I wish to find the correlation between the change in K angle (continuous data) at a particular time post injury (continuous data) and pain scores (ordinal data). The change in the K angle and pain score are both dependent of the time post injury. Pain score improves and K angle can worsen. which statistical test can be used for this?
Hi, Nirmal,
Your question is vague, so I have three sets of responses.
First, if you do NOT have a tempero-geometrically specific a priori hypothesis, below are some free-to-view papers which may describe what you seek.
The first two papers discuss multiple (mixed measurement scale) "independent" variables. The third discusses bivariate analysis. The fourth is a brief report which describes how maximum-accuracy (i.e., "optimal") non-parametric models are identified.
- https://odajournal.com/2016/09/19/novometric-analysis-with-ordered-class-variables-the-optimal-alternative-to-linear-regression-analysis/
- https://odajournal.com/2016/09/19/novometrics-vs-multiple-regression-analysis-age-and-clinical-measures-of-pcp-survivors/
- https://odajournal.com/2016/09/19/1595/
- https://odajournal.com/2014/04/06/a-statistical-guide-for-the-ethically-perplexed-chapter-4-panter-sterba-handbook-of-ethics-in-quantitative-methodology-routledge-2011-clarifying-disorientation-regarding/
For bivariate applications, modern maximum-accuracy methods are superior to legacy non-parametric methods, such as, for example:
- Spearman -- https://odajournal.com/2015/12/02/unioda-vs-spearman-rank-%cf%81-between-raters-reliability-of-scores-on-the-adverse-drug-reaction-probability-scale/
- Kendall -- https://odajournal.com/2014/11/23/unioda-vs-kendalls-coefficient-of-concordance-w-multiple-rankings-of-multiple-movies-2/
Second, perhaps you are interested in time-to-event, or in time-series analyses--with or without propensity-score adjustment?
- Linden, A., & Yarnold, P.R. (2018). Estimating causal effects for survival (time-to-event) outcomes by combining classification tree analysis and propensity score weighting. Journal of Evaluation in Clinical Practice, 24, 380-387. DOI: 10.1111/jep.12859
- Linden, A., & Yarnold, P.R. (2017). Modeling time-to-event (survival) data using classification tree analysis. Journal of Evaluation in Clinical Practice, 23, 1299-1308. DOI: 10.1111/jep.12779
- https://odajournal.com/2018/08/13/using-oda-in-the-evaluation-of-randomized-controlled-trials-application-to-survival-outcomes/
- Linden, A., & Yarnold, P.R. (2017). Using classification tree analysis to generate propensity score weights. Journal of Evaluation in Clinical Practice, 23, 703-712. DOI: 10.1111/jep.12744
- https://odajournal.com/2017/06/08/1808/
- Linden, A., & Yarnold, P.R. (2016). Using machine learning to identify structural breaks in single-group interrupted time series designs. Journal of Evaluation in Clinical Practice, 22, 855-859. DOI: 10.1111/jep.12544
- https://odajournal.com/2018/03/25/the-australian-gun-buyback-program-and-rate-of-suicide-by-firearm/
On the other hand, if you would like to try a different approach to temporal modeling, maximum-accuracy Markov models are an excellent option. On the ODA webpage (https://ODAJournal.com) type "Markov" (without the quotation marks) in the search box to find numerous papers. For example, here are links to three articles which discusses modelling and/or predicting the temporal association of two attributes:
- https://odajournal.com/2019/02/18/optimal-markov-model-relating-two-time-lagged-outcomes/
- https://odajournal.com/2020/04/23/optimal-weighted-markov-analysis-modeling-weekly-rg-score/
- https://odajournal.com/2020/04/25/optimal-weighted-markov-analysis-predicting-serial-rg-score/
Third, you may have a structural a priori hypothesis which posits some type of constrained and/or repeating structure/relationship. In this case, I recommend the following book (extremely cheap used copies are available via the internet)--which includes examples of nonstandard hypotheses: for example, circular; circular nearest-neighbor; circular "spokes of a wheel"; triangular temporal flow; and others.
- https://www.apa.org/pubs/books/4316000
Alternatively, a PDF copy of the latest book on maximum-accuracy methods (Maximizing Predictive Accuracy) is available, with MegaODA and CTA software, on the resources page of https://ODAJournal.com
Modified pearsons , Logistic regression
If you can categorise the continuous data then Kruskal Wallis will also do interpretation in each of these will be different as they work on different null hypothesis.
https://stats.idre.ucla.edu/spss/whatstat/what-statistical-analysis-should-i-usestatistical-analyses-using-spss/
http://www.mash.dept.shef.ac.uk/Resources/MASH-WhatStatisticalTestHandout.pdf
https://www.edvancer.in/DESCRIPTIVE+STATISTICS+FOR+DATA+SCIENCE-2
You can use spearmans Rank correlation by making the continuos variable ordinal by ranking.
I agree with most of the researchers above and just want to summarize. If you want to measure the strength of the correlation between these variables, then you should use nonparametric methods (with or without data transformations). If your goal is to identify hidden or any pattern of association between these variables, then ANNs are the best method.