Real-world examples of positive correlations include the relationship between ice cream and crime rates, which both increase when temperatures are warmer. Other examples are the relationship between an individual’s height and weight, and the relationship between a person’s age and the number of wrinkles they have.

Examples of Positive Correlation

A scatterplot illustrating a positive correlation, such as the relationship between weight and height, displays data points that roughly form an upward-sloping line from the bottom left to the top right. This visual pattern indicates that as one variable (weight) increases, the other variable (height) also tends to increase.

Visual Example of Positive Correlation: Height and Weight

A psychologist conducts a study and finds that as the number of hours people spend on social media per week increases, their self-reported feelings of loneliness also tend to increase. Which of the following terms best describes the relationship found between these two variables?

A classic example of a positive correlation is the relationship between an individual's height and weight. As a person's height increases, their weight also tends to increase, demonstrating that the two variables change in the same direction.

Example of Positive Correlation: Height and Weight

A clear demonstration of a positive correlation is the relationship between individuals' stress levels and the number of physical symptoms they experience. When these hypothetical data points are graphed on a scatterplot, the overall trend reveals that as stress scores increase, the frequency of physical symptoms also tends to increase. This upward pattern indicates that the two variables move in the same direction, which is the defining characteristic of a positive relationship.

Example of a Positive Correlation: Stress and Physical Symptoms

A clear example of a positive correlation can be seen when plotting students' scores on the Rosenberg Self-Esteem Scale administered on two occasions a week apart. Because higher scores on the first test are associated with higher scores on the second test, the data points on a scatterplot progress from the lower left to the upper right, visually demonstrating that the variables change in the same direction.

Example of a Positive Relationship: Rosenberg Self-Esteem Scale Scores

In psychological research, how is a positive relationship between two variables defined?

A positive relationship, or positive correlation, occurs when higher scores on one variable tend to be associated with higher scores on another variable. On a scatterplot, this is visually represented by data points that generally trend upward from the lower left to the upper right of the graph.

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The sign of a correlation coefficient, whether positive or negative, indicates the direction of the relationship between variables. Based on this directionality, correlations can be classified into three main types: positive, negative, and zero (no correlation).

Types of Correlation

A fundamental form of statistical relationship involves the connections or correlations between continuous, quantitative variables. In psychological research, understanding these relationships is crucial for determining how variations in one measurable quantity correspond to changes in another.

Relationships Between Quantitative Variables

Spielman, R. M., Jenkins, W. J., & Lovett, M. D. (2020, April 22). Psychology (2nd ed.). OpenStax. https://openstax.org/books/psychology-2e/pages/1-introduction

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KPU Research Methods in Psychology - 4th American Edition

A perfect positive correlation is indicated when the correlation coefficient, denoted by r, is equal to +1. This signifies a perfect direct linear relationship between two variables, meaning that as one variable increases, the other also increases by a perfectly predictable amount. The mathematical representation is: $$r = 1$$

Perfect Positive Correlation

A zero correlation exists when the correlation coefficient is exactly 0. This signifies that there is no discernible linear relationship between two variables. As a result, knowing the value of one variable provides no basis for predicting the value of the other.

Zero Correlation

A researcher investigates the relationship between the number of hours a student spends playing video games per week and their grade point average (GPA). The study yields a correlation coefficient of r = -0.65. Which statement provides the most accurate analysis of this finding?

Correlations can be described using everyday language that indicates how variables change together. For example, the statement "there is no relationship between height and weight" describes a zero correlation. Statements such as "usually, the taller someone is, the thinner they are" or "usually, the shorter someone is, the heavier they are" describe a negative correlation, where the two variables move in opposite directions. Conversely, a positive correlation is represented by a statement such as "as height increases, typically weight increases," indicating that both variables move in the same direction.

Verbal Descriptions of Correlations

A negative relationship, or negative correlation, occurs when higher scores on one variable tend to be associated with lower scores on another variable. On a scatterplot, this type of relationship is illustrated by data points that generally trend downward from the upper left to the lower right of the graph.

Negative Relationship

Positive Relationship

Pearson's $$r$$ is a specific statistical metric utilized to describe and quantify the correlations between quantitative variables. It provides a standardized measure to evaluate the strength and direction of the linear relationship between two continuous factors.

Pearson's r

A linear relationship is a statistical association between quantitative variables in which the data points on a scatterplot are reasonably well fit by a single straight line. Both positive and negative correlations are examples of linear relationships, provided their points form a straight linear trend rather than a curve.

Linear Relationship

A nonlinear relationship is a statistical association between quantitative variables where the data points on a scatterplot are better represented by a curved line rather than a single straight line. Unlike linear relationships, nonlinear correlations exhibit a changing rate or direction across the range of the variables. Because standard correlation metrics like Pearson's $$r$$ only measure linear trends, they can misleadingly indicate a weak relationship even when a strong nonlinear pattern is present.

Nonlinear Relationship

When psychological researchers examine a statistical relationship to determine how variations in one continuous, measurable quantity correspond to changes in another, what type of variables are they investigating?

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