One-way ANOVA

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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.

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

If the group means are more spread out compared to how spread out the individuals are, then conceptually, the means are significantly different from each other.

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

[edit] 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).

ANOVA is a relatively robust procedure with respect to violations of the normality assumption (Kirk, 1995) If data are ordinal, a non-parametric alternative to this test should be used - Kruskal-Wallis one-way analysis of variance.