Glossary

The help text of the "?" buttons. Each entry shows whether Alan R. Vazquez has reviewed it.

Step 1: Describe

The user writes the request for the experiment in plain words, in any language. "Interpret request" sends the text to the translation service. "Fill in the form yourself" opens an empty specification card. The request text and the clarification answers are the only data that leave the device.

Draft, not yet reviewed.

Step 2: Confirm

The specification card shows the factors, the runs, the minimum resolution, the replications, the center points, the randomization and the seed. Each value shows a quote from the request, a "default" label, an "Edited by you" label or an agreement flag. The user resolves each flagged value, and then "Generate design" becomes available. "Move up" and "Move down" change the factor order, which sets the design column of each factor.

Draft, not yet reviewed.

Step 3: Design

FrF2 makes the design in the browser from the confirmed specification. The tool checks the result before it shows the design. If a check fails, the tool shows the name of the failed check and does not show the design. The step shows the run sheet, the design properties and the R code.

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Outside the scope

The tool makes two-level regular fractional factorial designs and full factorials with the FrF2 package. Requests for factors with more than two levels, mixed levels, mixture designs or response surface modeling are outside the scope. Requests for optimal designs, designs for computer experiments or adaptive designs, and text that is not a design request, are also outside the scope. A fixed message names the category and gives no alternatives.

Draft, not yet reviewed.

Not supported in this version

This version does not support blocking, split-plot designs, hard-to-change factors, required estimable interactions or user-given generators. It does not support the choice of a catalogue design, the choice of a fraction or criteria other than minimum aberration, for example MaxC2. It does not support Plackett-Burman designs, foldover or the analysis of results. A fixed message names the feature and gives no alternatives.

Draft, not yet reviewed.

Factors

A factor is a variable that the experiment sets at two levels. Each factor has a name, a low level, a high level, an optional unit and a quantitative flag. The number of factors is $k$ in the notation $2^{k-p}$. If a request gives only the number of factors, the tool uses the FrF2 names A, B, C and so on.

Draft, not yet reviewed.

Factor order

The order of the factors in step 2 sets which factor gets which design column. The order does not change the WLP, the resolution or the number of clear 2FIs. It changes which named effects are aliased and which named factors have all 2FIs clear. "Move up" and "Move down" change the order.

Draft, not yet reviewed.

Levels

Each factor has two levels, a low level and a high level. The real levels are the values that the experiment uses, for example 150 and 200, or "slow" and "fast". The coded levels are $-1$ for low and $+1$ for high, and $0$ for a center point. If a request gives no levels, the default levels are $-1$ and $+1$.

Draft, not yet reviewed.

Unit

The unit is optional text that the tool shows with the factor name. The unit does not change the design. Units need no quote from the request, because they follow from the levels.

Draft, not yet reviewed.

Quantitative factor

A quantitative factor has levels that are numbers on a scale, for example a temperature. A factor with the levels "off" and "on" is not quantitative. Center points need all factors to be quantitative, because a center point is at the middle of each range. The quantitative flag needs no quote from the request, because it follows from the levels.

Draft, not yet reviewed.

Number of runs

The number of runs is the number of distinct runs in one replicate of the design. It is a power of 2 from 4 to 4096, and it equals $2^{k-p}$. If a request gives only a minimum resolution, FrF2 takes the smallest catalogue design that has at least this resolution. If no fraction has this resolution, FrF2 makes the full factorial.

Draft, not yet reviewed. Source: Groemping (2014).

Minimum resolution

The minimum resolution is the lowest resolution that the design must have. With a number of runs and a minimum resolution, the tool checks that the catalogue reaches this resolution before FrF2 makes the design. If the check fails, a message states the highest resolution in this number of runs. Fixed phrase rules map words to a resolution, for example "estimate all two-factor interactions" to resolution V.

Draft, not yet reviewed.

Replications

The number of replications is the number of times that the experiment runs the whole design. The default is one replication. With repeat only off, which is the default, each replicate is a true replication. With repeat only on, the repetitions are repeated measurements of the same runs.

Draft, not yet reviewed. Source: Groemping (2014).

Repeat only

Repeat only sets the FrF2 argument repeat.only. When it is on, the repetitions are repeated measurements of the same run, not new runs. The repetitions of a run stay together in the run order, and the randomization does not separate them. When it is off, which is the default, each replicate is a true replication.

Draft, not yet reviewed. Source: Groemping (2014).

Center points

Center points are extra runs at the middle of the range of each factor, so all factors must be quantitative. They add a check for curvature. The WLP and the resolution do not use them. The number of rows is the number of runs plus the number of center points, times the number of replications.

Draft, not yet reviewed. Source: Groemping (2014).

Randomization

By default, the run order is random. FrF2 sets the random order with the seed. With randomization off, the design is in standard order, and the R code has no seed. The run sheet shows the run order and the standard order of each run.

Draft, not yet reviewed. Source: Groemping (2014).

Seed

The seed is an integer from 1 to 2,147,483,647 that sets the random run order in FrF2. The default seed is the local date of the device as yyyymmdd, for example 20261014. The same seed, design and software versions give the same run order. The language model never selects a seed.

Draft, not yet reviewed.

From your text (evidence)

Each value that is not a default has a quote from the request in the "From your text" column. The tool checks that the quote occurs in the request and contains the value. If the check fails, the card marks the value "Check this value", and the user confirms or edits it. Other labels are "default", "default (today's date)" for the seed, and "Edited by you".

Draft, not yet reviewed.

Agreement flags

In ensemble mode, up to four voters read the request: three language models (OpenAI, Anthropic, Google) and TypeSafe Jev, which answers only closed questions. The card shows "4 of 4 agree" when the voters agree, or each value with its count ("16 runs: 3; 32 runs: 1"). The tool leaves out a failed or late voter ("3 of 4 checked"); with fewer than two valid voters, the card says "Not cross-checked". Agreement is a signal, not a vote: the user selects a value when the voters disagree.

Draft, not yet reviewed.

Design notation

The notation $2^{k-p}$ describes a design with $k$ factors, $p$ generators and $2^{k-p}$ runs. The $k-p$ base factors form a full factorial, and each of the $p$ added factors comes from a generator. A full factorial has $p = 0$ and $2^k$ runs. For example, a $2^{7-3}$ design has 7 factors, 3 generators and 16 runs.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Chapter 5.

Guarantee statement

A minimum aberration (MA) design minimizes $A_3$ first, then $A_4$, and so on, among the designs of the same size. FrF2 selects each fractional design from its catalogue. Until Alan R. Vazquez reviews the guarantee table, the statement names only the catalogue entry, for example "Design from the FrF2 catalogue, entry 7-3.1." The statement makes no MA claim.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Chapter 5; Groemping (2014).

Resolution

The resolution is the length of the shortest word in the defining relation: $R = \min\{j \ge 1 : A_j > 0\}$. In resolution III, no main effect is aliased with another main effect, but some main effects are aliased with two-factor interactions (2FIs). In resolution IV, no main effect is aliased with another main effect or a 2FI, but some 2FIs are aliased with each other. In resolution V, no main effect or 2FI is aliased with another main effect or 2FI.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Chapter 5.

Word length pattern (WLP)

The word length pattern (WLP) is $(A_1, \ldots, A_k)$, and $A_j$ counts the words of length $j$ in the defining relation. The tool computes the WLP from the design matrix, not only from the catalogue. The WLP counts words of every length, because the definition of minimum aberration uses the full WLP. If all $A_j = 0$, the design is a full factorial.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Chapter 5; Xu and Wu (2001).

Generators

A generator sets the column of an added factor equal to the product of some base factor columns, for example $E = ABC$. The generators give the defining relation, for example $I = ABCE$. The design has one generator for each added factor, so a $2^{k-p}$ design has $p$ generators. The tool reads the generators from the FrF2 catalogue entry and shows them with the real factor names.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Chapter 5; Groemping (2014).

Clear two-factor interactions

A two-factor interaction (2FI) is clear if it is not aliased with any main effect or any other 2FI. The definition comes from FrF2 and does not take interactions of three or more factors into account. A full factorial has all $\binom{k}{2}$ 2FIs clear. The report lists the clear 2FIs with the real factor names and gives their number.

Draft, not yet reviewed. Source: Groemping (2014); Wu and Hamada (2021), Chapter 5.

Factors with all 2FIs clear

A factor has all 2FIs clear if every 2FI that contains the factor is clear. In the FrF2 design for 9 factors in 32 runs, only the factor in position 9 has this property. The factor order in step 2 sets which named factors have this property. In a design of resolution V or higher, and in a full factorial, every factor has this property.

Draft, not yet reviewed. Source: Groemping (2014).

Aliased main effects

Two effects are aliased when the design cannot separate them: their estimates come from the same column. The list shows the alias chain of each main effect that is aliased with a 2FI, with the real factor names in factor order. Only resolution III designs have main effects aliased with 2FIs. The list does not show interactions of three or more factors, because of the effect hierarchy principle.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Chapter 5; Groemping (2014).

Aliased 2FIs

The list shows the alias chains of the 2FIs that are aliased with other 2FIs, with the real factor names in factor order. The chains leave out interactions of three or more factors, because of the effect hierarchy principle. The factor order in step 2 sets which named 2FIs are aliased with each other. A full factorial has no aliasing, so it has no alias chains.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Chapter 5; Groemping (2014).

Run order

The run order is the order in which the experiment carries out the runs. By default, FrF2 sets a random run order with the seed. The standard order is the order of the full table before randomization. With randomization off, the run order equals the standard order.

Draft, not yet reviewed. Source: Groemping (2014).

FrF2 messages

FrF2 messages are the warnings and messages that FrF2 gave while it made the design. The tool shows them as text.

Draft, not yet reviewed.

Run sheet

The run sheet has one row for each run, in run order. Each row shows the standard order, the real levels and the coded levels. The standard order is the order of the full table before randomization. Large tables have pages.

Draft, not yet reviewed.

R code

The R code is the exact code that ran in the browser to make the design. It uses the pkg::fun() style, for example FrF2::FrF2(), and it has no library() call. With the same R and package versions, the code gives the same design and run order.

Draft, not yet reviewed.

Effect hierarchy

Low-order effects are more likely to be active than high-order effects. Main effects and two-factor interactions (2FIs) are usually more important than interactions of three or more factors. Thus, the evaluation of a two-level fractional factorial design usually does not look at interactions of three or more factors. The tool follows this principle, as FrF2 does.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Section 4.6; Li, Sudarsanam and Frey (2006).

Effect sparsity

Only a few effects (main effects or two-factor interactions) are active. An active effect has a larger absolute size than the noise.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Section 4.6; Box and Meyer (1986).

Effect heredity

This principle applies only to interactions. Strong heredity: an interaction is more likely to be active if the main effects of all its factors are active. Weak heredity: an interaction is more likely to be active if the main effect of at least one of its factors is active.

Draft, not yet reviewed. Source: Wu and Hamada (2021), Section 4.6; Hamada and Wu (1992).