Starting with simple experiments
Experiments such as those described on the previous page are often complex. There are three aspects to this complexity.
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 |
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 |
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 |