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Dataplot: Tabulated Designs

Introduction The Dataplot distribution comes with a number of data files that contain many common designs.

The links for these file are to the NIST ftp site. If you have downloaded and installed Dataplot, local copies of the files are available in the "DEX" subdirectory of the Dataplot auxillary directory. For Windows, the default auxillary directory is "C:\DATAPLOT". For Unix/Linux, the default auxillary directory is "/usr/local/lib/dataplot".

LIST Command You may view any of these files within Dataplot by entering the command
    LIST <file-name>
where <file-name> is one of the files listed below.

The header lines in the specified will, in most cases, contain the instructions for reading the file into Dataplot.

Specifying the Location of the Dataplot Auxillary Directory If Dataplot cannot find the requested file when you enter a READ or LIST command, this indicates that the Dataplot auxillary directory is not installed in the expected location on your local platform. Contact your local system installer to determine the location of the Dataplot auxillary directory on your local platform.

If the Dataplot auxillary directory is not in the default location, you can define the environment variable DATAPLO$ (on Windows and Unix/Linux platforms) to tell Dataplot where the Dataplot auxillary directory is actually located. The Dataplot installation notes contain instructions for defining this variable for Windows and Unix/Linux platforms. For other platforms, contact your local system installer for guidance.

Categories for the Dataplot Design Files The designs are organized by problem/design category.
  1. Comparative Designs

  2. Screening Designs

  3. Regression Designs

  4. Optimization Designs

  5. Mixture Designs


Comparative Designs
Completely Randomized Designs Because of their intrinsic simplicity (only one factor and no blocking factors) and their ease of construction, there is no formal index of Completely Randomized Designs.

All completely randomized designs are defined by three specifications:

    k = number of factors (= one for completely randomized designs)
    l1 = number of levels
    r = number of replications
Thus the total sample size (number of runs) is
    n = k x l1 x r
Balance dictates that the number of replications be the same at each level of the factor (this will maximize the sensitivity of subsequent t (or F) testing).

We present two simple examples of completely randomized designs:

  1. Example 1:

    The most trivial Completely Randomized Design would consist off the following:

      k = one factor (X1)
      l = two levels of that single factor
      r = one replications per level
      n = two levels * 1 replication per level
         = two runs

    This results in the following design:

      X1

      1
      2
    Such a design is not usually run because it has no replication and therefore no measure of "within" variability. It is a priori impossible to determine if the two levels have a statistically significant effect on the response unless we have a handle on the nature variation of the data.

  2. Example 2:

    A more typical example of a completely randomized design is the following:

      k = one factor (X1)
      l = four levels of that single factor
      r = three replications per level
      n = four levels * three replications per level
         = 12 runs

    This results in the following design:

      X1

      1
      1
      1
      2
      2
      2
      3
      3
      3
      4
      4
      4
A detailed discussion of completely randomized designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Randomized Block Designs The following table shows the layout for randomized block designs.
    Name of Design Number of Factors
    k
    Number of Runs
    n
    2-factor RBD 2 l1 * l2
    3-factor RBD 3 l1 * l2 * l3
    4-factor RBD 4 l1 * l2 * l3 * l4
    ... ... ...
    k-factor RBD k l1 * l2 * l3 * ... lk
where
    l2 = number of levels (settings) of factor 2
    l3 = number of levels (settings) of factor 3
    l4 = number of levels (settings) of factor 4
    lk = number of levels (settings) of factor k
The following is an example of a Randomized Block Design consisting of
    k = two factors (one primary factor X1 and one blocking factor X2)
    l1 = four levels of factor X1
    l2 = three levels of factor X2
    r = one replication per cell
    n = l1 * l2 = 4 * 3 = 12 runs
This results in the following design:
    X1 X2

    1 1
    1 2
    1 3
    1 4
    2 1
    2 2
    2 3
    2 4
    3 1
    3 2
    3 3
    3 4
A detailed discussion of randomized block designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Latin Square (and Related) Designs The following Latin Square, and related, designs are available: Additional discussion of Latin square, Graeco-Latin square, and Hyper-Graeco-Latin square designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Screening Designs
Full Factorial Designs The following lists the full factorial designs that are available as built-in data files in Dataplot. Additional discussion of full factorial designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Fractional Factorial Designs The following table lists the fractional factorial designs that are available as built-in data files in Dataplot. The diagonal elements of the table are full factorial designs that are given above.

2-Level Full and Fractional Factorial Designs
n\k 2 3 4 5 6 7 8 9 10 11
4 2**2 2**(3-1)
III








8
2**3 2**(4-1)
IV
2**(5-2)
III
2**(6-3)
III
2**(7-4)
III




16

2**4 2**(5-1)
V
2**(6-2)
IV
2**(7-3)
IV
2**(8-4)
IV

font>


32


2**5 2**(6-1)
VI
2**(7-2)
IV
2**(8-3)
IV
2**(9-4)
IV
2**(10-5)
IV
2**(11-6)
IV
64



2**6 2**(7-1)
VII
2**(8-2)
V
2**(9-3)
IV
2**(10-4)
IV
2**(11-5)
IV
128




2**7 2**(8-1)
VIII
2**(9-2)
2**(10-3)
V
2**(11-4)
V

Additional discussion of fractional factorial designs is contained in the NIST/SEMATECH e-Handbook of Statistics.

Dataplot  / Dataplot Designs ]

Taguchi Designs The following table lists the Taguchi designs that are available as built-in data files in Dataplot.

Note: The L36B design is temporarily unavailable.

Taguchi Designs
n\k 3 4 5 6 7 10 11 12 13 15 21 22 26 27 31 40 63
4 L4
2
















8 . . . . L8
2












9 . L9
3















12 . . . . . . L12
2










16 . . L16b
4
. . . . . . L16
2







18 . . . . L18
3,6












25 . . . L25
5













27 . . . . . . . . L27
3,2








32 . . . . . L32b
4,2
. . . . . . . . L32
2


36 . . . . . . . . . . . L36
3
. L36b
3,2



50 . . . . . . . L50
5,2









54 . . . . . . . . . . . . L54
3,2




64 . . . . . . . . . . L64b
2
. . . . . L64
4
81 . . . . . . . . . . . . . . . L81
3

Additional discussion of Taguchi designs is contained in the NIST/SEMATECH e-Handbook of Statistics.

Dataplot  / Dataplot Designs ]

Plackett-
Burman Designs
Dataplot contains built-in data files for the following Plackett-Burman designs: Additional discussion of Plackett-Burman designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Regression Designs
Principles in Choosing Design Points Regression designs do not have explicit designs. Designs in the regression context refers to how one selects the values for the points of the independent variables.

Although there are not specific designs, there are several principles to use in selecting these points.

  1. The points should be selected to minimize the variance of the parameter estimates.

  2. More points should be selected where the variability in the dependent variable is the greatest.
Additional discussion of regression designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Optimization Designs
Some Common Optimization Designs Dataplot contains data files for the following optimization (also referred to as response surface designs): Additional discussion of response surface designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Mixture Designs
Simplex-
Lattice Designs
Simplex-lattice designs are defined by the following parameters:
  1. the number of factors = k
  2. the degree = d
  3. the number of runs = n
Dataplot contains data files for the following simplex-lattice mixture designs: Additional discussion of simplex-lattice designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Simplex-
Centroid Designs
Dataplot contains data files for the following simplex-centroid mixture designs: Additional discussion of simplex-centroid designs is contained in the NIST/SEMATECH e-Handbook of Statistics.
Dataplot  / Dataplot Designs ]

Simplex-
Centroid-
Augmented Designs
Dataplot does not currently provide any built-in simplex-centroid-augmented designs.
Dataplot  / Dataplot Designs ]

Snee-
Marquardt-
Designs
Dataplot does not currently provide any built-in Snee-Marquardt designs.
Dataplot  / Dataplot Designs ]

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Date created: 6/5/2001
Last updated: 10/30/2013

Please email comments on this WWW page to alan.heckert@nist.gov.