Difference between revisions of "Gamma Statistic"
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An pair of observed instances (x1, y1), (x2, y2) can be: | An pair of observed instances (x1, y1), (x2, y2) can be: | ||
* Concordant, if the values of both variables for one case are higher (or lower) than the corresponding values for the other instances. | * Concordant, if the values of both variables for one case are higher (or lower) than the corresponding values for the other instances. | ||
− | * Discordant, if the value of one variable for one instance is higher than the corresponding value for the other instance, and vice-verse | + | * Discordant, if the value of one variable for one instance is higher than the corresponding value for the other instance, and vice-verse for the other variable. |
− | for the other variable. | + | * Tied, if the two instances have the same value on one or on both variables. |
− | * Tied, if the two instances have the same value on one or on both | ||
− | variables. | ||
== Formula == | == Formula == |
Latest revision as of 12:05, 4 May 2024
Contents
Definition
The Gamma Statistic is a measure of association for ordinal variables. It is based on comparing the value of two variables for all possible instances of associated pairs.
Preliminaries
An pair of observed instances (x1, y1), (x2, y2) can be:
- Concordant, if the values of both variables for one case are higher (or lower) than the corresponding values for the other instances.
- Discordant, if the value of one variable for one instance is higher than the corresponding value for the other instance, and vice-verse for the other variable.
- Tied, if the two instances have the same value on one or on both variables.
Formula
Where P is the count of concordant instances and Q is the count of discordant instances