description | example | calculator (will open in another window)

Formula

SSwithin = SStotal - SSamong
 dfamong = r-1 dfwithin = N-r
x = individual observation
r = number of groups
N = total number of observations (all groups)
n = number of observations in group

Steps (assuming three groups)

Create six columns: "x1", "x12", "x2", "x22", "x3", and "x32"
1. Put the raw data, according to group, in "x1", "x2", and "x3"
2. Calculate the sum for group 1.
3. Calculate (Sx)2 for group 1.
4. Calculate the mean for group 1
5. Calculate Sx2 for group 1.
6. Repeat steps 2-5 for groups 2 and 3
7. Set up SStotal and SSamong formulas and calculate
8. Calculate SSwithin
9. Enter sums of squares into the ANOVA table, and complete the table by calculating: dfamong, dfwithin, MSamong, and MSwithin, and F
10. Check to see if F is statistically significant on probability table with appropriate degrees of freedom and p < .05.

• An example of the application of this formula
• Practice by creating your own data and then check your work with the Virtual Statistician One-Way ANOVA Calculator (will open in another window) (Only works with n = 8)
• A description of the One-Way Analysis of Variance