Correlations

Correlations

Often you will not only look at one set of data but at two or more and you want to find out if there is a connection between these groups. For example:

• Tall people tend to be heavier than small people. Or put another way: The taller people are, the heavier they tend to be.
• The more beer you’ve had the less capable you are of driving your car.
• More intelligent parents tend to have more intelligent children.

These correlations seem intuitively plausible. You can, however, easily claim the following: Shoesize correlates with language ability.

Correlations between interval-scaled data can be visualized using scatterplots.
In your Excel file you find the correlations between a grammar and a vocab test for six students (Table 2). The figure shows the scatterplot for this correlation.

Table 2: Results of a grammar and a vocabulary test among six students

Figure 3: Perfect correlation

• Excel can calculate a correlation coefficient for you (function: KORREL).
• Usually correlations are not perfect.
• Correlation coefficients can take a value between -1 and +1.
• The larger the absolute value of the coefficient the stronger the correlation.
• Positive values indicate positive correlations.
• Negative values indicate negative correlations.

Exercise 5: Using Excel, calculate a correlation coefficient and design a scatterplot on the basis of the data for grammar and vocabulary test results of the six students in the Excel file. Afterwards, see what happens if you change the results of the grammar and vocabulary tests for individual participants in example table 2.