I am looking at understanding if a correlation exists between survey data on broader attitudes based on Likert scales and positive or negative perceptions. Perceptions are actually also on a scale (very positive, somewhat positive, neutral, somewhat negative, very negative), but was thinking of collapsing to just positive or negative. I am wondering what statistical test would work best.
If attitudes and perceptions are measured with multiple items, you can also use factor covariances from CFA, which will be dis-attenuated from measurement error.
I don't think that there is a perfect answer to your question. You deal here with ordinal data, which by definition should not be evaluated with parametric tests. Non-parametric correlation tests (e.g. Spearman's) produce a high rate of false-positive significances as ties go in favor of significance while in reality they mean very little. If you keep it at the univariate level (just comparing two scales at once), it's best to measure for concordance/discordance (test for Goodman and Kruskal’s gamma; https://statistics.laerd.com/spss-tutorials/goodman-and-kruskals-gamma-using-spss-statistics.php). For multivariate evaluations, however, which avoid undesired alpha-errors, to the best of my knowledge no non-parametric methods exist and many scientists use parametric methods (e.g. multivariate linear models) despite the fact that no proportionality is given for ordinal scales (e.g. you cannot claim that a person is twice as happy when she/he is "very happy" as compared to a "happy" person).
Oh yeah and: Do NOT collapse the data! The information loss is tremendous.
Alexandr Parlesak, your point is right, people always missed things up. there is a clear distinction between parametric and non-parametric. thank
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