Partitioning the Sums of Squares (7 of 7)

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Source    df    Ssq     Ms     F     p
 Groups   2    8.000  4.000  3.60 0.071
 Error    9   10.000  1.111
Total    11   18.000  1.636
The third column contains the sums of squares. Notice that the sum of squares total is equal to the sum of squares groups + sum of squares error. The fourth column contains the mean squares. Mean squares are estimates of variance and are computed by dividing the sum of squares by the degrees of freedom. The mean square for groups (4.00) was computed by dividing the sum of squares for groups (8.00) by the degrees of freedom for groups (2). The fifth column contains the F ratio. The F ratio is computed by dividing the mean square for groups by the mean square for error. In this example,

F = 4.000/1.111 = 3.60.

There is no F ratio for error or total. The last column contains the probability value. It is the probability of obtaining an F as large or larger than the one computed in the data assuming that the null hypothesis is true. It can be computed from an F table. The df for groups (2) is used as the degrees of freedom in the numerator and the df for error (9) is used as the degrees of freedom in the denominator. The probability of an F with 2 and 9 df as larger or larger than 3.60 is 0.071.


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