The tables of descriptive statistics can be used to assist in calculating the correlation.
Summary Statistics for the Data
N M SD Skew Kurt
Outcome1 4.000 2.000 2.449 0.544 -2.944
Outcome2 4.000 6.000 2.449 0.544 -2.944
Covariances for the Data
Outcome1 Outcome2
Outcome1 6.000 3.000
Outcome2 3.000 6.000
Correlations for the Data
Outcome1 Outcome2
Outcome1 1.000 0.500
Outcome2 0.500 1.000
The table of inferential statistics shows the key elements to be calculated.
Hypothesis Tests for the Correlations
R SE df t p
Outcome1 & Outcome2 0.500 0.612 2.000 0.816 0.500
Descriptive Statistics: The descriptive statistics are calculated separately for each variable.
Sum of Cross Products: The Sum of Cross Products (“SCP”) is not easily determined solely from the summary statistics of the output, but rather from the data.
\[SCP = \sum ( X - M_X ) ( Y - M_Y ) = ( 0 - 2.000 ) ( 4 - 6.000 ) + ( 0 - 2.000 )( 7 - 6.000 ) + ( 3 - 2.000 )( 4 - 6.000 ) + (5 - 2.000)(9 - 6.000) = 9.000\]
Covariance: The Covariance (“COV”) is a function of the Sum of Cross Products and the sample size:
\[COV = \frac{SCP}{(N - 1)} = \frac{9.000}{(4 - 1)} = 3.000\]
Pearson Correlation Coefficient: The Pearson Correlation Coefficient (“r”) is a function of the Covariance and the Standard Deviations of both variables:
\[r = \frac{COV}{(SD_X) (SD_Y)} = \frac{3.000}{(2.449) (2.449)} = .500\]
Correlations provide a measure of statistical relationship between two variables.
For the participants (N = 4), the scores on Outcome 1 (M = 2.00, SD = 2.45) and Outcome 2 (M = 6.00, SD = 2.45) were moderately correlated, r(2) = .50.
Note that correlations can also have inferential information associated with them (and that this information should be summarized if it is available and of interest).
For the participants (N = 4), the scores on Outcome 1 (M = 2.00, SD = 2.45) and Outcome 2 (M = 6.00, SD = 2.45) were moderately but not statistically significantly correlated, r(2) = .50, 95% CI [-0.89, 0.99], p = .500.