Between-Group Variance

Definition

Between-group variance refers to the measure of how much the group means differ from the overall mean in a one-way ANOVA analysis. It quantifies the variability between the different groups or treatments being compared.

5 Must Know Facts For Your Next Test

1. Between-group variance is calculated by summing the squared differences between each group mean and the overall mean, and then dividing by the number of groups minus one.
2. A larger between-group variance indicates that the group means are more spread out, suggesting there are significant differences between the groups.
3. Between-group variance is the numerator in the F-ratio calculation, which is used to determine if the differences between the group means are statistically significant.
4. The between-group variance reflects the systematic, or treatment, differences between the groups, while the within-group variance reflects the random, or error, differences within each group.
5. Comparing the between-group variance to the within-group variance allows the researcher to determine if the differences between the groups are larger than what would be expected by chance alone.

Review Questions

• Explain the purpose of calculating the between-group variance in a one-way ANOVA.
  • The purpose of calculating the between-group variance in a one-way ANOVA is to quantify the variability in the group means. A larger between-group variance indicates that the group means are more spread out, suggesting there are significant differences between the groups being compared. This between-group variance is then compared to the within-group variance to determine if the differences between the groups are statistically significant, or if they are likely due to chance.
• Describe how the between-group variance is calculated and interpret its meaning.
  • The between-group variance is calculated by summing the squared differences between each group mean and the overall mean, and then dividing by the number of groups minus one. A larger between-group variance indicates that the group means are more spread out, suggesting there are significant differences between the groups. This between-group variance reflects the systematic, or treatment, differences between the groups, as opposed to the random, or error, differences within each group.
• Explain the relationship between the between-group variance, the within-group variance, and the F-ratio in a one-way ANOVA.
  • In a one-way ANOVA, the between-group variance is the numerator in the F-ratio calculation, which is used to determine if the differences between the group means are statistically significant. The F-ratio compares the between-group variance to the within-group variance, which represents the random, or error, differences within each group. If the between-group variance is significantly larger than the within-group variance, the F-ratio will be large, and the researcher can conclude that the differences between the group means are unlikely to have occurred by chance, suggesting there are significant differences between the groups.

Related terms

One-Way ANOVA: A statistical test used to determine if there are any statistically significant differences between the means of three or more independent groups.

Within-Group Variance: The measure of how much the individual scores within each group differ from their respective group means.

F-Ratio: The test statistic used in a one-way ANOVA that compares the between-group variance to the within-group variance.