You observe a statistically significant positive correlation between exercise and cases of skin cancer—that is, the people who exercise more tend to be the people who get skin cancer. This correlation seems strong and reliable, and shows up across multiple populations of patients.
Without exploring further, you might conclude that exercise somehow causes cancer! Based on these findings, you might even develop a plausible hypothesis: perhaps the stress from exercise causes the body to lose some ability to protect against sun damage. This shows up in their data as increased exercise. At the same time, increased daily sunlight exposure means that there are more cases of skin cancer. Both of the variables—rates of exercise and skin cancer—were affected by a third, causal variable—exposure to sunlight—but they were not causally related.
Distinguishing between what does or does not provide causal evidence is a key piece of data literacy. Determining causality is never perfect in the real world. However, there are a variety of experimental, statistical and research design techniques for finding evidence toward causal relationships: e.
Beyond the intrinsic limitations of correlation tests e. For example, imagine again that we are health researchers, this time looking at a large dataset of disease rates, diet and other health behaviors.
Suppose that we find two correlations: increased heart disease is correlated with higher fat diets a positive correlation , and increased exercise is correlated with less heart disease a negative correlation.
This is also referred to as cause and effect. Spurious Correlations is an entertaining resource that shares examples that show strong relationships between variables but that are not caused by one another. At least, they should not be. Source: tylervigen. Sticking to food examples, could cheese be the secret fuel that powers civil engineers in their studies? Both charts show strong correlations between dependent and independent variables.
However, these are likely classic cases of "correlation does not imply causation. The correlation and causation examples above show the importance of getting the difference right is critical. Avinash Kaushik, Digital Marketing Evangelist at Google, wrote in about how not understanding the difference can be very problematic. Kaushik highlighted an article from The Economist that asserted that eating more ice cream can boost student scores on the PISA reading scale.
Oh, and look there is a red line, what looks like a believable distribution, and a R-squared! But Kaushik wants us to think a bit harder about the data at hand, and not take things at face value. He points out that there is nothing to ground the causation of one and the other despite a reasonable correlation. There may appear to be a link connecting IQ to ice cream consumption.
However, the data doesn't definitively reveal anything aside from that obvious correlation. In our everyday lives, we have access to more data than ever before. Decisions, opinions, and even business strategies can depend on our ability to tell the difference between them. Kaushik uses the example above to remind people to be more skeptical of claims that draw bold conclusions from correlated data points.
He encourages readers to look deeper at the data and avoid easy decisions. Causality vs. Molnar warns that:. It can be difficult to infer causation between two variables. Randomized controlled experiences and other statistical tests are often needed to validate if one variable does, in fact, impact another.
Moreover, while correlations can be useful measures, they have limitations. As we saw in the correlation vs. In today's data-driven world, being more skeptical of specific findings before making bold claims, as Kaushik suggests, is essential.
A strong correlation means that we can zoom in much, much further until we have to worry about this relation not being true. If we take our strong positive and strong negative correlation from above, and we also zoom in to the x region between 0 — 4, we see the following:. The top row shows us what the strong correlations look like when we zoom into the x between 0 — 4 region. To get into the region where this correlation no longer holds, we have to zoom in pretty far, which is what we can see in the bottom row of the above graph.
Here, we zoomed into the region where x is between 0. At this scale, our correlations are no longer visible, even in a weak manner. Another commonly misunderstood thing about correlations is that the correlation strength depends on the slope.
Take a look at the following graphs. All of them, except for one, show a strong correlation with the exact same strength. Notice how we can have a strong correlation regardless of if we have a large left column or small middle column slope.
The right-most column shows a graph with no correlation, despite there being essentially no noise. This is because of the way correlations are defined: how much a change in one variable affects the other variable. You may have noticed that the middle column of the above graph looks more like a perfect correlation than the left-most column.
This is because the correlation strengths depend on the scale of your noise relative to the slope. So for the middle and left column to have the same correlation strength, the scale of the noise in the middle column has to be smaller than the scale of the noise in the left column, since the middle column has a smaller shallower slope. Noise references the variation in your data. We can see on our y-axis that the y values go from about 0 — 4, yet the width of our line is about 2.
Our data still fluctuates a little, but not very much. In this case, we have little noise. The right-most column has no fluctuations at all and shows a perfect, straight line with no noise. We also only compared our noise to the y-values, but both x and y data points will have noise that affects them. The best way to visualize this would be in a histogram , which could look like this:.
Normally, after you plot the data points that you do have, a distribution shape emerges and you can estimate the shape of the distribution based on the points that you do have.
The perfect distribution is what your distribution would look like if you had infinite amount of data points. This distribution can take on any shape; it does not have to be a normal distribution, like the one shown above. The variation from a perfect distribution that we see in the histogram is another form of noise. So in all data analyses that you ever do, noise is something to keep in mind, and ideally, you would minimize the impact of noise in your data. Your data is always going to be affected by noise, but if you want to try to reduce the amount of noise in your data, you can try to control for some of the sources of noise.
So what you want to do is identify your biggest sources of noise , i. They can also come in many different forms, such as linear, quadratic, exponential, logarithmic and basically any other function you can think of.
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