Correlation and Causality
The correlation between two variables,
The following statements come from three different online blogs:
The oft-heard admonition against inferring cause from correlation is dangerous for two reasons. First, this warning implies that causal arguments are legitimate or not depending on the kind of statistical tool(s) used to analyze data. That notion of what’s needed to illuminate causal forces totally disregards the importance of research design. Statistical procedures can be helpful in studies that investigate cause; however, researchers concerned with causality must take care to reduce or eliminate alternative hypotheses for any causal connections suggested by their data. The warning that correlation ≠ cause is also dangerous because it functions to keep the logical and mathematical equivalence of certain statistical procedures hidden from view. Data can sometimes be analyzed in different ways and yet produce the exact same results. It’s important for researchers (and for the readers of their research reports) to know about these equivalencies. Otherwise, they will think that different analyses are accomplishing different objectives, when in fact those different analyses are doing exactly the same thing.
To show that correlation Suppose we randomly assign 100 people with headaches to two groups, a treatment group ( Many researchers would choose to analyze the data from this headache study with an independent-samples What’s important to realize is that the data of this hypothetical study could be examined using a correlation coefficient. If this had been done, the The data for this study might look like.
Had the results from this hypothetical study been correlated, they would have been identical to the results of the The Later in this book, we will consider misconceptions concerning
Would you like to see some convincing evidence that a correlation coefficient To locate the scores you will be analyzing, visit this book’s companion Web site (http://www.psypress.com/statistical-misconceptions). Once there, open the folder for Chapter 3 and click on the link called “Correlation and Causality.” There you will find the data along with detailed instructions (prepared by this book’s author) on how to enter a small set of raw scores into an online Java applet and how to get the applet to analyze the data in two different ways. You will also be given a link to that Java applet. The results provided by these two analyses you perform may surprise you! Note 1: The resulting correlation could be referred to as Pearson’s Note 2: A study’s internal validity is considered to be high if no confounding variables exist that might make (1) inert treatments appear to be potent or (2) potent treatments appear to be inert. When random assignment is used to form comparison groups, many (but not all) potential threats to internal validity vanish. |