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I'm wondering whether there are any statistical properties that should differentiate count data and parametric data. In other words, is there an aspect of my data that I can analyze, or a test I can run, that will allow me to determine whether the data is parametric or nonparametric?

My specific research involves peer nominations, in which a participant's score is based on the number of times the individual is nominated out of a list of peers as fitting a given criterion (e.g., "Circle the names of everyone in your class who is really popular").

Recently, I've been involved in an argument about the nature of peer nomination data-- specifically, whether it is count data or parametric data. Although scoring is based on the count of nominations, it is also possible to see each nomination or non-nomination as a binary data point which, when combined, measure a continuously distributed latent variable.

If there's a general way to differentiate count vs. parametric data, it would provide me with a way of addressing this argument.

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    $\begingroup$ The things you're arguing about aren't contradictory terms. In fact, "parametric data" isn't even a defined term. I suspect you want to ask whether the data needs to be analyzed through non-parametric statistical methods. $\endgroup$
    – John
    Commented Feb 10, 2014 at 21:56
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    $\begingroup$ 'parametric' and 'count' are not mutually exclusive categories. Many count models (indeed, most) are finite-parametric. Rather than trying to classify on what may be a non-existent distinction, the right thing to do is to try to write down your model (how the variables are related); it should be much clearer then $\endgroup$
    – Glen_b
    Commented Feb 10, 2014 at 21:59
  • $\begingroup$ That's a fair assessment. My issue really comes from whether the data can be subjected to analyses of internal reliability. For some variables, researchers have argued that we "wouldn't expect" consistency for peer nominations, and that peer nominations should therefore not be subject to internal reliability measures. $\endgroup$
    – mfenig
    Commented Feb 10, 2014 at 22:00
  • $\begingroup$ Can you flesh out the two opposing models? It's not clear what you are actually trying to model. $\endgroup$
    – user31668
    Commented Feb 11, 2014 at 1:26
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    $\begingroup$ The question as you explain it in comments have little to do with original wording of Q! Can you please edit to update the question? $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jul 9, 2018 at 10:08

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So first, just like the comments have been saying the opposite of parametric is non-parametric. As for whether we can tell if data is parametric or non-parametric, the answer is no. This is because being parametric or non-parametric is not a characteristic of the data. Parametric or non-parametric is a characteristic of the model we think generated said data. All that we can do is to compare models and say which one seems more likely to have generated said data.

In general, its good practice to make a simple parametric model first, see how well it fits the data, and if the fit is insufficient, consider moving to a non parametric model. (Ocham's razor after all). Or if you would like to be Bayesian, you can compute probabilities that model A generated the data over model B. But we can't really compute said probabilities over the space of all parametric and non-parametric models, such a space is much too big to say anything meaningful.

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