Variances

Definition

Variances measure the spread of data points around the mean in a dataset. In the context of ANOVA, they are used to compare the variability between groups and within groups.

5 Must Know Facts For Your Next Test

1. Variance is calculated as the average of the squared differences from the mean.
2. In One-Way ANOVA, variances are partitioned into between-group variance and within-group variance.
3. The F-statistic in ANOVA is computed using the ratio of between-group variance to within-group variance.
4. A high F-statistic indicates that there is more variability between groups than within groups, suggesting a significant difference among group means.
5. Degrees of freedom for variances are different: between-group variance uses k-1 degrees of freedom (where k is the number of groups), while within-group variance uses N-k degrees of freedom (where N is the total number of observations).

Review Questions

• What does variance measure in a dataset?
• How is the F-statistic in ANOVA related to variances?
• What do high and low F-statistics indicate about group differences in ANOVA?

Related terms

F-Statistic: A ratio used in ANOVA tests that compares between-group variance to within-group variance.

Degrees of Freedom: The number of values in a calculation that have freedom to vary; used to determine critical values in statistical tests.

Mean Square: An estimate of population variance calculated by dividing sum of squares by corresponding degrees of freedom.