# INTRODUCTION TO ANALYSIS OF VARIANCE

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Analysis of variance is a statistical technique for partitioning the total variation of our data into useful components, which provide means of measuring different sources of variation among the means of several populations.

Contents

### Basic Concepts In Analysis of Variance

1. Factors: These are the independent variables whose effect on the response is of interest to the analyst.

It is also described as the qualities or properties according to which data are classified. e.g machines, shift, day, gender, etc.

2. Levels of a Factor: These refer to the factors that are utilized in the experiment.

It is generally used to describe classification. e.g Gender-male and female, Machine-No. 1, No. 2, No. 3, shift-early, middle, late, or perhaps day and night.

3. Experimental Unit: This is a substance or variable on which the test is performed.

They constitute the distinct elements on which treatments are applied to generate responses. e.g Gender, CGPA of students, etc.

4. Replication: This is the repetition of experiments on a level of a factor so as to increase the precision of the estimate and to obtain an estimate of the sampling error.
5. Randomization: This is a procedure that is employed in the assignment of experimental treatments to experimental units so as to eliminate bias.

It can be done through any random process such as the tossing of coins, the use of a table of random numbers, etc.

### One Way Analysis of Variance

This is a one-factor experiment with no blocking and it provides the simplest analysis in experimental design.

it provides the simplest analysis of completely randomized design (CRD) or zero way heterogeneity design.

In this design, the treatments are allotted to the experimental units at random.

1.  The design allows flexibility. Any number of treatments and replicate may be used.
2. The statistical analysis is easy even if replicates are unequal or if the experimental errors differ from treatment to treatment.
3. The method of analysis remains simple when the results from some units or from whole treatment are missing or are rejected.

### Limitations

1. When the experimental material is homogenous.
2. Where an appreciable fraction of all the units is likely to be destroyed or fail to respond.
3. In small experiments where increased accuracy from alternative design does not outweigh the loss of error degrees of freedom.
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