Separate your data points according to group. An analysis of variance is meaningless without a clear separation of within-data groups. For example, if the data came from students in a school, and you were interested in the differences and variances related to sex, separate the data into "male" and "female" groups. For convenience, write these groups as "x" and "y."
List the data points in a table or statistical program by group. Also count the number of data points for each group, and label these numbers as "nx" and "ny."
Compute the mean correction. Do this directly from the tables. Add up all the values of "x" and "y" and call the resulting value "T." Add "nx" and "ny" and call the sum "N." The mean correction, "C," then equals T^2/N.
Calculate the total sum of squares, "SST". Square all the data points "x" and "y." Sum the squares of these data points. Subtract "C" from this sum to yield "SST."
Find the between-groups sum of squares value, "SSB." Return to the original set of data points "x" and "y." Sum these sets separately, like you did to calculate the mean correction, "C." This time, square these sums separately. Divide the resulting sums by the number of data points that are associated with the sums, "nx" and "ny," respectively. Add these two sums together and subtract the mean correction. The resulting value is "SSB".
Compute "SSW," the within-group sum of squares value. Use the formula SSW = SST -- SSB.
Calculate the degrees of freedom for error, "dfE." Use the equation dfE = nx + ny -- 2.
Find the between-group mean square value, "MSB." Divide "SSB" by 2.
Find the mean square error value, "MSE." Divide "SSW" by "dfE."
Calculate the F statistic. Divide MSB by MSE. This is your final test statistic.