Correlation and Causality
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When the authors state that inferring that correlation between two variables implies causality between them is a frequent misinterpretation (in statistics and in education) what they mean to say is that the existence of a relationship between two variables is not sufficient to state that one variable causes the other. First, when one speaks of correlation between two variables one speaks of an association (a relationship) between those variables. Second, when one speaks of causation, or causality, one speaks of cause and effect (meaning that one variable is the cause and the second variable the inevitable effect). In order to understand more clearly why believing that correlation implies causation is erroneous one can fall back on the classic example of smoking and lung cancer. There is no question that there is a relationship between smoking and lung cancer, but proposing that smoking alone causes lung cancer (and that increased smoking increases lung cancer rates) is wrong. Other factors, or confounders, can explain the correlation between smoking and lung cancer; such factors include enhanced diagnosis, increased pollution, and genetic predisposition.
Based on what has been said, it follows that implying causality between assessments and learning simply because there is correlation between them is a mistake (and also potentially dangerous). There is a relationship between assessments and learning, but it cannot be said that assessments cause students to learn. True, students who perform well on assessments have generally learned more than those who perform poorly. However, it cannot be written in stone that assessments are the cause of learning. The correlation between both variables might be explained by a number of confounders such as cheating, good guessing (in multiple choice assessments), and memorization (which is not the same as learning). Teachers must remember that effective learning can be explained by factors other than good results on assessments. In fact, in order to potentiate effective learning it is imperative that teachers come to realize that correlation by no means implies causality.