How do the 15‐85 percentiles work for scoring ranges - theliberators/columinity.docs GitHub Wiki

We often include the range of scores in Columinity when we show the results. For example:

The average score is indicated by the green arrow (75). This is a median average for team reports and a (weighted) mean average for reports with multiple teams. The green bar reflects the range and extends from 61 to 86. This bar is based on the 15% to 85% percentiles of the distribution of scores in the team for a factor. This includes all answers per participant for each question loading on that factor. This means that in practice, 70% of team members' scores fall within 61-86 (with 75 as the average). By extension, 15% of the team members score below 61, and 15% score above 86.

Example

If you take the range 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, the 15% percentile is 1.65 and the 85% percentile is 9.35. For the range 1, 2, 3, 4, they are 1.75 - 4.25 (rounded to 4). 15% of the values are below 1.75 and 85% are below 4. So the start and endpoint of the green bar do not reflect a literal answer a participant gave (although they could by coincidence).

Why not lowest and highest scores?

Why does the green bar not show a team's lowest to highest score instead? This is because we have noticed that doing so encourages teams to search for which member gave the lowest (or highest) score. When the green bar is based on percentiles, there is more anonymity because the bar's start and end do not reflect a single participant. Another reason is that a 15-85% percentile puts more focus on the scores of the majority and less on extremely low or high scores. We feel this encourages better conversations.