Analysis of variance, ANOVA, is a collection of statistical models used to analyze the differences between group means and their associated procedures. In ANOVA, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. It provides a statistical test of whether or not the means of several groups are equal. Therefore it generalizes t-test to more than two groups. Doing multiple two-sample t-tests would result in an increased change of committing a type 1 error. Analysis of variance is useful in comparing three or more means for statistical significance.

ANOVA is a particular form of statistical hypothesis testing heavily used in the analysis of experimental data. A statistical hypothesis test is a method of making decisions using data. A test result is called statistically significant if it is deemed unlikely to have occurred by change, assuming the truth of the null hypothesis. A statistically significant result is less than a threshold justifies the rejection of the null hypothesis. In an application of ANOVA, the null hypothesis is that all groups are simply random samples of the same population.

The terminology of ANOVA is largely from the statistical design of experiments. The experimenter adjusts factors and measures responses in an attempt to determine an effect. Factors are assigned to experimental units by a combination of randomization and blocking to ensure the validity of the results. ANOVA is the synthesis of several ideas and it is used for multiple purposes. ANOVA is a statistical tool used in many ways to develop and confirm an explanation for the observed data.

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