Understanding correlation matrix

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.


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.


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:

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

Can you answer these questions?

Possible answers

  1. K Eng expressive and K Eng receptive r = .78
  2. K L1 vocabulary and  K Eng receptive r = -.08
  3. S L1 vocabulary and  K Eng receptive r = -.28
  4. K L1 vocabulary and  K Eng receptive r = -.08
  5.  A variable cannot correlate with itself
  6.  p. < 0.0001 suggests a better evidence level than p < 0.05
  7. 158
  8. It would be a replication of the bottom-left triangle


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