Factorial design
An efficient design for experiments with two or more factors uses each possible combination of factor levels (called treatments) in the same number of experimental units. The repeat measurements for each treatment are called replicates and the design is called a factorial design.
The design on the previous page was an example of a factorial design for two factors but similar designs are also used for three or more factors.
Strength of asphaltic concrete
An experiment was conducted by a civil engineer to assess the effect of the compaction method on asphaltic concrete. Two types of aggregate were used in the experiment.
Compaction method | ||||||||
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Aggregate type | Static | Regular kneading |
Low kneading |
Very low kneading |
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Basalt |
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Silicious |
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In this experiment, three samples were tested at each combination of aggregate type and compaction type — i.e. there were 3 replicates — and the tensile strength (psi) was recorded.
Surface treatment and abrasion
Abrasion resistance in materials is often measured by rubbing specimens against a standard abrasive and recording either the decrease in thickness or the loss in weight. The table below describes results from a factorial experiment on coated fabrics to assess the effect of three factors.
Two types of filler were used in each of 3 proportions and half of the pieces of fabric were given a surface treatment before testing. The response measurement was the weight loss (mg) after 3000 revolutions of the testing machine.
No surface treatment | Surface treatment | ||||
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Percentage Filler |
Filler A | Filler B | Filler A | Filler B | |
25% | 527 561 |
456 377 |
475 466 |
296 325 |
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50% | 621 664 |
426 476 |
561 540 |
301 235 |
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75% | 724 743 |
460 426 |
626 682 |
322 304 |