Purpose

Experiments are conducted to discover how certain variables that can be controlled by the experimenter affect the values of one or more 'response' variables.

It is important that the objectives are clearly defined in terms of response and controlled variables before going further in the design of an experiment.

Experimental units

Experiments usually involve discrete 'experimental units'. Depending on the type of experiment, the experimental units could be:

The experimental units that will be used in an experiment are first selected. One or more response measurements will be made from each unit during the course of the experiment.

Controlled variables

In an experiment, the researcher is able to control the values of one or more variables that can potentially influence what happens to the unit during the course of the experiment. Simple experiments only have a single controlled variable but many experiments involve several variables that are controlled.

The controlled variables in an experiment are determined by its objectives and are called factors. They may be:

For each individual factor, its distinct values are called its levels.

In some experiments, the 'control' of an explanatory variable may arise only through the choice of experimental units. For example, in an experiment involving two production lines, it may be decided to use 10 items from each production line, in which case the production line would be treated as a categorical explanatory variable.

Design

The combination of levels for all factors that are used with any experimental unit are collectively called a treatment and we say that the experimenter can control which treatment to apply to each experimental unit.

In a simple experiment with a single controlled factor, the treatments are simply the factor levels. However in an experiment that controls the temperature, pressure and duration of a chemical reaction, each possible combination of levels of these three factors is a separate treatment.

The experimental design is the method used to decide which treatment to apply to each experimental unit.

Good experimental design can reduce the number of experimental units that are required and can therefore save a considerable amount of time and money. It can also result in better understanding of the process underlying the data.

Response variable

One or more response measurements are made from each experimental unit, the measurements being dictated by the objectives of the experiment. The experiment aims to discover whether each factor affects the responses and, if so, by how much.

Although advanced methods exist to simultaneously analyse several response measurements, it is usually sufficient to examine the effects of the factors on each response separately.

Strength of Portland cement

An experiment was conducted to determine how four different mixing techniques affected the strength of Portland cement. Four slabs of cement were manufactured using each mixing method and their tensile strength was measured.

Mixing technique Tensile Strength (lb/in2)
1
2
3
4
  3129  
3200
2800
2600
  3000  
3300
2900
2700
  2865  
2975
2985
2600
  2890  
3150
3050
2765

Experimental units
Concrete slab
Controlled variable
Mixing technique (categorical)
Response
Tensile strength
Design
Four slabs were manufactured and tested using each mixing technique in random order.

Catalyst surface area

Researchers conducted an experiment to investigate how the mole contents of cobalt and the calcination temperature affected the surface area of an ison-cobalt hydroxide catalyst. Four cobalt levels and five temperatures were used in the experiment and one sample of catalyst was created and tested at each of the 20 combinations of a cobalt level and temperature. The table below shows the results of the experiment.

Temperature (°F)
  Cobalt (mole)   200 300 400 500 600
0.6   90.6     82.7     58.7     43.2     25.0  
1.0 127.1 112.3 19.6 17.8 9.1
2.6 53.1 52.0 43.4 42.4 31.6
3.0 40.9 37.9 27.5 27.3 19.0

Experimental units
Samples of catalyst
Controlled variables
Temperature and cobalt content (both numerical)
Response
Surface area
Design
All combinations of the factor levels (treatments) were used once and manufacture and testing of the 20 samples was done in random order.

Torque of locknuts

A manufacturer was finding unwanted differences in the torque values of a locknut that it made. Torque is the work (i.e. force × distance) required to tighten the nut. An experiment was therefore conducted to determine what factors affected the torque values. The type of plating process was isolated as the most probably factor to impact torque. Researchers also wanted to assess the difference in torque between threading the locknut onto a bolt or a mandrel (like a bolt but harder). Twenty locknuts were manufactured with different types of plating: cadmium and wax (C&W), no plating (HT) and phosphate and oil (P&O); ten were tested on bolts and ten on mandrels. A manual torque wrench was used to determine the torque of each.

Plating type
     C&W HT P&O
Bolt   20   16  
16   19
17   14
18   15
15   24
  26   30  
40   26
28   38
38   45
38   38
  25   45  
40   49
30   33
17   30
16   20
Mandrel   24   23  
18   14
17   18
17   12
15   11
  32   28  
22   27
30   28
35   30
32   30
  10   14  
13   11
17   14
16   15
15   16

Experimental units
Individual locknuts
Controlled variables
Plating type and bolt type (both categorical)
Response
Torque to tighten
Design
Ten locknuts were manufactured and tested for each combination of plating type and bolt. The 60 treatments were tested in random order.