what does it mean to say that two variables are negatively correlated?

Learning Objectives

• Explain what a correlation coefficient tells us about the human relationship between variables
• Describe why correlation does not mean causation

Did you know that every bit sales in water ice foam increment, so does the overall charge per unit of crime? Is it possible that indulging in your favorite flavor of ice foam could send y'all on a crime spree? Or, afterwards committing crime do yous think you might make up one's mind to treat yourself to a cone? In that location is no question that a relationship exists between water ice cream and crime (e.g., Harper, 2013), but it would be pretty foolish to determine that 1 thing actually acquired the other to occur.

It is much more likely that both ice foam sales and offense rates are related to the temperature outside. When the temperature is warm, there are lots of people out of their houses, interacting with each other, getting bellyaching with one another, and sometimes committing crimes. As well, when it is warm exterior, we are more likely to seek a cool treat similar water ice cream. How do we decide if there is indeed a relationship between two things? And when there is a relationship, how tin can we discern whether it is attributable to coincidence or causation?

Correlational Research

Correlation means that there is a relationship between ii or more variables (such as ice cream consumption and crime), just this human relationship does non necessarily imply cause and effect. When 2 variables are correlated, it simply means that as 1 variable changes, so does the other. We tin can measure correlation past computing a statistic known equally a correlation coefficient. A correlation coefficient is a number from -1 to +ane that indicates the force and management of the human relationship between variables. The correlation coefficient is ordinarily represented by the alphabetic character r.

The number portion of the correlation coefficient indicates the forcefulness of the relationship. The closer the number is to 1 (be it negative or positive), the more strongly related the variables are, and the more predictable changes in 1 variable volition be as the other variable changes. The closer the number is to zero, the weaker the relationship, and the less predictable the relationships between the variables becomes. For case, a correlation coefficient of 0.9 indicates a far stronger relationship than a correlation coefficient of 0.3. If the variables are not related to one some other at all, the correlation coefficient is 0. The example in a higher place nigh ice cream and criminal offense is an example of two variables that nosotros might wait to accept no human relationship to each other.

The sign—positive or negative—of the correlation coefficient indicates the direction of the relationship (Figure 1). A positive correlation ways that the variables move in the same direction. Put another fashion, information technology means that as i variable increases so does the other, and conversely, when one variable decreases so does the other. A negative correlation means that the variables motion in opposite directions. If two variables are negatively correlated, a decrease in one variable is associated with an increase in the other and vice versa.

The example of water ice foam and law-breaking rates is a positive correlation considering both variables increment when temperatures are warmer. Other examples of positive correlations are the human relationship between an private'south height and weight or the human relationship between a person's historic period and number of wrinkles. 1 might await a negative correlation to be between someone's tiredness during the day and the number of hours they slept the previous dark: the amount of slumber decreases every bit the feelings of tiredness increment. In a real-globe example of negative correlation, student researchers at the University of Minnesota found a weak negative correlation (r = -0.29) between the average number of days per week that students got fewer than 5 hours of sleep and their GPA (Lowry, Dean, & Manders, 2010). Proceed in mind that a negative correlation is not the same as no correlation. For example, we would probably detect no correlation between hours of slumber and shoe size.

Equally mentioned earlier, correlations have predictive value. Imagine that you lot are on the admissions committee of a major university. Y'all are faced with a huge number of applications, just yous are able to accommodate merely a small percentage of the applicant pool. How might y'all decide who should be admitted? You might try to correlate your current students' college GPA with their scores on standardized tests like the Saturday or Human activity. By observing which correlations were strongest for your current students, you could use this information to predict relative success of those students who accept applied for admission into the university.

Effigy 1. Scatterplots are a graphical view of the strength and direction of correlations. The stronger the correlation, the closer the data points are to a straight line. In these examples, nosotros run across that at that place is (a) a positive correlation between weight and height, (b) a negative correlation between tiredness and hours of sleep, and (c) no correlation between shoe size and hours of slumber.

Try It

Correlation Does Not Betoken Causation

Correlational research is useful because it allows us to find the forcefulness and management of relationships that exist between ii variables. However, correlation is limited considering establishing the beingness of a human relationship tells usa lilliputian nearly cause and consequence. While variables are sometimes correlated considering one does cause the other, it could also be that some other factor, a confounding variable, is actually causing the systematic move in our variables of involvement. In the water ice cream/crime rate example mentioned earlier, temperature is a misreckoning variable that could account for the relationship between the two variables.

Even when we cannot bespeak to clear confounding variables, nosotros should non assume that a correlation betwixt two variables implies that ane variable causes changes in another. This tin can be frustrating when a cause-and-issue relationship seems clear and intuitive. Recollect back to our discussion of the research done by the American Cancer Lodge and how their research projects were some of the start demonstrations of the link between smoking and cancer. It seems reasonable to presume that smoking causes cancer, only if we were limited to correlational research, nosotros would exist overstepping our premises past making this assumption.

Unfortunately, people mistakenly brand claims of causation as a part of correlations all the time. Such claims are especially common in advertisements and news stories. For case, recent research found that people who eat cereal on a regular basis achieve healthier weights than those who rarely eat cereal (Frantzen, Treviño, Echon, Garcia-Dominic, & DiMarco, 2013; Barton et al., 2005). Gauge how the cereal companies report this finding. Does eating cereal really cause an individual to maintain a healthy weight, or are there other possible explanations, such as, someone at a healthy weight is more probable to regularly consume a healthy breakfast than someone who is obese or someone who avoids meals in an effort to diet (Figure two)? While correlational research is invaluable in identifying relationships amidst variables, a major limitation is the disability to establish causality. Psychologists desire to make statements about cause and effect, merely the just way to practice that is to conduct an experiment to answer a research question. The next department describes how scientific experiments comprise methods that eliminate, or command for, culling explanations, which allow researchers to explore how changes in one variable cause changes in another variable.

Try It

Watch It

Watch this clip from Freakonomics for an instance of how correlation doesnotindicate causation.

Figure 2. Does eating cereal really cause someone to exist a healthy weight? (credit: Tim Skillern)

Illusory Correlations

The temptation to make erroneous cause-and-effect statements based on correlational research is non the only mode we tend to misinterpret information. We besides tend to brand the fault of illusory correlations, especially with unsystematic observations. Illusory correlations, or false correlations, occur when people believe that relationships be between two things when no such relationship exists. One well-known illusory correlation is the supposed effect that the moon'due south phases take on human behavior. Many people passionately assert that human behavior is afflicted by the phase of the moon, and specifically, that people act strangely when the moon is full (Effigy iii).

Figure 3. Many people believe that a full moon makes people behave oddly. (credit: Cory Zanker)

There is no denying that the moon exerts a powerful influence on our planet. The ebb and flow of the bounding main's tides are tightly tied to the gravitational forces of the moon. Many people believe, therefore, that it is logical that we are afflicted by the moon too. Afterward all, our bodies are largely fabricated upwardly of h2o. A meta-assay of nearly 40 studies consistently demonstrated, all the same, that the relationship between the moon and our behavior does not be (Rotton & Kelly, 1985). While we may pay more attention to odd behavior during the full phase of the moon, the rates of odd beliefs remain constant throughout the lunar cycle.

Why are nosotros and so apt to believe in illusory correlations similar this? Often we read or hear almost them and simply accept the information as valid. Or, nosotros accept a hunch virtually how something works and then wait for show to support that hunch, ignoring prove that would tell the states our hunch is false; this is known as confirmation bias. Other times, we discover illusory correlations based on the information that comes most easily to mind, even if that information is severely express. And while nosotros may feel confident that nosotros can use these relationships to improve understand and predict the earth effectually u.s., illusory correlations can take significant drawbacks. For example, research suggests that illusory correlations—in which certain behaviors are inaccurately attributed to certain groups—are involved in the formation of prejudicial attitudes that can ultimately pb to discriminatory beliefs (Fiedler, 2004).

Endeavour It

Think Information technology Over

We all accept a tendency to brand illusory correlations from fourth dimension to time. Try to think of an illusory correlation that is held by you lot, a family member, or a close friend. How do you lot call back this illusory correlation came about and what can exist done in the future to combat them?

Glossary

crusade-and-issue relationship:changes in one variable cause the changes in the other variable; can be determined only through an experimental inquiry blueprint

confirmation bias:tendency to ignore evidence that disproves ideas or beliefs

confounding variable:unanticipated outside factor that affects both variables of interest, ofttimes giving the simulated impression that changes in one variable causes changes in the other variable, when, in authenticity, the exterior factor causes changes in both variables

correlation:relationship between two or more variables; when two variables are correlated, one variable changes as the other does

correlation coefficient:number from -1 to +1, indicating the strength and direction of the relationship betwixt variables, and usually represented by r

illusory correlation:seeing relationships between two things when in reality no such relationship exists

negative correlation:ii variables alter in different directions, with one becoming larger as the other becomes smaller; a negative correlation is not the same thing as no correlation

positive correlation two variables change in the same direction, both becoming either larger or smaller

wayperes1939.blogspot.com

Source: https://courses.lumenlearning.com/wmopen-psychology/chapter/reading-correlational-research/

Share this post