# All statistics for Create Plackett-Burman Design

Find definitions and interpretation guidance for every statistic that is provided with create Plackett-Burman.

## Factors

The number shows how many factors are in the design.

### Interpretation

The factors are the variables that you control in the experiment. Factors are also known as independent variables, explanatory variables, and predictor variables. Factors assume only a limited number of possible values, known as factor levels. Factors can have text or numeric levels. For numeric factors, you select specific levels for the experiment, even though many values for the factor are possible.

For example, you are studying factors that could affect plastic strength during the manufacturing process. You include factors for additive and temperature in the experiment. The additive is a categorical variable. Additive can be type A or type B. Temperature is a continuous variable. Because temperature is a factor, only two temperatures settings are in the experiment: 100°C and 200°C. If the design includes a center point, the numeric factor can have three levels (100°C, 150°C, and 200°C).

## Replicates

The number shows how many replicates are in the design.

### Interpretation

Replicates are multiple experimental runs with the same factor settings (levels). One replicate is equivalent to the base design, where you conduct each factor level combination once. With two replicates, you perform each factor level combination in the base design twice (in random order), and so on.

For example, if you have 3 factors with 2 levels each and you test all combinations of factor levels (full factorial design), the base design represents 1 replicate and has 8 runs (23). If you add 2 replicates, the design includes 3 replicates and has 24 runs.

When planning your experiment, consider the following when you decide whether to add replicates:
• If you are trying to create a prediction model, multiple replicates can increase the precision of your model.
• If you include replicates, you might be able to detect smaller effects or have greater power to detect an effect of fixed size.
• Screening designs (2-level factorial designs), which are used to reduce a large set of factors, usually don't include replicates.
• Your resources can dictate the number of replicates you can run. For example, if your experiment is extremely costly, you might be able to run the base design only one time.

For information on the difference between replicates and repeats, go to Replicates and repeats in designed experiments.

## Base runs

The number of base runs is the number of unique factor level combinations in the base design. The total number of runs is the number of base runs times the number of replicates.

### Interpretation

Use the number of base runs to identify the design. A run is an experimental condition or factor level combination at which responses are measured. Each run corresponds to a row in the worksheet and results in one or more response measurements, or observations. For example, you do a full factorial design with two factors, each with two levels. Your experiment has four runs:

The base runs are the initial design, or starting point, from which Minitab can build the final design. You can add replicates, which then add runs to the base number of runs. For example, you create an 8-factor definitive screening design. The base number of runs is 17. With 2 replicates, the total number of runs is 34.

Run Factor 1 Factor 2 Response
1 -1 -1 11
2 1 -1 12
3 -1 1 10
4 1 1 9
5 1 -1 8
6 1 1 12
7 -1 1 10
8 -1 -1 11
###### Note

When doing an experiment, the run order should be randomized.

Each run corresponds to a design point, and the entire set of runs is the design. Multiple executions of the same experimental conditions are considered separate runs and are called replicates.

## Total runs

The total number of runs is the number of base runs times the number of replicates. The total number of runs equals the number of rows in the worksheet.

### Interpretation

Use the number of total runs to verify that the experiment is the right size for your resources. A run is an experimental condition or factor level combination at which responses are measured. Usually, each run corresponds to a row in the worksheet and results in one or more response measurements, or observations. For example, you do a full factorial design with two factors, each with two levels and have two replicates. Your experiment has eight runs:
Run Factor 1 Factor 2 Response
1 -1 -1 11
2 1 -1 12
3 -1 1 10
4 1 1 9
5 1 -1 8
6 1 1 12
7 -1 1 10
8 -1 -1 11
###### Note

When doing an experiment, the run order should be randomized.

Each run corresponds to a design point, and the entire set of runs is the design. Multiple executions of the same experimental conditions are considered separate runs and are called replicates.

## Base blocks

The number shows how many blocks are in the design. If each replicate has the same number of blocks, then the base blocks and total blocks are equal.

### Interpretation

Blocks account for the differences that might occur between runs that are performed under different conditions. For example, an engineer designs an experiment to study welding and cannot collect all of the data on the same day. Weld quality is affected by several variables that change from day-to-day that the engineer cannot control, such as relative humidity. To account for these uncontrollable variables, the engineer groups the runs performed each day into separate blocks. The blocks account for the variation from the uncontrollable variables so that these effects are not confused with the effects of the factors the engineer wants to study.

## Total blocks

The number shows how many blocks are in the design. If each replicate has the same number of blocks, then the base blocks and total blocks are equal.

### Interpretation

Blocks account for the differences that might occur between runs that are performed under different conditions. For example, an engineer designs an experiment to study welding and cannot collect all of the data on the same day. Weld quality is affected by several variables that change from day-to-day that the engineer cannot control, such as relative humidity. To account for these uncontrollable variables, the engineer groups the runs performed each day into separate blocks. The blocks account for the variation from the uncontrollable variables so that these effects are not confused with the effects of the factors the engineer wants to study.

## Center points

The number shows how many center points are in the design.

### Interpretation

Use center points to detect curvature in the response and to estimate pure error.

Center points are runs where numeric factors are set midway between their low and high levels. For example, if a numeric factor has levels 100 and 200, the center point is set at 150. If you have text factors, then Minitab adds a center point at each level of the text factor and the midway level of the numeric factors. For example, your design includes a text factor with the levels A and B and a numeric factor with the levels 100 and 200. If you add 1 center point to the base design, Minitab adds 1 center point at levels A and 150 and 1 center point at levels B and 150. Thus, Minitab adds 2 center points for each center point that you specify.

If the design includes more than 1 block, then Minitab adds the number of center points that you specified to each block. For example, if you specify 2 center points per block and 2 blocks to your design, and the factors are numeric, Minitab adds 2 center points in block 1 and 2 center points in block 2.

Increasing the number of replicates does not add additional center points unless you also increase the number of blocks. For example, if you specify 3 center points, 2 replicates, and 1 block, then the design includes 3 center points.

## Design table

The design table shows the factor settings for each experimental run. Because the design table takes up less space than the worksheet, it can be useful for reports with limited space.

Letters represent the factors and follow the order that you used when you created the design. In each row, − indicates that the factor is at the low setting and + indicates that the factor is at the high setting. A 0 indicates that a numeric factor is midway between the low and high settings.

### Interpretation

Use the design table to see the factor settings for each run and the order of the runs in the design. In these results, the design table shows the experimental conditions or settings for each of the factors for the design points. The run order is random. For example, in the first run of the experiment, Factors B, E, and F are at the high setting. Factors A, C, D, and G are at the low setting. Factor H is at the middle setting. The design includes 2 center points, which are runs 12 and 34.

### Definitive Screening Design

Design Summary Factors: 8 Replicates: 2 Base runs: 17 Total runs: 34 Base blocks: 1 Total blocks: 1 Center points: 2
Design Table (randomized) Run Blk A B C D E F G H 1 1 0 + + + + + + + 2 1 0 0 0 0 0 0 0 0 3 1 + - - + 0 + - + 4 1 - - + - - + 0 + 5 1 + + - - - 0 + + 6 1 - + 0 + - - - + 7 1 + - + + - - + 0 8 1 + - 0 - + + + - 9 1 - - + - - + 0 + 10 1 + 0 + - + - - + 11 1 0 0 0 0 0 0 0 0 12 1 - + + - 0 - + - 13 1 0 - - - - - - - 14 1 - + + - 0 - + - 15 1 + - + + - - + 0 16 1 - - - 0 + - + + 17 1 0 - - - - - - - 18 1 - + 0 + - - - + 19 1 + + - + + - 0 - 20 1 + + + 0 - + - - 21 1 + - 0 - + + + - 22 1 - 0 - + - + + - 23 1 - - + + + 0 - - 24 1 + + - - - 0 + + 25 1 + - - + 0 + - + 26 1 + 0 + - + - - + 27 1 - + - - + + - 0 28 1 + + - + + - 0 - 29 1 - - + + + 0 - - 30 1 - 0 - + - + + - 31 1 0 + + + + + + + 32 1 - + - - + + - 0 33 1 - - - 0 + - + + 34 1 + + + 0 - + - -
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