Coursera students

If you are using this chapter with the Coursera MOOC (massive open online course), then we wish to welcome you and want to let you know that this book is generally part of a larger set of notes. The cross-references in this chapter will point you to other parts, where background knowledge is provided.

This chapter was written for engineers originally, but you will see the examples are very general and can be applied to any other systems.

You can safely skip over the section on Experiments with a single variable at two levels; that section is not covered in the MOOC. You can also initially skip the section on Why learning about systems is important, but make sure you come back and read it.

5.1. Design and analysis of experiments in context

This chapter will take a totally different approach to learning about and understanding systems in general, not only (chemical) engineering systems. The systems we could apply this to could be as straightforward as growing plants or perfecting your favourite recipe at home. Or they may be as complex as the entire production line in a large factory producing multiple products and shipping them to customers.

In order to learn about a system, we have to disturb it and change it. This is to ensure cause and effect. If we do not intentionally change the system, we are only guessing, or using our intuition. To disturb the system, we change several factors. When we make these changes, we say that we have “run an experiment”.

In this chapter we learn the best way to intentionally disturb the system to learn more about it. We will use some of the tools of least squares modelling, visualization and univariate statistics that were described in earlier chapters. Where necessary, we will refer back to those earlier sections.

5.2. Terminology

The area of designed experiments uses specific terminology.

Every experiment has these two components:

  1. An outcome: the result or the response from an experiment.

  2. One or more factors: a factor is the thing you can change to influence the outcome. Factors are also called variables.

An important aspect about the outcome is that it is always measurable–in some way. In other words, after you finish the experiment, you must have some measurement.

Let’s use an example of growing plants. The outcome of growing a plant might be the height of the plant, or the average width of the leaves, or the number of flowers on the plant. These are numeric measurements, also called quantitative measurements. Qualitative measurements are also possible. For example, perhaps the outcome is the colour of the flower: light red, red, or dark red. A qualitative outcome might also be a description of what happened, for example, pass or fail.

An experiment can have an objective, which combines an outcome and the need to adjust that outcome. For example, you may want to maximize the height of the plant. Most often you want to maximize or minimize the outcome as your objective. Sometimes, though, you want the outcome to be the same even though you are changing factors. For example, you might want to change a recipe for your favourite pastry to be gluten-free but keep the taste the same as the original recipe. Your outcome is taste, and your objective is “the same”.

Every experiment always has an outcome. Every experiment does not have to have an objective, but usually we have an objective in our mind.

Another term we will use is factors. In the plant example, you could have changed three factors:

  1. The amount of water that you give the plant each day

  2. The amount of fertilizer that you give the plant each week

  3. The type of soil you use, A or B

All experiments must have at least one factor that is changed. We distinguish between two types of factors: numeric factors and categorical factors.

Numeric factors are quantified by measuring, such as giving 15 mL of water or 30 mL of water to the plant each day. An important point about numerical variables is that there is some order to them. 15 mL of water is less than 30 mL or water. Another name for this type of factor is a quantitative factor.

Categorical factors usually take on a limited number of values. For example, soil type A or soil type B could be used to grow the plants. Categorical variables have no implicit ordering. You could have switched the names of soil A and soil B around. Categorical variables and qualitative variables can be used as synonyms.

Most categorical variables can be converted to continuous variables, with some careful thought. For example: no water vs some water (categorical) can be converted to 0 mL and 40 mL (now it is numeric). In the case of soil A vs soil B it might be that soil A contains a higher level of nutrients in total than soil B, so a numeric version of this factor could be measured as nutrient load.

If you were working in the area of marketing, you might try three different colours of background in your advertising poster. Those 3 colours are categorical variables in the context of the experiment.

Most experiments will have both numeric and categorical factors.

When we perform an experiment, we call it a run. If we perform eight experiments, we can say “there are eight runs” in the set of experiments.