Reading the data · Relative position
Percentiles, ties and reference groups
Can a material’s percentile change without its measurements changing?
A percentile describes position within a chosen reference group. Changing that group changes the interpretation, even when the selected material stays exactly the same.
Try the interactive demoStart with something familiar
Your place in a queue can change when different people join, even if you have not moved. A percentile similarly depends on which other samples are in the comparison, not just on your own score.
A tied group
80, 100, 100, 120
Rank convention
Both tied values receive the same rank
Notice what changes
First choose comparable records: the same known use and component. A rank without its group is like a race result without saying which race was run.
Understand why
Then count strictly smaller values using the displayed rank convention. Tied values share a position. The fitted smooth curve is not what determines the rank.
Connect it to wood and making
Finally inspect sample size and bias. Small groups give coarse jumps; a large group selected only from premium materials can also shift the rank. More rows alone do not guarantee a representative database.
Put names to the ideas
A group is part of the result
Compare known instrument use and component before comparing scores. A violin top and a cello back are not automatically members of one meaningful performance ranking.
State the tie convention
This demo mirrors the existing percent-rank helper: 100 × count strictly below x divided by N − 1, with the selected sample included. Equal values share rank; there is no interpolation from a fitted curve.
Small samples have coarse ranks
With two records, results can jump between 0 and 100. With fewer than two valid records the percentile is unavailable. A large but biased group can still be misleading.
The # symbol means “count.” N includes the selected record, and this percent-rank convention divides by N − 1. That is different from a literal fraction of all records, which would divide by N.
A worked example
For [80, 100, 100, 120], both 100s have a displayed rank of 33.3%. This rank convention is not literally the fraction of all records beaten, which would use N as denominator.
Explore it yourself
Keep the selected score fixed and switch cohort size or selection bias. Inspect the actual count and the tied-values example alongside the displayed rank.
- Percent-rank
- 47.8%
- N
- 24
- Strictly lower
- 11
Tie example [80, 100, 100, 120]: both 100s rank 33.3% under the stated percent-rank convention.