Bivariate correlation procedure computes correlation coefficients (with significance levels) between variables and measures how variables are related (i.e a measure of the association between any two variables, ignoring the effect of all other variables). According to the type of data under analysis there are two measures of correlation that can be used:
SPSS for Windows can be used for both these statistical methods using the step below:
1) Product-moment correlation coefficient or Pearson's
correlation coefficient
The product-moment correlation coefficient or Pearson's correlation
coefficient is a parametric measure of the relationship between two variables.
The variables must be measured on an interval scale and have come from
normally distributed populations. This is calculated using the following
equation.
Where Sx and Sy are the sample standard deviations of the two variables,
and 
and 
are
the means of the two variables. Pearson's coef. can vary between
1 and -1 with 0 indicating no correlation.
Pearson's coef can be computed using SPSS for Windows through the following step:
SPSS can test the significance of the correlation coefficient using
the Student t test. The null hypothesis is that the two sets of measurements
are random samples from two independent, normally distributed population
of measurements. Any apparent correlation in the sample data is due
to sampling fluctuations (
=
0). The alternative hypothesis is that there is correlation between
the two samples (is
not 0). A one or two tailed test can be selected using the following
steps in SPSS for Windows.
After clicking OK, you will then find the result you want in the output viewer.
2) Spearman's Rank Correlation Coefficient
Spearman's Rank Correlation Coefficient is a non parametric measure
of the relationship between two sets of ordinal (ranked) values using the
following formula:
Where d is the difference in ranking for each item, and n is the number of items ranked.
SPSS for Windows can be used to calculate Spearman's Rank coef. using the following step:
SPSS can test the significance of the correlation coefficient using
the Student t test. The null hypothesis is that the two sets of measurements
are random samples from two independent, normally distributed population
of measurements. Any apparent correlation in the sample data is due
to sampling fluctuations (=
0). The alternative hypothesis is that there is correlation between
the two samples (is
not 0). A one or two tailed test can be selected using the following
steps in SPSS for Windows.