# Analysis of Variance

ANALYSIS OF VARIANCE 3

Analysisof Variance

Analysisof Variance is an arithmetical method used to examine differencesbetween two or more means. A mean is the average in a range ofnumbers (Freedman,Pisani and Purves 2007). In simple terms it can be referred to as ananalysis of means but analysis of variance is more suitable sinceconclusions about means can be drawn by analyzing variance (Freedman,Pisani and Purves 2007). Therefore, the main reason for conducting ananalysis of variance is to find out if there is any differencebetween groups on some variable. For instance, let us use anexperiment to find out the relationship between people’s religionand what they view as the perfect family size. In such an experiment,the dependent and the independent variables is the religion andvarious religious groups represented by the chosen sample. In thisexample, let us say we recruit 15 Catholics, 15 Protestants and 15Jewish. Owing to the fact that, there exist various levels ofreligion, ANOVA can be carried out. After the interview, data ofevery category of religion is very well recorded as well as meanrecorded (Freedman,Pisani and Purves 2007). In this experiment let us take the resultsas: average number recorded by Catholics group is 4, the protestantgroup as 3 and the Jewish group as 2.

Atfirst sight, it seems that there is a definite difference betweenthese three groups in their opinions about the perfect family size.However, we must remember that this could be due to chance and thesemeans could change if we recruited 15 different Catholics, 15different Protestants and 15 different Jewish. Therefore, an analysisof variance is highly important since it will control suchuncertainties and determine statistically, if the difference isvalid. An analysis of variance will determine whether the differencesbetween the three groups are statistically noteworthy and hencevalidate whether religious affiliation influence people’s opinionson the ideal family size.

Reference

Freedmam,D. A.,Pisani, R. &amp Purves, R. (2007).Statistics,4th edition. W.W. Norton &amp Company