Try the methods
Change one decision and watch the conclusion change. All data on this page are synthetic teaching data, not findings from a psychological study. Nothing is recorded or sent.
One point can change a correlation
Eight fixed observations show a positive pattern. A ninth point has x = 10. Change its y value to see how an outlier affects Pearson’s r.
With the ninth point at (10, 0), r = 0.13.
Without the ninth point, r = 0.90. At (10, 0), r = 0.13; at (10, 10), r = 0.94. The pattern is an illustration, not an estimate about people.
Inspect the exact synthetic data
| Point | X | Y |
|---|---|---|
| 1 | 1 | 2 |
| 2 | 2 | 4 |
| 3 | 3 | 3 |
| 4 | 4 | 5 |
| 5 | 5 | 4 |
| 6 | 6 | 7 |
| 7 | 7 | 6 |
| 8 | 8 | 8 |
| 9 | 10 | 0 |
A correlation summarizes a pattern in these measured values. It does not tell you whether X causes Y, Y causes X, or another variable influences both. Inspect the scatterplot as well as the coefficient. Read about correlational studies and effect sizes.
Who enters the sample?
Imagine a population of 16 synthetic scores, from 20 to 95 in steps of five. Its mean is 57.5. Change the selection rule and compare the sample with the population you want to describe.
Sample mean: 57.5, from 6 scores.
Selected scores: 20, 35, 50, 65, 80, 95
Read the comparison without controls
| Selection | Sample size | Mean |
|---|---|---|
| Spread across range | 6 | 57.5 |
| Scores ≥ 70 | 6 | 82.5 |
| Scores ≤ 45 | 6 | 32.5 |
All three samples have the same size. Their selection rules produce different descriptions. The spread sample happens to match this population mean, but it is not a random sample and cannot demonstrate a generally unbiased procedure. Inspect sampling and confidence intervals.
What can you conclude?
In a constructed study, students choose whether to use a study app. At the end of the term, app users have higher quiz scores. Both groups take the same quiz. There is no random assignment and no baseline score.
Read the answer and explanation
The supported claim is an association in this sample. Prior achievement, motivation or available study time could affect both app choice and scores. The study neither isolates the app’s effect nor establishes that it has no effect. A better comparison would define the intervention, measure relevant baselines and consider an ethical randomized design. Inspect randomized experiments.