Previously, I wrote two blog posts on correlation, so it was not my intention to write the third one so quickly.

However, today I have been working with Damian – a young student preparing for an MSc in Social Sciences.

Damian had read three journal articles at home, which we were discussing during our Skype session.

I asked Damian to interpret correlation coefficients presented in a matrix in one of the journal papers.

Since it did not go very well, I thought that perhaps more students might struggle with the task.

**Explanation**

The correlation matrix is a table which shows relationships between variables in the study.

More precisely the table shows the correlation coefficients between variables.

The matrix also shows p-values indicating if these relationships are statistically significant.

The correlation matrix can be easily computed with software programmes such as SPSS, STATA or R.

**Example**

Damian was asked to explain the relationships among variables in the study on the basis of a correlational matrix which was pretty similar to the one present below.

**I asked the questions like:**

- Can you find an example of a strong correlation at level p < 0.0001?
- Can you find an example of a negative correlation?
- Can you find an example of a weak correlation at level p < .05?
- Can you find an example of a weak correlation which is not statistically significant?
- Can you explain why some values have been replaced with ‘ -‘ ?
- What is the difference between p < 0.05 and p. < 0.0001?
- How many participants were in the study?
- Why is the upper-right triangle of the matrix empty?

Can you answer these questions?

**Possible answers**

- K Eng expressive and K Eng receptive r = .78
- K L1 vocabulary and K Eng receptive r = -.08
- S L1 vocabulary and K Eng receptive r = -.28
- K L1 vocabulary and K Eng receptive r = -.08
- A variable cannot correlate with itself
- p. < 0.0001 suggests a better evidence level than p < 0.05
- 158
- It would be a replication of the bottom-left triangle