Name: reading correlation coefficients
Uploaded: 2020-02-12T11:07:40.000Z
Duration: 2 min 20 s
Channel: JoVE

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High School

Biology

BIO.2

BIO.2.B

Correlations

Sometimes, researchers may choose to more passively interact with a phenomenon, rather than to intervene and manipulate the behaviors of interest.

For instance, perhaps a scientist wants to know if there&rsquo;s an association between eating a plant-based diet and sleep. In this case, she quantitatively measures two variables by asking participants to report how many vegetables they consumed that day, and later, how many hours they slept.

This design is known as correlational research&mdash;examining whether relationships exist between two variables.

After collecting both series of measurements, the researcher can visualize the data for each unit, in this case each person, on a graph&mdash;a scatterplot&mdash;with the variables&mdash;daily vegetable consumption and amount of sleep&mdash;placed on either axis.

Statistically, correlations are determined by calculating the correlation coefficient, commonly denoted as r&mdash;a number between -1 and 1 that indicates the direction, the sign, of the association and its overall strength, how tight the points align.

Here, the correlation could be positive, which means that the two variables move in the same direction. That is, people who consumed very few veggies slept less, where

correlations

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between variables. The correlation coefficient is usually represented by the letter r.

The number portion of the correlation coefficient indicates the strength 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 one variable will 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 instance, 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 another at all, the correlation coefficient is 0.

The sign&mdash;positive or negative&mdash;of the correlation coefficient indicates the direction of the relationship. A positive correlation means that the variables move in the same direction. Put another way, it means that as one variable increases so does the other, and conversely, when one variable decreases so does the other. A negative correlation means that the variables move 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.

Examples of positive correlations are the relationship between an individual&rsquo;s height and weight or the relationship between a person&rsquo;s age and number of wrinkles. One might expect a negative correlation to exist between someone&rsquo;s tiredness during the day and the number of hours they slept the previous night: the amount of sleep decreases as the feelings of tiredness increase. In a real-world 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, &amp; Manders, 2010). Keep in mind that a negative correlation is not the same as no correlation. For example, we would probably find no correlation between hours of sleep and shoe size.

Correlations have predictive value. Imagine that you are on the admissions committee of a major university. You are faced with a huge number of applications, but you are able to accommodate only a small percentage of the applicant pool. How might you decide who should be admitted? You might try to correlate your current students&rsquo; college GPA with their scores on standardized tests like the SAT or ACT. By observing which correlations were strongest for your current students, you could use this information to predict relative success of those students who have applied for admission into the university.

Correlation Does Not Indicate Causation

Correlational research is useful because it allows us to discover the strength and direction of relationships that exist between two variables. However, correlation is limited because establishing the existence of a relationship tells us little about cause and effect. While variables are sometimes correlated because one does cause the other, it could also be that a third variable is actually causing the systematic movement in our variables of interest. For example, wealth may be positively correlated with intelligence, but that is likely because wealthy people can afford higher education, which in turn increases intelligence.

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This text is adapted from <a href="https://cnx.org/contents/Sr8Ev5Og@10.24:mfArybye@16/2-3-Analyzing-Findings" target="_blank">OpenStax, Psychology. OpenStax CNX.</a>

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not ...

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KEY TERMS AND CONCEPTS

reading correlation coefficients

Correlation describes a relationship between two or more variables. It does not automatically mean that one variable causes the other. When variables are correlated, one changes as the other changes, and that relationship can be measured with a correlation coefficient.

A correlation coefficient is a number from -1 to +1. It is usually written as r. The number shows the strength of the relationship. Values closer to 1, whether positive or negative, show a stronger relationship and make changes more predictable. Values closer to 0 show a weaker relationship. If two variables are not related at all, the correlation coefficient is 0.

The sign of the correlation coefficient shows direction. A positive correlation means both variables move in the same direction. When one increases, the other increases too. When one decreases, the other decreases too. A negative correlation means the variables move in opposite directions. If one decreases, the other increases.

Real-life examples help show the difference. Height and weight are often positively correlated. Age and the number of wrinkles are also positively correlated. Tiredness during the day and the number of hours slept the night before may show a negative correlation. Student researchers at the University of Minnesota found a weak negative correlation, r = -0.29, between the number of days per week students got fewer than 5 hours of sleep and their GPA. Sleep hours and shoe size would likely show no correlation.

Correlations can also help with prediction. A university admissions committee might compare current students’ college GPA with SAT or ACT scores. If a strong correlation appears, that information can help predict how well future applicants may do. Correlational research is useful for finding the strength and direction of a relationship, but it still does not prove cause and effect. Sometimes a third variable may be driving the pattern, such as wealth appearing linked to intelligence because higher income can provide access to education.

Reading Correlation Coefficients

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Correlation describes a relationship between two or more variables. It does not automatically mean that one variable causes the other. When variables are correlated, one changes as the other changes, and that relationship can be measured with a correlation coefficient. A correlation coefficient is a number from -1 to +1. It is usually written as r. The number shows the strength of the relationship. Values closer to 1, whether positive or negative, show a stronger relationship and make changes...

cause and effect

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Correlation can be misleading when two variables move together for a different reason. A confounding variable, or hidden factor, may be causing the pattern instead of one variable directly affecting the other. The ice cream and crime example shows this clearly. When temperatures rise, more people go outside, buy ice cream, and may also have more chances for conflict. A correlation does not prove causation. Even when a relationship looks strong, we should not assume that one variable causes the...

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key terms and concepts

Learn how to read correlation coefficients, including positive and negative correlations, strength, direction, prediction, and why correlation does not prove causation.

Reading Correlation Coefficients | JoVE K12

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Reading Correlation Coefficients

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