Analysis of Variance: Key Statistical Analysis
- 1. ANOVA Name of the Faculty: Dr. Baiju P Department: Economics Course Code: MEC204C23 Course Title: Data Analysis using Advance Statistical Tools
- 2. • When interpreting an ANOVA table, focus on the F-statistic, associated p-value, and the source of variation to determine whether there are significant differences among group means.
- 7. Source of Variation: Between Groups (Treatment) Variability (SSB) This represents the differences among the group means. The larger this value, the more the group means differ from each other. Within Groups (Error or Residual) Variability (SSW): This represents the differences within each group. It measures the variation that cannot be attributed to the treatment effect.
- 8. Degrees of Freedom (df): Between Groups (DFB): The degrees of freedom associated with the between-groups variability. It is the number of groups minus one. (k-1) Within Groups (DFW): The degrees of freedom associated with the within-groups variability. It is the total number of observations minus the number of groups. (N-k)
- 9. Mean Squares (MS): Between Groups (MSB): This is the mean square for the between-groups variability. It is obtained by dividing the sum of squares (SSB) by the degrees of freedom (DFB). Within Groups (MSW): This is the mean square for the within-groups variability. It is obtained by dividing the sum of squares (SSW) by the degrees of freedom (DFW).
- 10. F-Statistic: F-Value: The F-ratio is calculated by dividing the between-groups mean square (MSB) by the within-groups mean square (MSW). A larger F-value suggests that the variation between groups is more than what would be expected by chance.
- 11. p-Value: p-Value: This indicates the probability of obtaining the observed F-ratio (or a more extreme one) if the null hypothesis is true. A smaller p-value (typically below 0.05) suggests that there is a significant difference among the group means.
- 12. Conclusion: Reject or Fail to Reject the Null Hypothesis If the p-value is less than the chosen significance level (e.g., 0.05), you may reject the null hypothesis. This implies that there is significant evidence to suggest that at least one group mean is different from the others.