182. One-Way ANOVA

Compares the means of three or more groups based on one independent variable

• :
• : At least one differs from the others

Step 1: Calculate Between-Group Variation ()

• : Number of observations in group
• : Mean of group
• : Overall mean of all groups

Step 2: Calculate Within-Group Variation ()

• : Observation in group

Step 3: Calculate Total Variation ()

Step 4: Calculate Mean Squares

• Mean Square Between ()

• Mean Square Within ()

• : total number of observations
• : number of groups

Step 5: Calculate the F-statistic

Step 6: Decision Rule

• Compare the F-statistic to the critical value from the F-distribution table (based on chosen significance level ).
• Alternatively, compare the p-value to the significance level .
• Reject if the F-statistic is greater than the critical value or if the p-value is less than , indicating that at least one group mean is significantly different.