Factorial ANOVA - LSS Glossary

Factorial ANOVA is a statistical technique 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.

Hypotheses statements for Factorial ANOVA

The null hypothesis for factorial ANOVA is 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. The significance level, usually denoted by alpha (α), is set prior to conducting the test. A commonly used value for alpha is 0.05.

Assumptions for Factorial ANOVA

To use Factorial ANOVA, the data should meet certain assumptions.. These assumptions include:

Normality: The data must follow normal distribution within each group.
Independence: The observations must be independent of one another.
Equal variances: The groups that are being compared must have equal variances.

When the data do not meet these assumptions, we can use alternative techniques such as non-parametric tests or transformed data.

Calculations for Factorial ANOVA

The calculations for factorial ANOVA involve several steps. These include:

Determining the number of levels for each independent variable
Calculating the overall mean of the data
Calculating the sum of squares between the groups (SSbetween)
Calculating the sum of squares within the groups (SSwithin)
Calculating the sum of squares for each independent variable (SSA, SSB, etc.)
Calculating the sum of squares for the interaction of the independent variables (SSAB, SSAC, etc.)
Calculating the degrees of freedom for the between, within, and each independent variable and their interactions
Calculating the mean square for each source of variation
Calculating the F-ratio for each source of variation
Comparing the calculated F-ratios to the critical values from the F-distribution to determine the p-value

Post-Hoc Tests

If factorial ANOVA 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.

Interpretation of results

The results of factorial ANOVA can be used to determine whether there is a significant interaction between the independent variables, as well as whether there are significant main effects for each independent variable separately. It also allows to understand the relationship between the dependent variable and each independent variable and how they interact with each other.

Factorial ANOVA is a powerful tool for analyzing the relationship between more than two independent variables and a single dependent variable. It is important to understand the assumptions and potential limitations of the technique before using it, and to use post-hoc tests 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