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The analysis of variance (ANOVA) is the most common null hypothesis test used when researchers need to compare the means of more than two groups or conditions. It serves as a necessary extension of the $$t$$-test, which is strictly limited to evaluating differences between exactly two means (such as a single sample mean against a population mean, or the means of two distinct groups).

Analysis of Variance

The one-way ANOVA is a specific type of analysis of variance used to compare the means of more than two samples ($$M_1, M_2 \ldots M_G$$) to determine if there are statistically significant differences among them. This statistical test is specifically applied within between-subjects designs where a single independent variable is manipulated across multiple independent groups.

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