Yes, you can calculate the sum of squares (SS) without having the raw scores, provided you have the standard deviation and the number of data points (n). Here's how:
Steps to Calculate Sum of Squares
- Calculate the Variance: Square the standard deviation. Variance (σ²) = (Standard Deviation)²
- Multiply by n: Multiply the variance by the number of data points (n). Sum of Squares (SS) = Variance n or SS = σ² n
Formula
The formula summarizing this calculation is:
*SS = n σ²**
Where:
- SS = Sum of Squares
- n = Number of data points in the dataset
- σ² = Variance
Example
Let's say you have a dataset with:
- Standard Deviation = 5
- Number of data points (n) = 20
- Calculate Variance: Variance = (5)² = 25
- Calculate Sum of Squares: SS = 20 * 25 = 500
Therefore, the sum of squares for this dataset is 500.
Why This Works
The sum of squares represents the total squared deviation of each data point from the mean of the dataset. Variance is the average of these squared deviations. Multiplying the variance by 'n' essentially scales the average squared deviation back to the total squared deviation, hence giving you the sum of squares.
Limitations
- This method only works if you know both the standard deviation (or variance) and the number of data points. If either is missing, you cannot calculate the sum of squares without additional information.
- This calculation provides the sum of squared deviations. The exact meaning of this value depends on the context (e.g., in ANOVA, it could be the sum of squares between groups or within groups). Ensure you understand the specific sum of squares you are trying to calculate.
