What is tied data in the context of a rank correlation coefficient?

Question

I am not in statistics field.

I have seen the word "tied data" while reading about Rank Correlation Coefficients.

• What is tied data?
• What is an example of tied data?

Answer 1

It means data that have the same value; for instance if you have 1,2,3,3,4 as the dataset then the two 3's are tied data. If you have 1,2,3,4,5,5,5,6,7,7 as the dataset then the 5's and the 7's are tied data.

Answer 2

"Tied data" comes up in the context of rank-based non-parametric statistical tests.

Non-parametric tests: testing that does not assume a particular probability distribution, eg it does not assume a bell-shaped curve.

rank-based: a large class of non-parametric tests start by converting the numbers (eg "3 days", "5 days", and "4 days") into ranks (eg "shortest duration (3rd)", "longest duration (1st)", "second longest duration (2nd)"). A traditional parametric testing method is then applied to these ranks.

Tied data is an issue since numbers that are identical now need to be converted into rank. Sometimes ranks are randomly assigned, sometimes an average rank is used. Most importantly, a protocol for breaking tied ranks needs to be described for reproducibility of the result.

Answer 3

It's simply two identical data values, such as observing 7 twice in the same data set.

This comes up in the context of statistical methods that assume data has a continuous and so identical measurements are impossible (or technically, the probability identical values is zero). Practical complications arise when these methods are applied to data that are rounded or clipped so that identical measurements are not only possible but fairly common.