<P> In statistics, one - way analysis of variance (abbreviated one - way ANOVA) is a technique that can be used to compare means of two or more samples (using the F distribution). This technique can be used only for numerical response data, the "Y", usually one variable, and numerical or (usually) categorical input data, the "X", always one variable, hence "one - way". </P> <P> The ANOVA tests the null hypothesis that samples in all groups are drawn from populations with the same mean values . To do this, two estimates are made of the population variance . These estimates rely on various assumptions (see below). The ANOVA produces an F - statistic, the ratio of the variance calculated among the means to the variance within the samples . If the group means are drawn from populations with the same mean values, the variance between the group means should be lower than the variance of the samples, following the central limit theorem . A higher ratio therefore implies that the samples were drawn from populations with different mean values . </P>

When should one way anova be used and why
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