Understanding SS of Contrasts
Sum of squares for a contrast measures one planned comparison inside an analysis of variance. It focuses on a question chosen before reviewing results. A contrast combines group means with coefficients. Positive coefficients form one side. Negative coefficients form the other side. Coefficients normally add to zero, so the comparison tests a real difference between weighted means.
Why Planned Contrasts Help
General ANOVA tells you whether groups differ somewhere. It does not tell which theory driven comparison caused that difference. Contrast sums of squares solve that problem. They isolate the variation explained by one planned pattern. This makes the result easier to report, especially when treatments follow ordered doses, named conditions, or designed experimental questions.
Inputs That Matter
The calculator needs each group mean, sample size, and standard deviation. It can estimate the pooled error term from those standard deviations. You may also enter a known mean square error from an ANOVA table. The coefficient list must match the group order. A coefficient of zero removes a group from the comparison. Unequal sample sizes are handled through the denominator.
How Results Are Read
The contrast value shows the weighted mean difference. The SS value shows variation explained by that contrast. Because a single contrast has one degree of freedom, its mean square equals its sum of squares. The F ratio compares that value with the error mean square. A small p value suggests the planned comparison is larger than expected from error variation.
Reporting Notes
Report the contrast coefficients, contrast estimate, SS, F value, error degrees of freedom, and p value. Include the adjusted alpha when several contrasts were planned. The partial eta squared value gives an effect measure for the comparison. It should be interpreted with study design and sample size in mind.
Practical Checks
Review coefficient order before trusting results. Confirm the means use the same units. Avoid building contrasts after seeing patterns, unless you describe them as exploratory. Planned contrasts are most useful when they match a hypothesis written before analysis. This approach also keeps the calculator transparent. Each number comes from visible inputs. You can compare manual notes, classroom examples, and ANOVA software output without changing the core hypothesis later or design.