Statistical Analysis for Education and Psychology Researchers

Corrected Sum-of-Squares and Crossproducts

(^) MATHS SMATHS RAVEN
MATHS 60.400000 223.600000 −25.800000
SMATHS 223.600000 1030.400000 −125.200000
RAVEN −25.800000 −125.200000 31.600000
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
MATHS 10 5.6000 2.5906 56.0000 1.0000 10.0000
SMATHS 10 115.4000 10.6909 1154 95.0000 133.0000
RAVEN 10 1,8000 1.8738 18.0000 1.0000 7.0000
Pearson Correlation Coefficients /Prob>|R| under Ho: Rho=0/N=10
MATHS SMATHS RAVEN
MATHS 1.00000 0.89629 −0.59055
0.0 0.0004 0.0723
SMATHS 0.89629 1.00000 −0.69384
0.0004 0.0 0.0260
RAVEN −0.59055 −0.69384 1.00000
0.0723 0.0260 0.0

Figure 8.9: SAS output for bivariate

correlations between the variables

MATHS, SMATHS and RAVEN

Interpretation

The second line of output shown in Figure 8.9 contains the names of the variables
included in the correlation analysis. This list of variables is followed by a table of the
corrected sums of squares and cross products for the variables. The names of the
variables form the rows and columns of this table. For example, the sums of squares for
the variable RAVEN is found in the body of the table where the third row and third
column intersect, the value here is 31.6. The cross product sums of squares is at the
intersection of two different variables for example 223.6 is the cross product sums of
squares for SMATHS×MATHS.
The next section of output contains simple summary statistics. In this example the
sample size for all the cells of the correlation matrix is the same because there is no
missing data. The sample size is therefore only printed in the summary statistics. If there
had been different sample sizes for each variable then n would have been printed for each
correlation in the correlation matrix in the following section.
The final section of output contains the correlation matrix of rows and columns headed
by each variable name. Each cell of the matrix, intersection between a row and a column
variables contains two values, the bivariate correlation coefficient and the associated p-
value. This probability value is the level of significance resulting from a test of the null
hypothesis, Prob>|R| under H 0 : Rho=0. For example, the value of the correlation between
MATHS and SMATHS is r=0.89629. This indicates a positive linear relationship
between the two variables. The associated p-value is 0.0004 which provides evidence in

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