I have collected data from an online survey that asked people to 'rate' a corpus of music track excerpts with 8 emotional adjectives such as 'happy', 'sad', 'angry', etc. They could only select one word for each excerpt.
Each rating for each song has been assigned an angle:
'happy' = 0º,
'excited' = 45º,
'angry' = 90º and so on. The angle increments in
45º with each of the 8 words until we get to
I have been using Spearman's rank correlation to correlate the set of angles with a range of different sets of numeric data which is in the interval:
[0,1]. So far, my correlations have been quite strong. However, the words I have used have been taken from a circular-based emotional model which has a large degree of periodicity. More specifically, one can transition through all 8 emotions either clockwise or anti-clockwise and end up back at the first emotion:
'happy' = 0º.
Does a Spearman account for this periodicity? Or, is there any other method that accounts for this type of property?
In summary, there are 'ties' in the vector of angles since a few songs were rated with the same emotional word, but no 'ties' with the aforementioned numerical data its being correlated with. The emotional descriptors (vector of angles) have been rated by humans, and the numerical data has been computationally rated. The sample size is
n = 20. All vectors are
20x1 and are being evaluated using
Link to the paper my circular model is 'based' on: Circumplex