There are two different formulas or methods that can be used to calculate SS.
a. Under what circumstances is the definitional
formula easy to use?
b. Under what circumstances is the computational
formula preferred?
a. The definitional formula is easy to use when the data is provided in the form of raw scores. This formula involves subtracting the mean of the data from each individual data point, squaring the result, and then summing all the squared values. By using the definitional formula, you are directly calculating the sum of squares (SS) based on the deviation of each data point from the mean.
b. The computational formula, on the other hand, is preferred when you have access to additional information such as the sum of the raw scores, the sum of the squared raw scores, and the total number of data points. This formula requires computing the sum of squares by subtracting the squared sum of the raw scores divided by the total number of data points from the sum of the squared raw scores. The computational formula is more efficient and less time-consuming when you already have these extra statistics available.
To summarize:
- The definitional formula is easy to use when you have raw scores and do not have access to additional information.
- The computational formula is preferred when you have additional statistics available, as it is more efficient.