What Does a Correlation Coefficient of Zero Mean?

Researchers find comparisons fascinating. A positive correlation is seen when variables move in the same direction, such as increased consumption of ice cream on the hottest days of summer.

A negative correlation occurs if a dramatic increase in the price of ice cream is associated with fewer sales and lost revenue. A zero coefficient would imply that ice cream sales in grocery stores do not rise or fall with outdoor temperature changes or price fluctuations, for instance.

Calculating the Zero Coefficient

In statistics, a correlation coefficient measures the direction and strength of relationships between variables. One of the most frequently used calculations is the Pearson product-moment correlation (r) that looks at linear relationships. Values of the r correlation coefficient fall between -1.0 to 1.0.

Example:

• -1.0 denotes a perfect negative correlation.

• +1.0 denotes a perfect positive correlation.

• A zero coefficient implies no linear correlation in a sample. If correlation is 0 (or around -0.1 and +0.1), the linear relationship between variables is very weak to nonexistent.

Types of Correlations

A zero coefficient occurs if r equals zero meaning there is no clustering or linear correlation. A zero coefficient does not necessarily mean that the variables are independent. Nonlinear correlations may still be possible if the correlation is zero, but those relationships cannot be measured using the Pearson product-moment correlation (r).

A positive correlation is indicated when the correlation coefficient (r) is more than zero. This means that both variables move in the same direction in steady increments. The closer to 1.0, the stronger the linear correlation. For instance, a positive correlation coefficient ( r= 0.8) between height and shoe size would indicate that taller people tend to have bigger feet than their shorter peers.

A negative correlation is indicated when the correlation coefficient (r) is less than zero. This means that variables move in opposite directions from one another. The closer to -1.0, the stronger the negative correlation. For instance, a correlation coefficient (r=-0.9) would show a strong negative correlation between monthly heating bills and changing seasonal temperatures in Maine.

Using a Scattergram

A scattergram is a graph with an x-axis and a y-axis used to compare paired scores when looking for correlations. Visual learners may find it particularly helpful to plot study results on a scattergram. Data on each variable is plotted on the x-axis, and then the data of the other variable is plotted on the y-axis. A dot is placed where the values intersect.

For example, you could plot the weight of each research study participant on the x-axis and height of each research study participant on the y-axis. If all the dots are fairly close in a straight line, it implies a correlation between the paired variables, such as height and weight. When the dots are all over the place with no observable pattern on the scatter gram, a zero correlation is indicated.

Correlation versus Causation

Repeatedly, teachers stress that correlation is not the same as causation. Many things just happen to correlate with one another, but that does not mean one factor causes the other. For instance, home invasions increase during the summer when more people leave windows open or patio doors ajar. Such a correlation does not imply that warm weather causes people to commit burglaries or assaults, however.

Determining a direct cause and effect relationship can be very difficult because many other variables can confound the results and limit conclusions. For instance, there may or may not be correlation or causation between skipping breakfast before school and struggling academically. A zero correlation would be expected if comparing students’ grades with spurious variables such as their shoe size or favorite color.