Correlations Between Congestion Ratings and Features of the Crowd in Raters’ Immediate Vicinity
| Crowd feature | Before obstacle | After obstacle | Overall |
|---|---|---|---|
| Density | |||
| Velocity |
Researcher Xiaolu Jia and colleagues monitored individuals’ velocity and the surrounding crowd density as a group of study participants walked through a space and navigated around an obstacle. Participants rated how congested it seemed before the obstacle, after the obstacle, and overall, and the researchers correlated those ratings with velocity and density. (Correlations range from to , with greater distance from indicating greater strength.) The researchers concluded that correlations with velocity were stronger than those with density for all three ratings and that the difference in strength was greatest after the obstacle.
Which choice best describes data from the table that support the researchers’ conclusion?
For table-based command-of-evidence questions, break a multipart conclusion into separate conditions and verify each one numerically. Here, first use absolute values to compare correlation strength for every category, then calculate the differences in strength to determine where the gap is greatest. Reject any choice containing even one inaccurate clause.
Hints
Identify both parts of the conclusion
The researchers make one claim about all three pairs of correlations and another about where the difference in strength is greatest. A supporting choice must address both parts accurately.
Compare strength rather than direction
Convert each correlation to its distance from . Do not treat a negative correlation as weaker merely because it has a negative sign.
Find the three strength gaps
For each rating, subtract the smaller absolute value from the larger absolute value. Then compare the three resulting differences.
Step-by-step Explanation
Translate correlation strength into absolute value
Because distance from determines correlation strength, compare the absolute values of the velocity and density correlations. The positive or negative sign indicates direction, not strength.
Compare the correlations for each rating
The absolute-value comparisons are:
- Before the obstacle:
- After the obstacle:
- Overall:
Thus, the velocity correlation is stronger for every rating.
Calculate the strength gaps
Subtract the density correlation’s absolute value from the corresponding velocity correlation’s absolute value:
- Before the obstacle:
- After the obstacle:
- Overall:
The largest strength gap is , which occurs after the obstacle.
Match the calculated gaps
Compare the three calculated differences with the choices in before-obstacle, after-obstacle, and overall order. The values , , and , respectively, match the table and show that the largest difference occurs after the obstacle.