A scatter plot displays two numerical variables measured on the same observational units. Each point represents one paired observation: its horizontal coordinate is one value and its vertical coordinate is the other.
The pairing is essential. A list of practice counts from one group and a list of task scores from a different group cannot be turned into meaningful pairs by sorting both lists. A scatter plot describes the relationship present in the actual matched records.
On this page
Put one record at one point
For a small synthetic example, let be a learner’s number of completed practice blocks and a task score out of 10. The five illustrative pairs are
They are invented teaching records, not CTS learner outcomes. The point represents a record with four practice blocks and a score of four; it does not state that a score of four always follows four blocks.
A scatter plot preserves the pairs
Diagram explanation and exact data
The observed association rises overall, but not every larger predictor has a larger response. Keep each response paired with its actual predictor.
| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 5 |
| 4 | 4 |
| 5 | 5 |
Label both axes, their units and the sample size. There are five records even though two score values repeat. If identical pairs occur, points can overlap, so a plotting method may need counts, transparency or a clearly explained offset. Do not mistake a single visible mark for proof that only one record exists there.
Describe direction, form and strength
Direction asks whether larger values generally occur with larger or smaller values. Form asks whether the pattern is approximately straight, curved, clustered or something else. Strength describes how closely points follow that form, not how steep the relationship is.
The five pairs suggest a positive association with noticeable scatter. An exact straight-line relationship would put every point on one line. Here, the two observations at and have the same score despite different practice counts, and the score drops between and .
Statistics Canada’s scatterplot guidance treats these displays as tools for inspecting relationships. A number such as correlation should supplement this inspection, not replace it.
A curve can have no linear correlation
Consider another deliberately constructed set:
These points lie exactly on , giving a clear U-shaped relationship. Their Pearson correlation is zero because the positive and negative sides balance in the linear calculation.
Zero linear correlation can hide a clear curve
Diagram explanation and exact data
These points satisfy y = x squared exactly. Pearson r is zero because the positive and negative linear contributions cancel, not because the variables are unrelated.
| x | y |
|---|---|
| -2 | 4 |
| -1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
“No linear correlation” is therefore not equivalent to “no relationship.” Use a scatter plot before deciding whether a straight-line summary is appropriate. A curved pattern, separate clusters or changes in spread may require a different analysis.
Do not join unrelated records into a time sequence
The order of rows in an ordinary cross-sectional data table may be arbitrary. Connecting the five learner records by a zigzag line would suggest a sequence that was never measured.
If observations genuinely follow the same object through time, a connected display can be useful, but time and repeated measurement become part of the interpretation. Distinguish a time-series path from a cloud of independent paired records.
Similarly, do not sort the and columns independently. The association would be changed or manufactured by breaking the original matches.
Examine unusual points and groups
A point far from the main pattern can affect a fitted line or correlation. First check its record, unit and eligibility. A point with an extreme value has potential leverage over a fitted slope, while a large vertical residual indicates disagreement with that line. These are different properties.
Groups can also create an apparent overall association. For example, age groups may differ in both time available for an activity and a measured outcome. The combined pattern may not describe the relationship within either group. Label meaningful groups where appropriate and examine whether aggregation changes the story.
A small synthetic illustration makes the mechanism clear: group A contains and group B contains . Within each group, rises by one as rises by one. The combined cloud includes a shift between groups as well as the within-group trend. Those are not automatically the same question.
Association does not establish causation
The practice-score example cannot show that extra practice caused the higher scores. Prior knowledge, task difficulty, motivation or the way participants were selected could affect the association. The direction could also be partly reversed if learners who find the task easier complete more blocks.
A causal claim requires an appropriate design and reasoning about alternatives. Random assignment can help establish a treatment comparison under suitable conditions, whereas random sampling supports population generalisation. Neither should be inferred merely from the appearance of a scatter plot.
Keep the descriptive statement modest: “These five synthetic records show a positive overall association.” It is both accurate and more informative than claiming the plot proves an intervention works.
From a scatter plot to a model
If a straight-line pattern is plausible, Correlation quantifies linear association and Linear Regression estimates a line for prediction or description. Both use the same paired observations as this page so the calculations can be checked against the figure.
After fitting, inspect residuals and the range of the predictor. A line can be computed even when it is not a good description. Predictions beyond the observed range need additional justification rather than confidence in a plotting tool.
Practice questions
- What does the point mean in the practice-block example?
- The five points on above have Pearson correlation zero. Does that show the variables are unrelated?
- Why should you not sort each column separately before making a scatter plot?
Check your answers
- One synthetic record has four completed practice blocks and a task score of four out of ten. It is a paired observation, not a deterministic rule for every learner.
- No. They have a perfect curved relationship. Pearson correlation describes linear association and can be zero for a U-shaped pattern.
- Independent sorting breaks the original pairs and can create an association that was not present in the collected records.
Related topics
Correlation develops the numerical measure of linear association. Linear Regression fits and checks a line, while Sampling Bias explains why the selection of records remains relevant to any conclusion.