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.

Rice yield and insecticides

Scientists investigating chemical control of brown planthoppers and stem borers in rice conducted an experiment to compare the effectiveness of six different foliar and granular insecticides. Twenty eight plots of land were used and the six different insecticides and a control treatment were each randomly applied to four of the plots. The table below shows the resulting yields of rice.

  Grain yield, kg/ha
Dol-Mix (1 kg)    2,537       2,069       2,104       1,797   
Dol-Mix (2 kg)
3,366 2,591 2,211 2,544
DDT + γ-BHC 2,536 2,459 2,827 2,385
Azodrin
2,387 2,453 1,556 2,116
Dimecron-Boom
1,997 1,679 1,649 1,859
Dimecron-Knap 1,796 1,704 1,904 1,320
Control
1,401 1,516 1,270 1,077
Experimental units
Individual plots of land. The 28 plots used were not adjacent (to ensure that plots were not affected by insects in neighbouring plots) but were as similar as possible.
Controlled variable (treatment)
Insecticide used. Only one insecticide (or the control treatment) was used in any plot.
Response
Yield of rice.

Lamb weight gain and hormones

An experiment was conducted to determine the effects of three different hormones, each at a single dose, on the weight gained by lambs. Sixteen lambs were used with four randomly allocated to each of the three hormone treatments and the remaining raised without any hormone added. The table below shows the weight gains of the lambs (pounds per animal per day).

      Weight gain of lambs    
Control 47 52 62 51
 Hormone A  54 65 75 59
Hormone B 50 54 67 57
Hormone C 57 53 69 57
Experimental units
Individual lambs. There were no known differences between the lambs at the start of the experiment.
Controlled variable (treatment)
Hormone used. Individual lambs were given one of the four treatments.
Response
Weight gain.

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