### Math 221 – Principles of Statistics

Scatterplots Reference Page

Purpose: Scatterplots are used to determine whether there is some kind of association between two variables.

Conditions: None, though scatterplots are be more informative when both variables are quantitative, or at least ordinal.

How to Create Them: Simply set up two axes, as for a graph, and label each axis with one of the variables. Carefully mark appropriate scales on your axes, then plot your data points the same way you plotted points in Algebra class. DO NOT CONNECT THE DOTS. There is no justification for doing so.

Interpretation: Once the plot is constructed, decide whether there is a pattern in the plot. If so, look for the following things in it:

Form: If the pattern is roughly straight, call it “linear.” In Math 221, all other patterns can safely be called “nonlinear.”  But to be more specific, you can use words and phrases like "bulging" and "fan-shaped."

Direction: If the pattern goes up as you go left-to-right, say there is a positive association between the two variables.  If the pattern goes down as you go from left-to-right, say there is a negative association between the two variables. If there is no clear positive or negative association, or if your perception of a positive or negative association depends on the presence of one or two points, say there is no association between the two variables.

Strength: The more closely the points follow the pattern you perceive, the stronger the association is. Weak associations tend to look more like strung-out blobs of points. If the scatterplot looks like a shotgun blast, there probably isn’t any association to speak of.

Deviations: Any point or group of points “far away” from the main body or main pattern should be labeled “unusual” and investigated. There are four types: Outliers are points far above or below the main pattern. Influential points are far away horizontally. Points far away both vertically and horizontally will strongly affect any calculations you make concerning relationships between the variables, as will influential points. Points far away that seem to follow the pattern are of less concern and therefore have no name of their own. In any case, unusual points tend to render conclusions drawn from scatterplots somewhat unreliable.

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