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Scatterplots are a graphical method used to display correlations and relationships between quantitative variables. They are particularly useful when the variable plotted on the $$x$$-axis—typically the independent variable—has a large number of distinct levels. In a scatterplot, scores are plotted at the intersection of the values on the $$x$$-axis and $$y$$-axis, with each individual data point representing a single participant's scores across the two variables. Unlike line graphs, the points in a scatterplot stand alone and are not connected by lines.

Scatterplots

A line of best fit, also referred to as a regression line, is a straight line drawn through a scatterplot that best represents the overall trend of the data points. It provides a visual summary of the relationship and correlation between the two quantitative variables being plotted.

Line of Best Fit

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 scatterplot demonstrating a negative correlation, like the relationship between tiredness and hours of sleep, displays data points that generally follow a downward-sloping line from the top left to the bottom right. This visual arrangement signifies that as one variable (tiredness) increases, the other variable (hours of sleep) tends to decrease.

Visual Example of Negative Correlation: Tiredness and Sleep

An example of no correlation, where two variables have no discernible relationship, is the connection between the number of hours a person sleeps and their shoe size. A scatterplot of this relationship shows data points scattered randomly with no clear pattern or line, indicating that knowing one variable provides no information for predicting the other.

Visual Example of No Correlation: Sleep and Shoe Size

Scatterplots are highly effective for visually illustrating the varying strengths and directions of Pearson's $$r$$. A perfect negative relationship ($$r = -1.00$$) is depicted as a tight, downward-sloping straight line, whereas a moderate negative relationship ($$r = -0.50$$) shows points loosely clustered around a downward trend. A value of $$r = 0$$ appears as a shapeless cloud of points, indicating no relationship. Conversely, a moderate positive relationship ($$r = +0.50$$) shows a loose upward trend, and a perfect positive relationship ($$r = +1.00$$) features points falling exactly on an upward-sloping diagonal line.

Example of Scatterplots for Pearson's r Values

When the variables plotted on the $$x$$-axis and $$y$$-axis of a scatterplot are conceptually similar and measured on the exact same scale—such as the same measure taken on two different occasions—researchers can emphasize this similarity by drawing both axes to be the exact same physical length.

Formatting Axes for Conceptually Similar Variables

In a scatterplot, two or more individuals may have identical scores, causing their data points to overlap perfectly. Researchers can visually indicate this overlap by offsetting the points slightly along the $$x$$-axis, printing the number of individuals in parentheses directly next to the point, or increasing the size or darkness of the point in proportion to the number of overlapping individuals.

Displaying Overlapping Points in Scatterplots

An APA-style scatterplot can effectively illustrate a strong positive correlation, such as the relationship between students' self-esteem scores measured one week apart. In this graph, the first set of scores is plotted on the $$x$$-axis and the second on the $$y$$-axis. Because the variables are conceptually identical and use the same numerical scale, both axes are drawn to the same length. A regression line can also be included to visually summarize the strong relationship ($$r = +0.96$$).

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