Hello Tom,

If the research question is best answered via correlation, then the Spearman (rank-order) correlation coefficient would work for you.

Good luck with your work!

David Morse Thank you very much for your answer, I will do as such.

Hi Tom

Correlation is used when both variables are of equal importance. Regression is used when one variable is used to try and predict another. Since you have said that GGGI is the independent variable and PTS the dependent variable, you should be using a regression approach rather than a correlation approach.

Since PTS is measured on a 5-point ordinal scale, it could be considered as continuous (although theoreticians would vehemently object to this). One of the major assumptions of linear regression is that the residuals are normally distributed, and this should be checked for. If necessary, quantile (median) regression can be used, which is somewhat similar David's suggestion above.

Adrian

The answer to the question is maybe. It depends on if there is an expectation that other outcomes exist or how one needs to use and interpret variables.

In your case, PTS is on a 5-point scale. If I take an average of several measures of PTS and arrive at a mean of 3.2 does this make sense? On a 5-point scale 3.2 is undefined because the scale is ordinal. If a value of 3.2 has meaning, then you might be dealing with a continuous variable that has been coded to fit into at 5 point scale.

In a study of sex, I can code male=0 and female=1. I can take the average of several samples and get an average sex of 0.35. If sex is a proxy to testosterone levels, then this might make sense. If sex can only be male or female then the outcome is nonsense because the value of 0.35 does not exist in a either 0 or 1 framework.

Timothy A Ebert , if you code a binary observable as 0/1, you get a count-variable, and the mean (or the expected value) is a proportion. That does make some sense, to my opinion. Clearly, the problem is to get the uncertainty associated with the mean as an estimate of the expected value, for wich the normal assumption is not ok (at least not for very small samples).

Tom, for this case you might consider an ordinal logistic regression with PTS as the dependent variable.

Coding sex as male=0, female=1 could give a mean proportion of males as 35%. This outcome is valid and could be useful or interesting. However, I think that if one treats sex as a continuous variable then one is saying that I could find an individual that was 35% male.

There are many other examples:

I do a fertilizer trial and apply nitrogen at 2, 16, and 128 kg/ha and measure plant growth. I did not test a treatment at 73 kg/ha, and therefore I have no idea what the outcome will be. I could treat this as ordinal data, maybe do a multiple comparison procedure. I could also treat nitrogen as a continuous variable. The risk in doing so is that with only three data points I might not be able to get the correct relationship: depending on the exact relationship between fertilization and plant growth. As I increase the treatment list with other rates of fertilizer it makes less and less sense to keep these data as ordinal.

The same scenario would be applied to a pesticide (something with imidacloprid) applied at 1, 10, and 100 pints/acre.

This is in contrast to a experiment where I apply dimethoate to one field, Imidacloprid to another, and azadirachtin to a third. In this experiment there is nothing between azadirachtin and imidacloprid. While one could code these as dimethoate=1, imidacloprid=2, and azadirachtin=3 for the variable "insecticide" one would never consider insecticide as a continuous variable.

So with PTS, I can see that at any one time it can have any one of 5 states. Yet, it is assessing a threat level that is not inherently ordinal. Think carefully about the consequences of using PTS as a continuous variable.

Another perspective is to ask if the choice in analysis results in qualitative differences in the interpretation of your data. This is a difficult path as it is subject to problems where you choose the analysis that gave the answers that you wanted. This might help:

https://www.tandfonline.com/doi/full/10.1080/00031305.2019.1583913

Sorry Timothy A Ebert to bother again... I think now response and predictors get confused. What you describe are examples for predictors (how much fertilizer or pesticide is given, what drug is administered), but the question was how to treat a (non-numerical) response. The rest of this post is not directly to you (you know all that) but in general for readers who might be interested, and for those experts out there who should correct me where I am wrong.

In general regression models (no matter if linear or non-linear and no matter what conditional response distribution one assumes), categorical predictors are coded into (numerical) design variables, so that a predictor with k categories will (usually) give k-1 design variables. The coding can be done in different ways, such as dummy-coding, contrast-coding, Helmert-coding, forward-difference-coding and others (https://stats.idre.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/). The coding will determine how the coefficients are interpreted. The regression over the design variables is then a multiple regression, if there is at least on predictor with k>2.

If the response is also categorical, it must also be numerically coded to be used in a regression analysis. There are the same options like for the predictors. This means, that a response with k categories is split into k-1 numerical response variables. Often, dummy-coding is used here to get the differences in the response between the "experimental" categories to a "reference" category. So the problem is split into k-1 logistic regressions (if k>2 then this is a multinominal logistic regression). If the response categories are ordered, each category is contrasted with the bulk of "lower" categories.

If the response is coded by (k-1) 0/1-coded variables, then the conditional distribution must be binomial. This might be approximated by a normal distribution if the sample size is large, but modern software can easily handle the binomial distribution. If the functional model describing the dependency between the design variables and the (possibly transformed) expectation of the response variable(s) is linear, this is a generalized linear model of the binomial family.

Coding the categories of an ordinal response with 1, 2, 3, ... is usually not sensible at all, just like for predictors (the choice of 1,2,3... is anyway arbitrary; why not using 0.2, 12.2, 12.8, 4523, ...?). It would make sense in those cases where the chosen values refer to some underlying quantity (that can not be measured directly; but that must be carefully validated, what usually is not an easy task). If 1,2,3... are taken as ranks, the model would be about the expected rank number, what is, to my opinion, a quite weired measure that is hard to interpret. If the analysis should be rank-based, one looses the possibility to answer many interesting questions (e.g. for interpretable effect sizes and for interactions), and one should then better use rank-correlation measures alltogether instead of going for a regression model.

Hi Tom Scanlon . If the PTS is a scale, it consists of several indicators (questions or ratings). It is common to use mean scores of such scales, and a histogram of scores will show the distribution. It is quite common to consider such scales as continuous in analyses. I agree with Adrian Esterman that you can use regression (if you really have a "scale").

Best

JK

I agree with David

Hi Tom,

I would check the normality of the continuous variable and decide to take one way ANOVA (for normal distribution) or Kruskal-Wallis test (if distribution is not normal).