Analyze ordinal association using pairwise summary tools. Check ties, switch directions, and validate data quickly. Download polished outputs and explore trends through interactive visuals.
Place matching observations in the same order. Use integers or decimal ranks, separated by commas, spaces, semicolons, or new lines.
The heatmap shows how often each ordered X level pairs with each ordered Y level.
Somers' D is a directional measure for two ordinal variables.
Somers' DY|X = (C − D) / (C + D + TY)
Somers' DX|Y = (C − D) / (C + D + TX)
A pair is concordant when higher X also has higher Y. A pair is discordant when higher X has lower Y. Pairs tied on both variables add no directional ordering information.
This page also reports Goodman-Kruskal gamma and Kendall tau-a for extra context.
Use this sample if you want to test the calculator quickly.
| Observation | Example X | Example Y |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1 | 2 |
| 3 | 2 | 2 |
| 4 | 2 | 3 |
| 5 | 3 | 3 |
| 6 | 3 | 4 |
| 7 | 4 | 4 |
| 8 | 4 | 4 |
| 9 | 5 | 5 |
| 10 | 5 | 5 |
It measures directional association between two ordinal variables. Positive values mean higher ranks tend to occur together. Negative values mean inverse ordering. Values near zero suggest weak monotonic structure.
Gamma ignores tied pairs in its denominator. Somers' D keeps the directional idea and includes ties on the dependent side, so it is usually more conservative for predictive ordering work.
The statistic is asymmetric. D(Y|X) asks how well X orders Y. D(X|Y) asks the reverse. They become identical only in limited situations.
Use paired ordinal codes with equal lengths, such as survey ratings, ranks, severity classes, or ordered categories converted to numbers like 1 through 5.
Pairs tied on both variables provide no ordering direction. Pairs tied on only one side affect the denominator, which can reduce the coefficient compared with gamma.
A negative value means higher ranks on one variable tend to pair with lower ranks on the other. It signals inverse ordinal association.
If every relevant pair is tied for the chosen direction, the denominator becomes zero. In that case, Somers' D cannot be estimated from the submitted data.
Not in this version. Recode ordered text categories into numeric ranks first, while preserving their original order across both input lists.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.