Starting with simple experiments

Experiments such as those described on the previous page are often complex. There are three aspects to this complexity.

Structure of the experimental units
The experimental units often differ from each other and this structure can be used in the design and analysis of the experiment. For example, the experimental units may be grouped into blocks.
Complexity of the treatments used
The effects of several different factors of interest may be assessed in the same experiment. For example, the researcher may vary the variety of a crop, and the amount of fertiliser and irrigation used when the crop is grown.
Complexity of the design
Some treatments may be applied at the level of the individual experimental units (e.g. varieties of tomato) whereas others must be applied to groups of experimental units (e.g. irrigation).

We will build up to this complexity gradually, starting with relatively simple experiments.

Homogeneous experimental units and a single factor

The most fundamental aspect of all experiments is that we apply treatments to experimental units, so we initially concentrate on the treatment structure for experiments with simple experimental units; later chapters will consider other complications.

This chapter restricts attention to the simplest possible type of experiment in which:

This is more useful than it seems because the concepts and methods that are introduced in this chapter are the basis for design and analysis of more complex experiments in later chapters.

Quality of silk

A measure of the quality of reeled silk is its "denier" — a number expressing the weight of a fixed length. Among many factors that affect denier, the temperature of the bath in which the cocoons are cooked is likely to be important. An experiment was conducted with two different bath temperatures, 105°F and 110°F. The table below shows the deniers in milligrams of 20 samples of silk at 105°F and 18 samples at 110°F.

Temperature
of bath (°F)
Individual denier values
105 250
225
229
205
206
228
220
249
226
237
255
206
258
214
243
236
222
225
221
243
110 235
230
258
245
225
315
207
250
260
247
268
254
256
251
220
225
224
 
258
 
Experimental units
Individual cocoons. The researchers used cocoons of the same age and size.
Controlled variable (treatment)
Temperature of bath.
Response
Denier measurement

Hardwood and paper strength

A manufacturer of paper used for making grocery bags is interested in improving the tensile strength of the product. Product engineering thinks that tensile strength is a function of the hardwood concentration in the pulp and that the range of hardwood concentrations of practical interest is between 5 and 20%. A team of engineers responsible for the study decides to investigate four levels of hardwood concentration: 5%, 10%, 15% and 20%. They decide to make up six test specimens at each concentration level using a pilot plant. All 24 specimens are tested on a laboratory tensile tester in random order.

Hardwood Observations
Concentration (%)   1     2     3     4     5     6  
5
10
15
20
7
12
14
19
8
17
18
25
15
13
19
22
11
18
17
23
9
19
16
18
10
15
18
20
Experimental units
Individual paper sample. The settings of the pilot plant making the settings were the same for each sample (other than the hardwood concentration).
Controlled variable (treatment)
Hardwood percentage in paper
Response
Tensile strength

Effect of copper on aquatic animals

A study was designed to determine the effect of copper concentrations in water on the lifetime of aquatic animals. Daphnia magna, small aquatic animals, were selected for the study since they have relatively short lifetimes.

Fifteen daphnia, each to be kept in separate containers, were available for the study. Five daphnia were randomly chosen for each of three copper levels for the water: no copper, 10 micrograms/litre and 40 micrograms/litre.

The lifetime (days) of each daphnia was recorded. One container was contaminated, so only 14 of the 15 measurements could be analysed. The experimental results are shown below:

Copper concentration
  None     20 µg/l     40 µg/l  
60
90
74
82
58
74
50
65
68
40
58
25
30
42

Experimental units
Individual daphnia. As far as we can tell, all are identical.
Controlled variable (treatment)
Copper concentration. We control this for individual daphnia.
Response
Lifetime