Let's say, I have two set of questions; one set is to detect depression (var1) where the response of each question is in Likert scale and another set of questions to detect hopelessness (var2) where responses are also in Likert scale. Assume that, I have 50 samples who will be tested for depression and hopelessness. Now. I have to find the correlation between the variables, var1 and var2.
To do that, I want to calculate the depression or hopelessness score for each sample by summing the questions score (i.e. Likert Scale value for each question) of each questionnaire (depression or hopelessness). Then, find the correlation using formula.
What does create problem?
As each question of our questionnaires is in Likert scale, they are ordinal (Likert scale is ordinal).
BISHOP and Herron remarks
If the data are ordinal, then non-parametric statistics are typically considered the most appropriate option for analysis.
This one also says
For ordinal scales, the correlation coefficient which is usually calculated is Spearman’s rho.
However, this one in an answer of SE question, says
But when you add up many measurements of the ordinal type, which is what you have in your case, you end up with a measurement which is really neither ordinal nor interval, and is difficult to interpret.
For Likert scale, the items are ordinal, but usually we do summing for the items to get total score, which is considered as continuous variable. then we do Pearson correlation
David L Morgan also remarks there
Twenty-five items are a lot for a single scale, which is what you would get if you simply added all the items together. That is standard practice for creating a continuous variable from a series of ordinal Likert items, but it requires careful attention to whether thee items do indeed form a single scale.
Therefore, as we are adding many measurements of the ordinal type questions score in case each of the questionnaire (depression and hopelessness scale), will the value (summation of all questions score for each person and questionnaire) still remain in ordinal type? If it becomes like an interval variable and continuous, can you please refer a book or paper which says this one?