Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

Tied Observations

The term tie is used in connection with rank order statistics. Tied observations are observations having the same value, which prohibits the assignment of unique rank numbers. As a way out tied observations are assigned to the average of their hypothetical ranks.

Example: The ranks of the following 11 observations should be calculated: 1.0, 8.2, 2.2, -2.0, -1.0, 2.2, 5.3, 2.2, 8.1, 7.0 und 5.3.

Sorting the values in ascending order results in the following (hypothetical) rank order:

Value  Rank
-2.0    1
-1.0    2
 1.0    3
 2.2    4
 2.2    5
 2.2    6
 5.3    7
 5.3    8
 7.0    9
 8.1    10
 8.2    11
As the observations 2.2 and 5.3 occur several times their ranks are replaced by the mean of these hypothetical ranks:
Value  Rank
-2.0    1
-1.0    2
 1.0    3
 2.2    5     (tie)
 2.2    5
 2.2    5
 5.3    7.5   (tie)
 5.3    7.5  
 7.0    9
 8.1    10
 8.2    11

Last Update: 2012-10-08