Introduction To Analysis Of Variance

Anova means Analysis Of variance

Anova means Analysis Of variance. What is Anova? Anova describes about variation in the data it splits total variation in the data into different parts in which some are controllable by experimenter and some are uncontrollable by experimenter.

Orientation of experimenter is to reduce controllable variations however this is not comes under Anova. Main purpose of Anova is to figure out variation due to a specific cause (Which is controllable) if this variation is large with respect to the variation due to an unexpected cause (Which is uncontrollable) then we can conclude that there is a significance difference in the data due to that specific cause.

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In Anova we have different types those are, One Way Anova, Two Way Anova, Latin Square Design. If the experimental unit is affected by only one cause in such cases we use One Way Anova. In this case specific cause is called as Treatment and unexpected cause is called as Random Error. For example if we want to test the hypothesis that is there is any difference among the tyres manufactured by different companies? Under null hypothesis we assume that there is no difference among the tyres manufactured by different companies. Under alternative hypothesis we assume that there is a difference among the tyres manufactured by different companies. In One Way Anova we have to split the total variation into two parts. The variation which is controllable is the variation due to different tyres and the variation which is uncontrollable is the variation due to Random Error (like damage of road, sudden accident) which is unexpected.

Now for the experimenter, the interest is to find out the variation due to different tyres and compare it with random error. If treatments variation is much larger than variation due to Random Error then we can say that there is a variation due to different treatments (Different tyres manufactured by different companies). We use F-statistic to compare the variation due to treatments and variation due to random error. The ratio of these two variations follows F distribution so we can compare this ration value with F distribution table value. Anova works based on some assumptions. Anova Assumptions are Normality, Independence and Homogeneity of variances. Assumptions of Anova are the most important key points for Anova theory. Normality assumption is valid because we are using F distribution to compare the ratio of two variations. This ratio follows F distribution if and only if the variations follow Chi-Square distribution if and only if observations follow normal distribution. We can check this normality assumption with some statistical tools like kolomogorov sminrov test, Chi-Square test for goodness of fit. We assume random errors are independent because these are not depends on any particular factors. If Homogeneity of variance is fails then application of Anova is not possible.

by: Omkar Nayak

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