The function of a one-way ANOVA check is to recognize the existence of a statistically far-ranging difference among several team means. The test actually supplies variances to assist determine if the way are same or not. In order to do a one-way ANOVA test, there space five an easy assumptions to be fulfilled:

Each population from i m sorry a sample is take away is suspect to it is in normal.All samples space randomly selected and also independent.The populations are suspect to have actually equal typical deviations (or variances).The variable is a categorical variable.The an answer is a numerical variable.

You are watching: The null hypothesis for the single factor anova states that all means are equal.

The Null and alternative Hypotheses

The null hypothesis is simply that all the group population method are the same. The alternate hypothesis is that at least one pair of method is different. For example, if there are k groups:

H0: μ1 = μ2 = μ3 = … = μk

Ha: At the very least two of the group way μ1, μ2, μ3, …, μk are not equal.

The graphs, a collection of crate plots representing the distribution of values through the group method indicated by a horizontal line through the box, aid in the knowledge of the theory test. In the very first graph (red crate plots), H0: μ1 = μ2= μ3 and also the three populations have the same distribution if the null hypothesis is true. The variance of the an unified data is around the exact same as the variance of each of the populations.

If the null hypothesis is false, climate the variance the the merged data is larger which is brought about by the different means as shown in the 2nd graph (green crate plots).

(a) H0 is true. All means are the same; the differences are due to random variation.

(b) H0 is no true. All means are no the same; the distinctions are too huge to be as result of random variation.

Concept Review

Analysis the variance extend the comparison of two groups to several, each a level the a categorical change (factor). Samples indigenous each group are independent, and also must be randomly selected from normal populations with same variances. We test the null hypothesis of equal means of the an answer in every group versus the different hypothesis that one or much more group way being various from the others. A one-way ANOVA hypothesis test identify if numerous population means are equal. The circulation for the check is the F distribution with 2 different degrees of freedom.

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Each populace from i m sorry a sample is taken is presume to it is in normal.All samples are randomly selected and also independent.The populaces are presume to have equal traditional deviations (or variances).