Dear Simone,

You should not use Pearson with an ordinal variable. However, Spearman works with both ordinal and scale so it is suitable.

Dear Simone,

this depends on the number of observations you have and the data distribution in both variables. At first I would creat a scatterplot of length vs. satisfaction with all observation pairs. If the data distribution is sufficiently well and if a linear or monotone trend can be identified, you cound interpret the patient satisfaction as continuous and calculate the Pearson or Spearman Correlation Coefficient. Nevertheless, keep in mind, that the more problematic issue is the ratio scale of the length acutally, since it cannot easily be used for regression models, due to its bounds between 0 and 1.

You could also use the numerator of the length as DV and the denominator as an independent variable and perform a ANCOVA on your data with the patient satisfaction as factor variable or as continuous variable. The results then tell you whether the denominator and the satisfaction have a significant influence on the numerator.

Hope this helps.

Dear Both 

Thank you very much for your prompt answers.

The number of observations is quite limited. Only 85. As it is suggested by a statistical online guide: https://statistics.laerd.com/spss-tutorials/pearsons-product-moment-correlation-using-spss-statistics.php and you suggested, I created a scatterplot of length and satisfaction in order to know if the data I own are linear or not. Unfortunately the result is attached. Definitely not linear..

I want to try to use the ANCOVA test and I will post the results. However how can I use the patient satisfaction as continuous variable ? Being a score 1-5 can only be considered an ordinal value

There is a third factor that I did not mention to simplify my question .. The length actually is the product a of subtraction ( Length post surgery- Length pre surgery). So I can even have negative results ...

Thank you very much for your help

It's difficult to tell because so many points overlap, but it looks like there might be a positive Spearman correlation in your plot.

Another way to look at this visually is to treat Diff as a categorical variable, and plot the median for Satisfc for each category.  For error bars, you might use the first and third quantiles for that category, or another measure of dispersion....

Dear Salvatore

Thank you very much for your reply. I have tried to stratified my data per group

Length -- Satisfaction 4-5 (76 patients)

Length -- Satisfaction 1-2-3 (14 patients)

But I had to aggregate satisfaction 1-2-3 because I did not have enough patients to analyse. I believe I have to  give up with my this calculation. 

I actually wasn't suggesting stratifying at all....

But if you are looking at stratifying, shouldn't DiffLength be the stratified variable?  Shouldn't DiffLength be treated as the independent variable?  (Maybe I don't understand the study).

In general, there are a few different tests you can use.  Spearman correlation makes sense.  Kruskal--Wallis makes sense if you treat DiffLength as categorical and Satisfc as ordinal.  Permutation tests, if you have a good invocation of them*, can treat either variable as ordered categories (ordinal). **

There are different ways to present this, but I think in general, the Spearman correlation will tell you if there is an association or not.  Beyond that, it's really just finding a good way to present your data.

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* The coin package in R is very flexible, able to do an independence test with either the independent or the dependent variable as categorical, ordinal, or continuous.

** Because you have only 6 measurements for DiffLength, you can think of it as categorical, ordinal, or continuous, depending on how you think about it.

Dear Salvatore 

Yes you are right when you say that I should treat the Length as independent variable.

In the end I decided to do the Spearman correlation mainly because I should do the same calculation for Length and Girth. As you said I could use the Length as categorical variable because there are only 7 values(One is negative and was not visible on the graph) However, the girth has 11 different values.

Here the results

As you can see I found a positive correlation with Girth and negative for Length

Good.  I think the Spearman is the most simple and easy-to-understand test.

Spearman test is the ideal test