Elementary Statistics and Computer Application

Terminologies and Types of factorial Experiment

• When two or more number of factors are investigated simultaneously in a single experiment such experiments are called as factorial experiments.

Terminologies

1. Factor: Factor refers to a set of related treatments. We may apply of different doses of nitrogen to a crop. Hence nitrogen irrespective of doses is a factor.
2. Levels of a factor: Different states or components making up a factor are known as the levels of that factor. eg different doses of nitrogen.

Types of factorial Experiment

• A factorial experiment is named based on the number of factors and levels of factors. For example, when there are 3 factors each at 2 levels the experiment is known as 2 X 2 X 2 or 23 factorial experiments.
• If there are 2 factors each at 3 levels then it is known as 3 X 3 or 32 factorial experiment.
• In general if there are n factors each with p levels then it is known as pn factorial experiment.
• For varying number of levels the arrangement is described by the product. For example, an experiment with 3 factors each at 2 levels, 3 levels and 4 levels respectively then it is known as 2 X 3 X 4 factorial experiment.
• If all the factors have the same number of levels the experiment is known as symmetrical factorial otherwise it is called as mixed factorial.
• Factors are represented by capital letters. Treatment combinations are usually by small letters.
• For example, if there are 2 varieties v0 and v1 and 2 dates of sowing d0 and d1 the treatment combinations will be
• vodo, v1do, v1do and v1d1.

Simple and Main Effects

• Simple effect of a factor is the difference between its responses for a fixed level of other factors.
• Main effect is defined as the average of the simple effects.
• Interaction is defined as the dependence of factors in their responses. Interaction is measured as the mean of the differences between simple effects.