GlossaryStatistics and interpretation
Rank
Rank is an ordered position within a defined set. Learn why ranks do not show gap sizes, can change with the comparison set, and need context.
A rank is an ordered position among a defined set, based on a particular measure and period. It states where a value falls relative to the included values. A rank does not show the size of the differences between places or establish an overall judgment about safety, quality, or performance.
Define what comes first
A ranking needs a direction. First place could mean the highest count, the lowest rate, or the shortest interval. It also needs a comparison set: a city can rank third among ten selected peers and twentieth among all eligible cities without its own value changing.
NIST describes ranks as positions of observations after ordering. For crime comparisons, the FBI's archived caution against ranking explains why the resulting order can conceal important differences in local conditions. NIST ordered-data explanation; FBI comparison caution.
Example
Hypothetical example: Four agencies have comparable rates of 100, 101, 102, and 200 per 100,000 residents. In a highest-to-lowest ranking, the agency at 102 ranks second.
Its gap from the third-ranked agency is one, while its gap from the first-ranked agency is 98. Adjacent positions do not imply equal differences. If another agency with a rate of 150 is added, the unchanged rate of 102 moves to third place.
Common confusion
A rank is not a percentile. A position such as third of ten needs a specified convention before it can be expressed as a percentile, especially when values are tied. Different tie rules can assign shared positions or skip later positions.
A movement in rank also does not necessarily mean the underlying measure improved or worsened. Other places can change, the comparison set can change, or revised data can alter the order.
Read the values behind the order
Show the underlying measure, its units, and the number of included places. Identify missing or excluded agencies and explain how ties and rounding are handled. Small numerical differences can produce different ranks even when uncertainty makes a precise ordering questionable.
Counts and rates generate different rankings because they answer different questions. A high-volume agency is not automatically a high-rate jurisdiction. Neither ordering alone establishes a resident's personal risk or an agency's effectiveness. Use rank as a description of a defined comparison, supported by the actual values and their limitations.