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 |
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 |
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 |