Reading a correlation

Topic: Descriptive statistics · more questions on this topic
‹ Classifying variables in a nutrition survey

The sample correlation between \log_{10} serum creatinine and serum sodium in a heart-failure cohort is -0.26, and the correlation between \log_{10} serum creatinine and age is 0.23.

  1. Which pair moves together, and which pair moves in opposite directions?

  2. Why is neither correlation, by itself, a reason to conclude that one variable causes the other?

  1. Serum creatinine and age move together: the correlation 0.23 is positive, so older patients tend to have somewhat higher creatinine. Creatinine and sodium move in opposite directions: the correlation -0.26 is negative. Both are weak; a correlation of about \pm0.25 means a straight line accounts for only about 6% of the variance of either variable.

  2. A correlation measures linear association in this sample only. It can arise because a third variable drives both, here perhaps overall illness or kidney function, because the causal arrow points the other way, or by chance. These are observational data, so nothing was assigned and no causal reading follows from the correlation alone.