weighted least-squares with weights decreasing linearly from*m - .5*to*.5*, but bounded above by*.65m*.

Russell V. Lenth

Daniel, C (1959)
Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments.
*Technometrics*, 1(4), 311-341

Dong, F (1993)
On the Identification of Active Contrasts in Unreplicated Fractional Factorials.
*Statistica Sinica* 3, 209-217

Hamada and Balakrishnan (1998)
Analyzing Unreplicated Factorial Experiments:
A Review With Some New Proposals.
*Statistica Sinica* 8, 1-41

Juan, J and Pena, D (1992)
A Simple Method to Identify Significant Effects in Unreplicated
Two-Level Factorial Designs.
*Communications in Statistics: Theory and Methods* 21, 1383-1403

Lenth, R (1989)
Quick and Easy Analysis of Unrelicated Factorials
*Technometrics* 31(4), 469-473

Zahn, D (1975)
Modifications of and Revised Critical Values for the Half-Normal Plot.
*Technometrics* 17(2), 189-200

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```
Lenth_PSE
8.9625
```

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