How does the SSCP matrix differ from the variance-covariance matrix?

How does the SSCP matrix differ from the variance-covariance matrix?

• A. SSCP expresses variability as averages; variance-covariance expresses totals
• B. SSCP expresses variability as totals; variance-covariance expresses averages
• C. SSCP uses diagonals only
• D. SSCP is for time series; variance-covariance is for cross-sectional data

Answer: (B)

In multivariate statistics, the SSCP (sum of squares and cross-products) matrix collects variability as totals. It sums the squared deviations and the products of deviations across observations, so its entries are totals rather than averages. The variance–covariance matrix, on the other hand, expresses variability as averages—the variances are the average of squared deviations and the covariances are the average product of deviations. These two are related by a simple scaling: Covariance matrix = SSCP divided by n−1 (for centered data and the usual sample covariance). Diagonals reflect this difference as well: SSCP diagonals are sums of squares, while the covariance matrix diagonals are variances (averages of those squares). Off-diagonals follow the same pattern—SSCP uses cross-product sums, covariance uses covariances (averaged cross-products). So the best description is that SSCP expresses variability as totals, whereas the variance–covariance matrix expresses averages. The other options don’t reflect this fundamental distinction.

In multivariate statistics, the SSCP (sum of squares and cross-products) matrix collects variability as totals. It sums the squared deviations and the products of deviations across observations, so its entries are totals rather than averages. The variance–covariance matrix, on the other hand, expresses variability as averages—the variances are the average of squared deviations and the covariances are the average product of deviations.

These two are related by a simple scaling: Covariance matrix = SSCP divided by n−1 (for centered data and the usual sample covariance). Diagonals reflect this difference as well: SSCP diagonals are sums of squares, while the covariance matrix diagonals are variances (averages of those squares). Off-diagonals follow the same pattern—SSCP uses cross-product sums, covariance uses covariances (averaged cross-products).

So the best description is that SSCP expresses variability as totals, whereas the variance–covariance matrix expresses averages. The other options don’t reflect this fundamental distinction.