Difference between spearmann correlation and fit command

Hello all,

I have some data that I want to analyze (EMG of muscles vs subjects' fatigue) in order to find the relation between two measurs.

At first, I used the 'corr' command to calculate the spearman correlation coefficient between the EMG and the fatigue for each subject. Afterwards, I used the 'fit' command to fit a linear model to my data.

To my surprise, in some cases (about 5% of the cases), the spearman correlation coefficient was positive, but the fitted linear model had a negative slope (or vice versa).

Shouldn't they have the same tendency? Or am I doing something wrong?

I'm attaching my matlab code, and excel file with some example data that shows the spoken discrepancy.

Thank you.

Answer 1

[Peter Perkins]

You're (correctly) fitting a linear model with a slope and an intercept. The "model" that a correlation coefficient is equivalent to has no intercept. Look at your figure to see why one is positive and the other negative.

Hope this helps.

[Gena]

Thank you for your answer, but there is still something that I don't understand. When you are saying that "the model has no intercept" you mean that the model is y=a*x (passes through the origin), if I understand it correctly. But what about other cases (as in the attached file) where the model of the correlation coefficient doesn't pass through the origin (and has a negative value, so as the slope of the fitted line)? What is the difference (after all, in both cases I'm using the same command - "corr")?

Thank you.

Answer 2

[Wayne King]

I would not put any faith in the correlation coefficient, the p-value is 0.9 and the reported rho is close to 0.

[Gena]

I agree, but that is not the issue. There are some other cases where the correlation is more significant, but the discrepancy still exists.

Thank you for the answer.