# Bivariate Correlations

This feature requires the Statistics Base option.

The Bivariate Correlations procedure computes Pearson's correlation coefficient, Spearman's rho, and Kendall's tau-b with their significance levels. Correlations measure how variables or rank orders are related. Before calculating a correlation coefficient, screen your data for outliers (which can cause misleading results) and evidence of a linear relationship. Pearson's correlation coefficient is a measure of linear association. Two variables can be perfectly related, but if the relationship is not linear, Pearson's correlation coefficient is not an appropriate statistic for measuring their association.

Confidence interval settings are available for Pearson and Spearman.

Example
Is the number of games won by a basketball team correlated with the average number of points scored per game? A scatterplot indicates that there is a linear relationship. Analyzing data from the 1994–1995 NBA season yields that Pearson's correlation coefficient (0.581) is significant at the 0.01 level. You might suspect that the more games won per season, the fewer points the opponents scored. These variables are negatively correlated (–0.401), and the correlation is significant at the 0.05 level.
Statistics
For each variable: number of cases with nonmissing values, mean, and standard deviation. For each pair of variables: Pearson's correlation coefficient, Spearman's rho, Kendall's tau-b, cross-product of deviations, and covariance.

## Data considerations

Data
Use symmetric quantitative variables for Pearson's correlation coefficient and quantitative variables or variables with ordered categories for Spearman's rho and Kendall's tau-b.
Assumptions
Pearson's correlation coefficient assumes that each pair of variables is bivariate normal.

## Obtaining Bivariate Correlations

This feature requires the Statistics Base option.

Analyze > Correlate > Bivariate...

1. Select two or more numeric variables.
The following options are also available:
Correlation Coefficients
For quantitative, normally distributed variables, choose the Pearson correlation coefficient. If your data are not normally distributed or have ordered categories, choose Kendall's tau-b or Spearman, which measure the association between rank orders. Correlation coefficients range in value from –1 (a perfect negative relationship) and +1 (a perfect positive relationship). A value of 0 indicates no linear relationship. When interpreting your results, be careful not to draw any cause-and-effect conclusions due to a significant correlation.
Test of Significance
You can select two-tailed or one-tailed probabilities. If the direction of association is known in advance, select One-tailed. Otherwise, select Two-tailed.
Flag significant correlations
Correlation coefficients significant at the 0.05 level are identified with a single asterisk, and those significant at the 0.01 level are identified with two asterisks.
Show only the lower triangle
When selected, only the correlation matrix table's lower triangle is presented in the output. When not selected, the full correlation matrix table is presented in the output. The setting allows table output to adhere to APA style guidelines.
Show diagonal
When selected, the correlation matrix table's lower triangle along with diagonal values are presented in the output. The setting allows table output to adhere to APA style guidelines.
2. You can optionally select the following:
• Click Options... to specify Pearson correlation statistics and missing values settings.
• Click Style... to specify conditions for automatically changing properties of pivot tables based on specific conditions.
• Click Bootstrap... for deriving robust estimates of standard errors and confidence intervals for estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression coefficient.
• Click Confidence Interval... to set the options for the estimation of the confidence intervals.

This procedure pastes CORRELATIONS and NONPAR CORR command syntax.