All statistics for Create General Full Factorial Design

Find definitions and interpretation guidance for every statistic that is provided with create general full factorial.

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.

Number of levels

The list shows the number of levels of each factor that is in the design. For example, you are studying factors that could affect plastic strength during the manufacturing process. You decide to include Additive and Temperature in your experiment. The additive is a categorical variable. It can only be type A or type B. Conversely, temperature is a continuous variable, but here it is a factor because only three temperatures settings of 100C, 150C and 200C are tested in the experiment. The number of levels for Additive is 2 and the number of levels for Temperature is 3. The number of levels line shows the numbers in the order of the factors: 2, 3.

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, numbers represent the factor levels.

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 that the design includes 27 runs, which are in 1 block. The runs are randomized. In the first run, factor A is set at level 1 and factors B and C are set at level 3.

Design Table (randomized) Run Blk A B C 1 1 1 3 3 2 1 1 1 1 3 1 2 2 2 4 1 1 2 3 5 1 2 3 3 6 1 3 3 2 7 1 3 1 3 8 1 3 3 3 9 1 3 1 2 10 1 2 2 3 11 1 2 1 3 12 1 1 3 1 13 1 1 2 2 14 1 2 3 1 15 1 1 1 2 16 1 3 3 1 17 1 3 2 1 18 1 1 1 3 19 1 1 3 2 20 1 2 1 2 21 1 3 2 3 22 1 2 1 1 23 1 2 3 2 24 1 2 2 1 25 1 3 2 2 26 1 1 2 1 27 1 3 1 1
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