Use correlation if you want to find the linear relationship between two ordinal or scale level variables, i.e., how well the data points fit into a straight line in a two-dimensional plane spanned by the two variables.
Note however that the correlation has nothing to do with the slope of such line (which indicates the strength of the effect of one variable on the other). For that you need to use regression analysis and look at the regression coefficient.
Find the correlation between two ordinal or scale variables:
Analyze -> Correlate -> Bivariate
Put the two variables into the variables box. If you put in more than two variables, SPSS will calculate the pairwise correlations.
Choose the type of correlation to be calculated in the Correlation Coefficients option. For scale level data, choose Pearson. For ordinal level or a mix of ordinal and scale level, choose Spearman or Kendall’s tau-b. The latter is more suitable when sample size is small.
In Test of Significance, choose two-tailed if you are interested in testing if the correlation is zero or nonzero. If you want to test specifically if the correlation is positive / negative, choose one-tailed.
Optionally, check the Flag significant correlations option.
Optionally, click Options button and select to show the means and standard deviations.
SPSS will then generate the correlation matrix showing the pairwise correlations between the variables.
First of all we look at the statistical significance of the resulting correlation coefficient:
For two-tailed test, the null hypothesis is that the correlation coefficient is zero. The alternative hypothesis is that the correlation coefficient is nonzero (or in other words there is some association between the two variables). We reject the null hypothesis when p<0.05 (or other values of levels of significance).
If one-tailed test is chosen and the correlation coefficient is positive, then the null hypothesis is that the correlation coefficient is non-positive (<=0). The alternative hypothesis is that the correlation coefficient is positive. Again we reject the null hypothesis when p<0.05 or other levels of significance. This test is helpful in determining if there is a positive association (i.e., not only nonzero) between the variables.
On the other hand, if one-tailed test is chosen but the correlation coefficient is negative, then the null hypothesis is that the correlation coefficient is non-negative (>=0). The alternative hypothesis is that the correlation coefficient is negative. Again we reject the null hypothesis when p<0.05 or other levels of significance. This test is helpful in determining if there is a negative association (i.e., not only nonzero) between the variables.
If the correlation coefficient is statistically significant, we can then further interpret its meaning as follows:
A value close to -1 means that there is strong negative correlation (i.e., when one variable increases the other variable decreases).
A value close to +1 means that there is strong positive correlation (i.e., when one variable increases the other variable increases).
A value of +/-0.7 or above is regarded as a strong correlation. A value close to +/-0.5 is only a medium correlation.
A value close to 0 means that there is no or weak correlation. That means there is no obvious linear relationship between the variables.
Note also that a strong correlation does not mean a strong effect of one variable on another. For example, if all the points fall on a horizontal line in an XY plane, then the correlation is very strong (i.e., there is an obvious linear relationship), but the X variable has no effect on the Y variable (because no matter how X changes, Y is always the same value). To study the strength of the effect of X on Y, you need to do a regression analysis and look at the regression coefficient, which indicates the slope of the line in this plane.
Find the correlation between two ordinal or continuous variables:
Analyses -> Regression -> Correlation Matrix
Put the two variables into the variables box on the right. If you put in more than two variables, Jamovi will calculate the pairwise correlations.
Choose the type of correlation to be calculated in the Correlation Coefficients option. For continuous data, choose Pearson. For ordinal level or a mix of ordinal and scale level, choose Spearman or Kendall’s tau-b. The latter is more suitable when sample size is small.
In Hypothesis, choose Correlated if you are interested in testing if the correlation is zero or nonzero. This corresponds to a two-tailed test. If you want to test specifically if the correlation is positive / negative, choose Correlated positively or Correlated negatively. This corresponds to a one-tailed test.
Optionally, check the Report significance and Flag significant correlations option.
Optionally, click Correlation matrix under Plot.
Jamovi will then generate the correlation matrix showing the pairwise correlations between the variables.
First of all we look at the statistical significance of the resulting correlation coefficient:
For Correlated (two-tailed test) in the Hypothesis, the null hypothesis is that the correlation coefficient is zero. The alternative hypothesis is that the correlation coefficient is nonzero (or in other words there is some association between the two variables). We reject the null hypothesis when p<0.05 (or other values of levels of significance).
For Correlated positivity (one-tailed test) in the Hypothesis, the null hypothesis is that the correlation coefficient is non-positive (<=0). The alternative hypothesis is that the correlation coefficient is positive. Again we reject the null hypothesis when p<0.05 or other levels of significance. This test is helpful in determining if there is a positive association (i.e., not only nonzero) between the variables.
On the other hand, if Correlated negatively (also one-tailed test) is chosen, then the null hypothesis is that the correlation coefficient is non-negative (>=0). The alternative hypothesis is that the correlation coefficient is negative. Again we reject the null hypothesis when p<0.05 or other levels of significance. This test is helpful in determining if there is a negative association (i.e., not only nonzero) between the variables.
If the correlation coefficient is statistically significant, we can then further interpret its meaning as follows:
A value close to -1 means that there is strong negative correlation (i.e., when one variable increases the other variable decreases).
A value close to +1 means that there is strong positive correlation (i.e., when one variable increases the other variable increases).
A value of +/-0.7 or above is regarded as a strong correlation. A value close to +/-0.5 is only a medium correlation.
A value close to 0 means that there is no or weak correlation. That means there is no obvious linear relationship between the variables.
Note also that a strong correlation does not mean a strong effect of one variable on another. For example, if all the points fall on a horizontal line in an XY plane, then the correlation is very strong (i.e., there is an obvious linear relationship), but the X variable has no effect on the Y variable (because no matter how X changes, Y is always the same value). To study the strength of the effect of X on Y, you need to do a regression analysis and look at the regression coefficient, which indicates the slope of the line in this plane.