ANOVA One Way - LSS Glossary

One way ANOVA is a statistical technique used to test the equality of means between two or more groups for a single continuous variable. It is a powerful tool for analyzing data and determining whether there are significant differences between groups.

Hypotheses

The null hypothesis for One Way ANOVA is that the means of all groups are equal. The alternative hypothesis is that at least one mean is different from the others. The researchers set the significance level, usually denoted by alpha (α), prior to conducting the test. A commonly used value for alpha is 0.05.

Assumptions for One Way ANOVA

To use one-way 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 of One Way ANOVA

The calculations for one-way ANOVA involve several steps. These include:

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 degrees of freedom for the between and within groups
Calculating the mean square between and within groups
Calculating the F-ratio
Comparing the calculated F-ratio to the critical value from the F-distribution to determine the p-value

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Post-Hoc Tests

If one-way 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.

One-way ANOVA is a powerful tool for analyzing data and determining whether there are significant differences between groups for a single continuous 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