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
Aggregate type Static Regular
kneading
Low
kneading
Very low
kneading
Basalt
68
63
65
126
128
133
93
101
98
56
59
57
Silicious
71
66
66
107
110
116
63
60
59
40
41
44

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
Percentage
Filler
Filler A Filler B   Filler A Filler B
25% 527
561
456
377
  475
466
296
325
50% 621
664
426
476
  561
540
301
235
75% 724
743
460
426
  626
682
322
304