Compare Patterns on Shared Scales
In “Association Versus Linear Association,” you learned that strength and form describe different features of a scatterplot. Strength concerns how closely the points follow the overall pattern; form concerns whether that pattern is roughly straight or curved. When two scatterplots show the same variables, comparing these features helps you describe how their associations differ.
A fair visual comparison starts by checking the axes. Matching variables, units, axis limits, and tick intervals makes a direct comparison easier to see and interpret. If the scales differ, a comparison is not automatically meaningless, but the differences can change how patterns look. Account for the scales before drawing conclusions—for example, by checking the axis labels and limits carefully or displaying the data on common axes.
For a comparison to make sense, also check that the plots concern the same explanatory and response variables, measured in the same units. If one plot shows practice hours versus a score out of 100 and another shows minutes versus a score out of 10, the pictures cannot be compared directly as displayed. First understand what differs; then use a suitable common display or explicitly account for the different units and scales.
Strength is judged relative to the pattern in each plot. In a roughly linear plot, consider how much the points scatter around the straight trend. In a curved plot, consider how closely they follow the curve. As you learned in “Judging Strength of an Association,” a strong pattern can be either straight or curved. The pattern’s shape does not determine its strength.
A Reliable Way to Write the Comparison
A useful comparison names the variables, identifies the feature being compared, and states the difference directly. Avoid making the reader infer the comparison from two separate descriptions. For instance, “Both plots show a positive, roughly linear association, but the points in Plot A fall more closely around the trend than the points in Plot B, so Plot A shows the stronger linear association” makes the comparison explicit.
When form differs, say so separately from strength. You might write, “Plot A is roughly linear, while Plot B bends upward and levels off.” If the points in one plot also follow their pattern more closely, add that comparison. If the plots have similar strength, say that too; not every pair of plots differs on both features.
Confirm that both plots show the same variables and units. Check axis limits and tick intervals; if they differ, account for the difference before comparing appearances.
Decide whether each overall pattern is roughly straight or has a systematic bend. Do not use “strong” as a substitute for “linear.”
Judge how closely the points follow each plot’s own overall pattern. Do not compare strength by steepness, axis range, or direction.
Name what the plots represent, contrast their forms and strengths, and avoid claiming a cause-and-effect relationship that the plots alone cannot establish.
Compare Strength When Form Is Similar
It is especially straightforward to compare strength when both plots have similar form. For two roughly linear patterns, look at how much the points vary around each straight trend. A tighter grouping around the trend indicates a stronger linear association; more scatter indicates a weaker one. This is a visual judgment, not a claim that every point must sit exactly on a line.
The table below gives invented observations for two fictional groups of students. In each plot, the explanatory variable is practice time in hours and the response is a skill score in points. Imagine plotting both groups with the same horizontal scale from 0 to 7 hours and the same vertical scale from 0 to 50 points. The listed pairs allow you to inspect the patterns; they are not real study results.
Worked Example: Comparing Two Practice-Time Plots
| Practice time (hours) | Group A score (points) | Group B score (points) |
|---|---|---|
| 1 | 16 | 8 |
| 2 | 19 | 27 |
| 3 | 27 | 18 |
| 4 | 28 | 39 |
| 5 | 36 | 24 |
| 6 | 39 | 43 |
Compare the scales. Both plots have practice time in hours on the horizontal axis and skill score in points on the vertical axis. With shared axes from 0 to 7 hours and 0 to 50 points, their visual spread can be compared directly.
Compare form. In both groups, scores tend to be higher at greater practice times. The overall patterns are positive and roughly linear; neither set shows a clear bend. Group B’s points fluctuate more from one practice time to the next, but that scatter does not create a systematic curve.
Compare strength. Group A’s points follow a straight upward trend more closely. Group B also has an overall upward trend, but its observations are more scattered around that trend. Thus, Group A shows the stronger linear association.
Comparison in context. For these invented observations, practice time and skill score have positive, roughly linear associations in both groups, but the association is stronger for Group A because its scores lie more closely around the upward pattern. This visual comparison does not establish that additional practice caused higher scores.
Notice what the comparison does not say: Group B is not weaker simply because its scores cover a different range, and Group A is not stronger because its trend is steeper. The relevant visual feature is the scatter of points around the overall pattern.
Compare Form Without Confusing It With Strength
Two plots can have different forms even when both have a positive direction. In one, the response may rise at a fairly steady rate, creating a roughly straight pattern. In another, the response may rise quickly at first and then level off, creating a curve. A comparison should name that difference in form directly.
The next invented example compares two plant varieties at different light levels. Both plots use the same explanatory variable, light level in hundreds of lux, and response variable, oxygen production rate in units per hour. Imagine that both are shown with horizontal limits from 0 to 5 and vertical limits from 0 to 20, with the same tick spacing.
Worked Example: Comparing Form in Light-Level Plots
| Light level (hundreds of lux) | Variety A oxygen rate (units/hour) | Variety B oxygen rate (units/hour) |
|---|---|---|
| 0 | 2 | 2 |
| 1 | 5 | 8 |
| 2 | 8 | 13 |
| 3 | 11 | 16 |
| 4 | 14 | 18 |
| 5 | 17 | 19 |
Describe the directions and forms. Both response values generally increase as light level increases, so both associations have a positive direction. Variety A’s rate rises by 3 units per hour for every one-unit increase in the listed light level, making its pattern roughly linear. Variety B’s increases become smaller across the listed levels: 6, 5, 3, 2, and 1 unit per hour. Its pattern rises and then levels off, so it is curved rather than roughly linear.
Compare strength cautiously. The table suggests a clear pattern for each variety, but form is the main difference supported here: Variety A is roughly linear, whereas Variety B follows a positive curve that flattens. Do not call one association stronger merely because its response values change more or because its pattern has a different shape. Strength concerns closeness to each pattern, not the amount of increase.
Comparison in context. In these invented observations, light level and oxygen production rate are positively associated for both varieties. The pattern is roughly linear for Variety A, while Variety B’s rate rises and then levels off, producing a curved form. These observations alone do not show that light level caused the differences.
The changing increases help reveal the bend in Variety B’s pattern, but a scatterplot remains the main display for judging form. In real data, individual observations vary; do not require the increases to be exactly constant for a relationship to be roughly linear, or strictly decreasing for a curve to be recognizable.
Compare Strength Around Curved Patterns
When both plots are curved, compare how closely each set of points follows its own curve. Do not compare one plot’s scatter around a curve with the other plot’s scatter around a straight line as if both had to follow the same shape. The question is whether each plot has a clear overall pattern and how closely its observations follow that pattern.
Here are fictional distance measurements from two cart trials. Both plots use time in seconds on the horizontal axis and distance in meters on the vertical axis. Imagine the same limits—0 to 5 seconds and 0 to 60 meters—and the same tick intervals for both plots.
Worked Example: Comparing Two Curved Cart-Trial Plots
| Time (seconds) | Trial A distance (meters) | Trial B distance (meters) |
|---|---|---|
| 0 | 1 | 4 |
| 1 | 3 | 0 |
| 2 | 9 | 14 |
| 3 | 17 | 12 |
| 4 | 33 | 40 |
| 5 | 49 | 46 |
Compare form. In both trials, distance generally increases as time increases, and the increases tend to become larger later in the trial. Both patterns bend upward rather than following a straight trend. The form is broadly similar: positive and curved.
Compare strength. Trial A’s observations stay relatively close to the upward curve. Trial B’s observations depart more from that general curve, including a dip from 0 to 1 second and a smaller distance at 3 seconds than at 2 seconds. Trial A therefore shows the stronger association with the curved pattern, while Trial B’s pattern is less consistent.
Comparison in context. In these invented cart trials, time and distance have positive, curved associations. The association is stronger in Trial A because its distances follow the upward curve more closely; Trial B has more scatter around the curved pattern. This comparison describes the plots and does not by itself identify why the trials differ.
This example also illustrates why strength is not the same as perfect consistency. Trial A does not have to form an exact curve for its association to be strong. The relevant comparison is how tightly observations follow the broad pattern, allowing for natural variation and measurement differences.
Scales and Fair Visual Comparisons
Shared scales make comparisons easier, but different scales do not make all comparison impossible. A plot with a compressed vertical axis can make points appear more tightly grouped; a plot with a stretched axis can make the same amount of scatter look larger. Different horizontal ranges can also show different portions of a curved pattern, potentially changing the form that is visible.
When axes differ, read the labels, units, limits, and tick intervals before comparing. If the variables and units match, you may be able to redraw or display both plots with common axes. If their ranges genuinely differ, explain what portion of the data is shown in each and avoid treating apparent visual size as a direct measure of strength. A direct comparison is easiest and fairest when the plotting scales match, but careful interpretation can still account for mismatched scales.
Common Mistakes and AP Exam Tips
- Calling a steeper pattern stronger: Steepness describes how rapidly the response changes relative to the explanatory variable. Strength describes how closely the points follow the pattern. Compare scatter around the pattern, not its slope.
- Calling a wider range stronger: A larger spread of response values does not by itself show a stronger association. Explain how tightly the points follow the overall pattern.
- Treating “linear” and “strong” as interchangeable: Form and strength are separate features. A plot can show a weak linear association or a strong curved association.
- Comparing plots without reading the axes: Different limits or tick intervals can distort a visual comparison. Check the scales and account for mismatches; do not claim that comparison is impossible solely because the axes differ.
- Describing each plot but not comparing them: “A is positive and B is positive” does not answer which is stronger or how their forms differ. State the contrast explicitly.
- Claiming that one variable caused another to change: A scatterplot shows association. Unless the study design supports a causal conclusion, describe what tends to occur together rather than asserting cause and effect.
For full credit, anchor the comparison in context and name the feature that supports it. For example: “Both groups show positive, roughly linear associations between practice time and skill score, but the association is stronger for Group A because its scores lie more closely around the upward trend.” If the plots differ in form, say so in a separate clause, such as “Variety A’s pattern is roughly linear, while Variety B’s rises and levels off.” These statements compare the plots rather than merely listing DUFS descriptions one at a time.
Check Your Understanding
Use the shared-scale and pattern-comparison ideas to answer each question.
- Two scatterplots show the same variables and units on matching axes. Plot A has points close to a straight upward pattern; Plot B has more scatter around a straight upward pattern. Which plot has the stronger association, and what visual feature supports your answer?
- One plot is roughly linear and the other curves upward before leveling off. Write a sentence comparing their forms without confusing form with strength.
- Two plots appear to have different amounts of scatter, but one has a compressed vertical axis. What should you check before comparing their strengths?
- Why is it incorrect to say that the steeper of two plots must have the stronger association?
- Write a contextual comparison sentence for two plots that share a positive curved form, with Plot B’s points following its curve more closely than Plot A’s.