Check the distributions of your dependent measures (Likert type scales) with the Shapiro test and histograms. If they look quite normal run parametrical tests, which are more powerful.

Jos Feys Thanks but what parametric tests would you then suggest?

If you want to treat the outcome variable as ordinal, use ordinal logistic regression, or generalized ordinal logistic regression if the proportional odds assumption is not sensible and defensible. If you do a Google search on , and replace package with the name of your statistical software, you should find resources.

HTH.

One more thing, Kenny Sunmboye. The terms parametric and non-parametric are typically used to describe tests or models, not variables or data. But even when used that way, the term non-parametric is rather imprecise. See this comment in the Vassar Stats online textbook, for example:

• http://vassarstats.net/textbook/parametric.html

HTH.

This is an interesting question.

Before going any further, there is a need to determine whether your data follows normal distribution or not. Testing for normality can be done through normal Q-Q plots, histograms, skewness, kurtosis, Kolmogorov-Smirnov or Shapiro-Wilk. I use Kolmogorov-Smirnov (population above 100) and Shapiro-Wilk (population below 100) – other authors may suggest different population threshold. The p-values for Kolmogorov-Smirnov and Shapiro-Wilk should be greater than 0.05 for normal distribution. If your data follow a normal distribution, then consider doing parametric tests. They are more powerful, as highlighted by Jos Feys. You may consider transforming data that does not follow a normal distribution to use parametric tests. However, not all transformations are successful.

Let me answer your questions:

Please do not assume your data is or requires non-parametric tests. It would be best if you do some normality tests to get to that point. I agree with the comment regarding the use of parametric and non-parametric terms by Bruce Weaver

1. Now if patient satisfaction (likely to be ordinal data) is my dependent variable and age is a continuous data (independent variable) which statistical test is appropriate especially if I’m assuming that my dependent variable is non-parametric.

For the first point I’m thinking would a one-way ANOVA be appropriate to see correlates between my ordinal data (likert scale obtained data for patient satisfaction) with age (continuous data)?

Remember, one-way ANOVA is a parametric test for testing statistically significant differences between the means of two or more independent groups. One-way ANOVA is not used for correlation testing. Three important requirements are that (i) your dependent variable should follow a normal distribution, (ii) your variance between the dependent and independent variables should be the same and (iii) your data should not have significant outliers.

Suggestion: Consider using Spearman’s Correlation. However, there should be a monotonic relationship between the variables before opting for Spearman’s Correlation. To test for a monotonic relationship, use a scatter plot. If your variables have a non-monotonic relationship, consider transforming your data (which may not be successful at times).

2. Now if patient satisfaction (likely to be ordinal data) is my dependent variable and the, gender, ethnicity and patient diagnosis data are all categorical data (independent variables) which statistical test is appropriate especially if I’m assuming that my dependent variable is non-parametric.

For the second point, would Kruskall-Wallis tests be appropriate to see correlates between ordinal data and categorical data?

Or should I just turn the Likert data into continuous data by finding a total satisfaction score for each respondent then apply other tests. In which case is this even an appropriate step to take, and what statistical tests would that be?

Suggestion: For dichotomous independent variable (gender) and ordinal dependent variable (patient satisfaction), consider Ordinal Logistic Regression.

For categorical independent (with three or more categories such as ethnicity if there are three or more categories) and ordinal dependent variable (patient satisfaction), consider either one-way ANOVA (if all assumptions are met) or Kruskal-Wallis H Test. If 'patient diagnosis' has two categories, use Ordinal Logistics Regression, if there are three or more categories, then use Kruskal-Wallis H Test.

I hope this helps, and it would be great to hear input from others.

Since your DV (i.e., patient satisfaction) is ordinal, as you have stated in your inquiry, and you have several IVs (i.e., age, gender, ethnicity, and patient diagnosis), you could go for ordered logistic regression, also known as the ordered logit model. You might check out the illustrations by Azen and Walker (2021) and UC Regents (2021), referenced below.

Azen, R., & Walker, C. M. (2021). Categorical data analysis for the behavioral and social sciences (2nd ed.). Routledge. https://www.routledge.com/Categorical-Data-Analysis-for-the-Behavioral-and-Social-Sciences/Azen-Walker/p/book/9780367352769

UC Regents. (2021). Ordinal logistic regression | SPSS data analysis examples. IDRE Stats – Statistical Consulting Web Resources. https://stats.idre.ucla.edu/spss/dae/ordinal-logistic-regression/

Good luck,

I disagree with the suggestion to test for normality of the outcome variable, and to use a parametric (presumably OLS) model if the test of normality is not statistically significant. I have a few reasons for disagreeing.

HTH.

Very nice question. I suggest you use Spearman's correlation for the first assertion, because it is a rank correlation. (https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/correlation-pearson-kendall-spearman/) and linear logistic regression for the second one, however if you want to see the weights of the different independent variables together you can use multiple logistic regression.

I think that with so many IVs and you are saying that your direct Vs are ordinal in the study you should use the oder legit model. Base on the information given you can one --way Anova if all things are present.

Dear Kenny,

First of all, your dependent variable (DV) can be considered as continuous (interval or ratio) variable, especially if there are enough levels (at least 5, better 7 or more). However, ANOVA cannot be used here as it requires a continuous DV and categorical Independent Variables (IVs), which is not your case, at least for age. More importantly, it is highly recommended to consider it as it is (Likert scale) and to analyze it as an ordinal variable and not as a metric or continuous variable; otherwise, continuous models will systematically lead to errors (Liddell and Krushcke, 2018). There are mainly 3 kinds or ordinal models: cumulative, sequential, and adjacent-category (Burkner and Vuorre, 2019). The cumulative models are the most frequently used ones. Examples of such models are ordered logit or ordinal logistic regression and ordered probit regression (Abreu et al, 2008; Fullerton, 2009; Mielenz et al, 2010).

Abreu MNS, Siqueira AL, Cardoso CS, and Caiaffa WT. (2008). Ordinal logistic regression models: application in quality of life studies. Cad. Saúde Pública, Rio de Janeiro, 24 Sup 4: S581-S591.

Burkner PC and Vuorre M. (2019). Ordinal regression models in psychology: A tutorial. Advances in Methods and Practices in Psychological Science, 2: 77–101.

Fullerton AS. (2009). A conceptual framework for ordered logistic regression models. Sociological Methods and Research, 38: 306-347.

Liddell T and Kruschke JK. (2018). Analyzing ordinal data with metric models: What could possibly go wrong? Journal of Experimental Social Psychology, 79 : 328–348.

Mielenz N, Spilke J, and von Borell E. (2010). Analysis of ordered categorical data with threshold models exemplified by plumage damage scores from laying hens differing in their genotype and rearing environment. Poultry Science, 89 :2521–2534.