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ANOVA provides a statistical test of whether the population means of several groups are equal, and therefore generalizes the t-test to more than two groups. ANOVA is useful for comparing or testing three or more group means for statistical significance. In ANOVA it is more conservative resulting in less type I errors and so is used for a more variety of calculations. Example of ANOVA would be in a group of people walking down the street how many people will smile back at you if you are smiling at them. This factors a group of male and a group of females as well as the types of smiles; teeth baring smile, grimace, blank stare, or look away. The null hypothesis could be if a smile is contagious. one part of the test could have a female smiling at people and another have a male smiling; Then there would be a column for sex(male/female) and another column of type of smile witnessed returned. The variance is used instead of the mean because there are more than 2 samples.

Reference:

Cipher, j., Grove, S. (2017). Statistics for Nursing Research: A Workbook for Evidence-Based Practice, 2nd Edition. Elsevier Inc.