# Basic Principles of Experimental Design

The basic principles of experimental design are (i) Randomization, (ii) Replication, and (iii) Local Control.

1. Randomization

Randomization is the cornerstone underlying the use of statistical methods in experimental designs.  Randomization is the random process of assigning treatments to the experimental units. The random process implies that every possible allotment of treatments has the same probability. For example, if the number of treatments = 3 (say, A, B, and C) and replication = r = 4, then the number of elements = t * r = 3 * 4 = 12 = n. Replication means that each treatment will appear 4 times as r = 4. Let the design is

 A C B C C B A B A C B A

Note from the design elements 1, 7, 9, and 12 are reserved for Treatment A, elements 3, 6, 8, and 11 are reserved for Treatment B, and elements 2, 4, 5, and 10 are reserved for Treatment C. P(A)= 4/12, P(B)= 4/12, and P(C)=4/12, meaning that Treatment A, B, and C have equal chances of its selection.

2. Replication

By replication, we mean the repetition of the basic experiments. For example, If we need to compare the grain yield of two varieties of wheat then each variety is applied to more than one experimental unit. The number of times these are applied to experimental units is called their number of replication. It has two important properties:

• It allows the experimenter to obtain an estimate of the experimental error.
• More replication would provide the increased precision by reducing the standard error (SE) of mean as $s_{\overline{y}}=\tfrac{s}{\sqrt{r}}$, where $s$ is sample standard deviation and $r$ is a number of replications. Note that increase in $r$ value $s_{\overline{y}}$ (standard error of $\overline{y}$).
3. Local Control

It has been observed that all extraneous source of variation is not removed by randomization and replication, i.e. unable to control the extraneous source of variation.
Thus we need to a refinement in the experimental technique. In other words, we need to choose a design in such a way that all extraneous source of variation is brought under control. For this purpose we make use of local control, a term referring to the amount of (i) balancing, (ii) blocking, and (iii) grouping of experimental units.

Balancing: Balancing means that the treatment should be assigned to the experimental units in such a way that the result is a balanced arrangement of treatment.

Blocking: Blocking means that the like experimental units should be collected together to far relatively homogeneous groups. A block is also called a replicate.

The main objective/ purpose of local control is to increase the efficiency of experimental design by decreasing experimental error.

This is all about the Basic Principles of the Experimental Design. Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

### 6 Responses

1. SILKY says:

Explain the historical perspective of Experimental principle.

• Muhammad Imdad Ullah says:

Thank you for visiting the site. I need time to post about the historical perspective of experimental principles/ Experimental Design.

2. afifa says:

Very nice plz provide the answer for the questions below .
What are the source of researchproblem.?
(Notes )

• Muhammad Imdadullah says:

don’t have such notes. However, can be searched from different net sources.

• Gerald says:

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• Gerald's friend says:

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