Analysis of Variance or ANOVA is a statistical technique used to test the equality of means between two or more groups. It is a powerful tool for analysing data and determining whether there are significant differences between groups.
One-Way Analysis of Variance
One-way Analysis of Variance is used to compare the means of a single continuous variable between two or more groups. It is used to test the null hypothesis that the means of all groups are equal. The alternative hypothesis is that at least one mean is different from the others.
Two-Way Analysis of Variance
Two-way Analysis of Variance is used to analyse the relationship between two independent variables and a single dependent variable. It is used to test the null hypothesis that the means of all groups are equal, regardless of the levels of the two independent variables. The alternative hypothesis is that at least one mean is different based on the levels of the two independent variables.
Factorial ANOVA
Factorial Analysis of Variance (ANOVA) is used to analyze the relationship between more than two independent variables and a single dependent variable. It is used to test the null hypothesis that the means of all groups are equal, regardless of the levels of all independent variables. The alternative hypothesis is that at least one mean is different based on the levels of one or more independent variables.
Assumptions of ANOVA
To use Analysis of Variance, certain assumptions must be met. These assumptions include:
- Normality: The data must be normally distributed within each group.
- Independence: The observations must be independent of one another.
- Equal variances: The variances of the groups being compared must be equal.
When these assumptions are not met, alternative techniques such as non-parametric tests or transformed data may be used.
Post-Hoc Tests
If Analysis of Variance results in a significant p-value, post-hoc tests can be used to determine which specific groups are significantly different from one another. These tests include the Tukey test, the Bonferroni test, and the Scheffe test.
Analysis of Variance is a powerful tool for analysing data and determining whether there are significant differences between groups. It can be used in a variety of settings and can be extended to include more than two independent variables. However, it is important to understand the assumptions and potential limitations of the technique before using it. Post-hoc tests can be used to further analyze the data and identify specific differences between groups.
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Sachin Naik
Passionate about improving processes and systems | Lean Six Sigma practitioner, trainer and coach for 14+ years consulting giant corporations and fortune 500 companies on Operational Excellence | Start-up enthusiast | Change Management and Design Thinking student | Love to ride and drive
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