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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.g., randomization, controlled experiments and predictive models with multiple variables. Beyond the intrinsic limitations of correlation tests (e.g., correlations cannot not measure trivariate, potentially causal relationships), it's important to understand that evidence for causation typically comes not from individual statistical tests but from careful experimental design. Example: Heart disease, diet and exerciseFor 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). Both of these correlations are large, and we find them reliably. Surely this provides a clue to causation, right? In the case of this health data, correlation might suggest an underlying causal relationship, but without further work it does not establish it. Imagine that after finding these correlations, as a next step, we design a biological study which examines the ways that the body absorbs fat, and how this impacts the heart. Perhaps we find a mechanism through which higher fat consumption is stored in a way that leads to a specific strain on the heart. We might also take a closer look at exercise, and design a randomized, controlled experiment which finds that exercise interrupts the storage of fat, thereby leading to less strain on the heart. All of these pieces of evidence fit together into an explanation: higher fat diets can indeed cause heart disease. And the original correlations still stood as we dove deeper into the problem: high fat diets and heart disease are linked! But in this example, notice that our causal evidence was not provided by the correlation test itself, which simply examines the relationship between observational data (such as rates of heart disease and reported diet and exercise). Instead, we used an empirical research investigation to find evidence for this association.
A correlation coefficient, often expressed as r, indicates a measure of the direction and strength of a relationship between two variables. When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables.
Correlational studies are quite common in psychology, particularly because some things are impossible to recreate or research in a lab setting. Instead of performing an experiment, researchers may collect data to look at possible relationships between variables. From the data they collect and its analysis, researchers then make inferences and predictions about the nature of the relationships between variables.
A correlation is a statistical measurement of the relationship between two variables. Remember this handy rule: The closer the correlation is to 0, the weaker it is. The closer it is to +/-1, the stronger it is. Correlation strength ranges from -1 to +1. A correlation of +1 indicates a perfect positive correlation, meaning that both variables move in the same direction together. A correlation of –1 indicates a perfect negative correlation, meaning that as one variable goes up, the other goes down.
A zero correlation suggests that the correlation statistic does not indicate a relationship between the two variables. This does not mean that there is no relationship at all; it simply means that there is not a linear relationship. A zero correlation is often indicated using the abbreviation r = 0. Scatter plots (also called scatter charts, scattergrams, and scatter diagrams) are used to plot variables on a chart to observe the associations or relationships between them. The horizontal axis represents one variable, and the vertical axis represents the other. Scatter Plot diagram.
Each point on the plot is a different measurement. From those measurements, a trend line can be calculated. The correlation coefficient is the slope of that line. When the correlation is weak (r is close to zero), the line is hard to distinguish. When the correlation is strong (r is close to 1), the line will be more apparent. Correlations can be confusing, and many people equate positive with strong and negative with weak. A relationship between two variables can be negative, but that doesn't mean that the relationship isn't strong. A weak positive correlation indicates that, although both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, indicates a strong connection between the two variables, but that one goes up whenever the other one goes down.
For example, a correlation of -0.97 is a strong negative correlation, whereas a correlation of 0.10 indicates a weak positive correlation. A correlation of +0.10 is weaker than -0.74, and a correlation of -0.98 is stronger than +0.79. Correlation does not equal causation. Just because two variables have a relationship does not mean that changes in one variable cause changes in the other. Correlations tell us that there is a relationship between variables, but this does not necessarily mean that one variable causes the other to change.
An oft-cited example is the correlation between ice cream consumption and homicide rates. Studies have found a correlation between increased ice cream sales and spikes in homicides. However, eating ice cream does not cause you to commit murder. Instead, there is a third variable: heat. Both variables increase during summertime. An illusory correlation is the perception of a relationship between two variables when only a minor relationship—or none at all—actually exists. An illusory correlation does not always mean inferring causation; it can also mean inferring a relationship between two variables when one does not exist. For example, people sometimes assume that, because two events occurred together at one point in the past, one event must be the cause of the other. These illusory correlations can occur both in scientific investigations and in real-world situations. Stereotypes are a good example of illusory correlations. Research has shown that people tend to assume that certain groups and traits occur together and frequently overestimate the strength of the association between the two variables.
For example, suppose someone holds the mistaken belief that all people from small towns are extremely kind. When they meet a very kind person, their immediate assumption might be that the person is from a small town, despite the fact that kindness is not related to city population. Psychology research makes frequent use of correlations, but it's important to understand that correlation is not the same as causation. This is a frequent assumption among those not familiar with statistics and assumes a cause-effect relationship that might not exist. Frequently Asked Questions
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Which best describes the strength of the correlation and what is true about the causation between the variables?
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