What is the meaning of analysis of variance

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What is the Meaning of Analysis of Variance?

Analysis of variance (ANOVA) is a statistical technique used to compare the means of two or more groups. It is used to determine if there are any statistically significant differences between the means of the groups. ANOVA is used in a variety of fields, including psychology, economics, and medicine.

ANOVA is based on the idea that the variation among group means is due to the differences between the groups, rather than random chance. The technique is used to test the hypothesis that the means of two or more populations are equal.

The first step in an ANOVA analysis is to calculate the variance of each group. This is done by subtracting the mean of each group from each individual observation in the group and then calculating the sum of the squared differences. The variance of each group is then calculated by dividing the sum of the squared differences by the number of observations in the group.

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The next step is to calculate the overall variance. This is done by subtracting the overall mean from each individual observation and then calculating the sum of the squared differences. The overall variance is then calculated by dividing the sum of the squared differences by the total number of observations.

Once the overall variance and the variance for each group have been calculated, the next step is to calculate the F-ratio. This is done by dividing the group variance by the overall variance. If the F-ratio is greater than 1, then there is a statistically significant difference between the means of the two or more groups.

ANOVA is a powerful tool for determining the differences between two or more groups. It is used in many fields, including psychology, economics, and medicine. It is important to understand the meaning of ANOVA in order to properly interpret the results of the analysis.

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