**Instructions:** This calculator conducts One-Way ANOVA for a group of samples, with the purpose of comparing the population means of several groups. Please type the sample data for the groups you want to compare and the significance level \(\alpha\), and the results of the ANOVA test for independent samples will be displayed for you (Compare up to 6 groups. Please leave empty the columns that you will not use):

## One Way Analysis of Variance

More about the *One-Way ANOVA test* so you can better understand the results delivered by this solver. First of all, ANOVA or Analysis of Variances is one of the most important fields in Statistic. The reason for this is that is goes into the core of analyzing the variation exhibited samples, by breaking down the total variation into various different sources of variation.

The most basic use of ANOVA is to test for the difference between the populations for several groups (2 or more). Let us recall that a t-test is used to compare the means of two groups, so then ANOVA is some sort extension that allows to perform comparisons for two or more groups.

As with any other hypothesis test, ANOVA uses a null and the alternative hypothesis. The null hypothesis is a statement that claims that all population means are equal, and the alternative hypothesis is the hypothesis that not all means are equal (observe that this does NOT imply that all means are unequal, it implies that al least one pair of means is unequal).

The main assumptions required to perform a one-way ANOVA are:

- The dependent variable (DV) needs to be measured at least at the interval level
- The groups must come from normally distributed populations
- The groups must come from normally populations with equal population variances

If the results of the ANOVA are significant, this is, the null hypothesis is rejected, we can perform a *Post-Hoc test* to assess exactly which pairs differ significantly. Examples of Post-Hoc tests are Fisher's LSD, Tukey's test, Bonferroni correction, etc.

When some of the assumption are not met (specifically the second are third), there are corrective options for some more robust statistics. When there are serious violations to the assumptions, it would be more appropriate to use a non-parametric alternative, like Kruskal-Wallis' Test.

This ANOVA calculator with steps provides you with enough information to reject or to fail to reject the null hypothesis, based on the F-ratio that is computed. If the null hypothesis is computed, you will need to conduct a Post-Hoc test.

A one-way ANOVA compares two or more sample means, but if you want to compare two sample means, then it may be more efficient to use our t-test for two independent samples.

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