A few examples of completely randomised experiments are provided below

Abrasion resistance of fabrics

In the manufacture of clothing, a wear-testing machine is used to measure the resistance to abrasion of different fabrics by measuring the weight loss after a fixed number of abrasion cycles. An experiment was conducted to compare four competing fabrics and the results are shown below:

Fabric
A B C D
  1.93  
2.38
2.20
2.25
  2.55  
2.72
2.75
2.70
  2.24  
2.68
2.31
2.28
  2.33  
2.40
2.28
2.25
Experimental units
Areas of fabric, all of the same size
Controlled variable
Fabric type (categorical)
Response
Abrasion loss
Randomisation
The 16 fabric samples were tested in random order.

If the samples of fabric A had been tested first, the testing machine could have altered as it warmed up, making the abrasion loss for fabric A seem lower than it should have been.

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
Randomisation
The 24 specimens were tested in random order.

If the samples had been tested in order, starting with the six with 5% hardwood, the operator or testing machine could have altered during the course of the experiment, biasing the results.

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
Randomisation
The 20 cocoons to be cooked at 105°F and the 18 cocoons to be cooked at 110°F were randomly selected.

If the researcher had subjectively picked 20 out of the 38 cocoons for the 105°F bath, larger ones might have been subconsciously picked, biasing the results.