# Analysis Of Variance ANOVA

Analysis of variance ANOVA is a statistical technique used to compare the distributions around the means of a feature or an attribute within and across groups. ### Analysis Of Variance ANOVA Definition

Analysis of variance ANOVA is a statistical technique used to compare the distributions around the means of a feature or an attribute within and across groups. It is a collection of steps that calculate variance in a data set, assign variance to various sources, and calculate the probability that the variance estimates differed by chance under the null hypothesis. Mean is the statistical measure of central tendency.

### Explanation

The Analysis Of Variance ANOVA approach is used to determine if differences in the means of several groups are likely to present in the population from which those groups are selected.

Analysis Of Variance ANOVA is a statistical method for comparing more than two sample means. It is among the more straightforward methods that fall under the general heading of “generic linear model.” A sample is first sorted into groups based on the values of one independent variable, often a discrete variable with a limited number of categories. The means of the dependent variable, a second variable, are computed within each group.

The variance of the individual instances within each group around that group’s mean is determined, and then the differences between the means for the various groups are contrasted.

The likelihood that the means are significantly different increases with the size of the mean difference (relative to the variation around each mean), making it less likely that one would commit a Type I (alpha) error by asserting that the groups have different means in the population from whom the sample is gathered.

### Analysis Of Variance ANOVA Example

Example 1

For instance, we could be interested in learning how socioeconomic class influences life expectancy. We would gather data on the sample’s social class and age at death, split it into six socioeconomic classes, and then compare the degree of variance within each class to the difference between the six classes. We will infer that social class significantly correlates with life expectancy if the variance within each class is noticeably less than the variation between them.

Example 2

By separating the variability of the observations into two types, ANOVA provides a way to determine whether the differences between the means are statistically significant. An example might be four groups of people with different educational qualifications for whom the mean wage level has been calculated. The variance within each group in the sample is one sort of variability, referred to as “within group” variability. The second category is “between groups” variability, which is the variance between group means. Likely, the population’s averages are unequal if this variability is high compared to the “within group” variability.

The following assumptions underlie the use of analysis of variance: (a) that each group is a representative sample drawn at random from a population that is considered normal; and (b) that the variances of the groups within the population are equal. 