One-way ANOVA

In statistics, one-way analysis of variance (abbreviated one-way ANOVA) is a technique used to compare means of two or more samples (using the F distribution). This technique can be used only for numerical data.  A one-way ANOVA has just one independent variable and one dependent variable.

The ANOVA produces an F statistic, the ratio of the variance among the means to the variance within the samples.

• Essentially, the ratio of variance is a comparison of the variance amongst the different groups to the variance amongst all the individuals within those groups. A higher ratio implies significant differences between the groups.

The degrees of freedom for the numerator is I-1, where I is the number of groups (means) The degrees of freedom for the denominator is N - I, where N is the total of all the sample sizes

Assumptions

The results of a one-way ANOVA can be considered reliable as long as the following assumptions are met:

• Response variable must be normally distributed (or approximately normally distributed).
• Samples are independent.
• Variances of populations are equal.
• The sample is a Simple Random Sample (SRS).