In general, an experiment is realized to search for information about a certain object. During experiment, through observation, measurement, . . . we obtain primary information, sometime known as raw one. From analysis these raw data, we can get deeper knowledge about object: its properties, relations between properties, . . therefore we can exploit it better. In order to obtain knowledge effectively, we have to design experiment: choosing right variables, well organizing procedure of experiment. After experiment, we have to analyze data by scientific methods to draw correctly useful information.

A general schema of an experiment in the field of science and technology is presented in Fig. 1.

Fig. 1 General schema of an experiment

The concepts in this schema will be explained below.

 

In an experiment, there are three main types of variables:

• Factors : these are variables that we would like to know their effects on the result of experiment. The values of factors can be manipulated and they are independent. For this reason, they are also known as independent variables. Some examples of factor are pH, temperature, additive content.
• Responses : values of responses depend on that of corresponding factors and we can change it only via changing values of factors. Responses are also denoted as dependent variables. Stiffness of product, preservation time are some examples of response.
• Noises : are special type of factor that we can not control or can not determine it exactly, quantitatively or qualitatively. Source of raw materials, laboratory conditions, skill of experimenters are some examples of noises.

Experiment is carried out with some values of factor, each value is known as a level. For ordinal, interval and ratio factor, there are high level, low level and, in many cases, center level.

In order to facilitate the data analysis and/or presentation, the values of factors can be coded. In the most frequently method of coding:

• high level is coded as + 1,
• low level is coded as - 1,
• center level is coded as 0.

 

Each treatment corresponds to one condition of the experiment. It means that each treatment corresponds to one level of factor or one combination of levels of factors.

Each treatment can be realized once (one run) or with replication (several runs). If the numbers of replicate of all the treatments are the same, experiment is balanced, otherwise it is unbalanced.

 

Matrix of factors is a table consisting of `c` columns corresponding to `c` factors, and `r` rows corresponding to `r` treatments (in cases of without replication) or `r` runs (in general cases). The values of factors can be coded or not. For clarity, the order of runs may be sorted in certain ways. Each column of this table can be considered as a vector.

Example 1

An experiment is realized with 3 levels of factor `X_1` and 4 levels of factor `X_2`. There is a combination of all the levels of two factor together. There are 12 treatments. If there is not replication, there are 12 runs.

3 levels of `X_1` are coded as +1, 0, and –1 ; 4 levels of `X_2` are coded as +1, 0,333, –0,333 and –1.

Matrix of coded factors of this experiment is presented on Table 1.

Table 1 Matrix of coded factors of experiment

Treatment/Run	`X_1`	`X_2`
1	- 1	- 1
2	- 1	- 0,3333
3	-1	0,3333
4	- 1	+ 1
5	0	- 1
6	0	- 0,3333
7	0	0,3333
8	0	1
9	1	- 1
10	1	- 0,3333
11	1	0,3333
12	1	1

The columns `X_1` and `X_2` are also denoted as vectors. Two vectors are orthogonal if:

`sum_i x_(1i)\ x_(2i)=0`(1)

If we add to this matrix columns corresponding to responses, we got the matrix of experiment.

 

In order to draw confident and precise conclusions, the experiments have to conform with these basic principles:

• Replication : in order to estimate and reduce errors.
• Randomization : the order of runs and/or treatments must be random. So we can averagely distribute the effect of uncontrollable factors to all the runs and/or treatments.

We can use other ways to increase the precision and confidence of experiments:

• Blocking
• Using of control treatments.

These methods are used to reduce random error to the minimum.

 

This is the simplest kind of experiment used to study the effect of one factor to responses. Experiment is realized with some levels of factor and we obtains the corresponding values for responses. After data analysis, we can evaluate this effect. Two most frequently used methods to analyze data are analysis of variance (ANOVA) and regression.