# Pearson vs. Spearman coefficient

#### exitus_letalis

##### New Member
In a paper I had recently read, the Pearson correlation coefficients between SF-36 and DASH (Disabilities of the Arm, Shoulder and Hand) total score in dialysis Patients were calculated. Is it appropriate? Should it be more appropriate to calculate the Spearman coefficients for rank variables?

#### Miner

##### TS Contributor
I cannot answer the application question. However, Pearson assumes continuous data with a linear relationship. Spearman can use linear or rank data (since it ranks the data anyway) and can handle linear or monotonically increasing/decreasing data. Given that and your knowledge of the application, you should be able to answer your question.

#### EdGr

##### Member
In my opinion, there is a good argument for using Spearman correlations anytime you have a Likert scale variable (1-5, say) because the data in such a scale is not interval level measurement. We don't know that the difference between 1 and 2 has the same meaning as the difference between 2 and 3, for example. This makes a linear relationship problematic.

But once you have a total score from a scale like SF-36 that averages many such items, I focus almost entirely on the distribution. Pearson will tend to exaggerate any associations if there are extreme values high on both scales, as can easily happen. Spearman yanks those high values down so they become merely the biggest ranks, no longer a football field away from the other values.

#### spunky

##### Doesn't actually exist
In my opinion, there is a good argument for using Spearman correlations anytime you have a Likert scale variable (1-5, say) because the data in such a scale is not interval level measurement.
What do you do about ties, though? When the domain of the random variable is bounded (only values between 1 and 5) you are going to end up having A LOT of ties and at some point you need to ask yourself whether you're correlating the variables or the correction for ties.

#### EdGr

##### Member
Good point. Actually it looks like most people prefer Kendall's tau for many tied observations over any form of Spearman in that case.

#### spunky

##### Doesn't actually exist
Good point. Actually it looks like most people prefer Kendall's tau for many tied observations over any form of Spearman in that case.
Which tau, though? Tau a, Tau b or Tau c?