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Table of Content

# Analysis of Variance

The analysis of variance is one of the powerful statistical tools for test of significance. The test of significance depends upon the t - distribution that is the difference between the two sample means. The main purpose of analysis of variance is to test the homogeneity of several means.

The analysis of variance is based on the some of the assumptions. They are discussed as follows. The first one is that the observations are independent in nature. The second one is that parent population from which observations are taken are considered to be normal. The third one is that various environmental effects are additive in nature.

The analysis of variance deals with seven subtopics they are - Null hypothesis and alternative hypothesis, variance, stochastic independence, degrees of freedom, sums of squares, f distribution and p value.

There are two types of analysis of variance they are one way classification and two way classification. Let us discuss them in detail.

First let us discuss about one way classification. Classification of the given statistics data according to the single criterion is known as one way classification and analysis of variance of the data is known as the one way analysis of variance. The main objective of analysis of variance is to examine is there any significantdifference between the inherent variability and class means. Analysis of variance is used in null and alternative hypothesis. The null hypothesis is defined as the testing of equality of population means. An alternative hypothesis is defined as checking at least two means are different. One way analysis of variance is also useful in testing hypothesis of more than two means. We can carry out equality of population means by the rejection region method.

In one way analysis of variance variances is used rather that the standard deviation to measure the variability of the given data. Let us consider there are n values that is x1, x2, x3 ………….. xn then the variance of the given data is given by the formula [sigma i=1 to n (xi – xbar)^2] / (n – 1) where xi represents the given observant at different values of i and xbar is the mean of the given observant and n is the no of observants.

The P value is one of the technique of the analysis of variance. P value theorem states that there is a significant difference between the given two groups when the value of the pH is less than 0.05 that is 5% of 100. Usually this value of the p is used as the cutoff value of the P.

In t test more than two tests are carried out then there is possibility of type I error. Type one error can be defined as rejecting the null hypothesis when it is correct.

Let us discuss about the two way analysis of variance. In two way analysis of variance the values of the response variable are affected by two factors.

The two way analysis variance in the observations are classified into three they are variants between treatment, variation between varieties and chance variation.

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