I have six dependent variables (continious) and two independent ones (one ordinal and one continious). My sample size is only 14 participants. I got some correction that Pearson Correlation Coefficient can't be used in such study as the sample size is pretty small (i.e., the normality assumption can be easily violated).
Any suggestion would be greatly appreciated!
With a sample size of 14, it will be almost impossible to produce significant results with any statistic, because your standard error and confidence intervals (or non-parametric equivalents) will be be too large.
Consider a Spearman rank correlation coefficient. It uses the ranks of the variables to measure the degree of association between two variables, and does not make any assumptions about the distribution of your data. It is appropriate when you at least have ordinal data.
Hi, Azzam,
N=14 is small, especially if there are many tied values (e.g., if ordinal-categorical "Likert-type" scales are used). For legacy methods, small samples and restricted measurement range both yield low statistical power.
Modern methods focus on making the most accurate possible predictions. This approach generally requires smaller samples than legacy methods to attain 90% statistical power to test a given hypothesis.
- https://odajournal.com/2020/02/08/statistical-power-analysis-in-oda-cta-and-novometrics-invited/
However, the crucial question is if the 95% CIs for accuracy of model- and chance-based classification overlap:
- https://odajournal.com/2020/06/11/generating-novometric-confidence-intervals-in-r-bootstrap-analyses-to-compare-model-and-chance-ess/
An inextricable problem with regression models is that they do not make accurate predictions--the effect of "regression toward the mean".
- https://odajournal.com/2013/09/20/maximizing-the-accuracy-of-multiple-regression-models-using-unioda-regression-away-from-the-mean/
IN CONTRAST: The analysis which I recommend handles (multi)categorical and/or ordered data, it has no distributional assumptions, it obtains the exact p-value for your hypothesis, and by formulation it identifies the most accurate model possible (yielding the greatest possible effect strength) which exists for your data.
Here it is vs. correlation and regression:
- https://odajournal.com/2016/09/19/novometric-analysis-with-ordered-class-variables-the-optimal-alternative-to-linear-regression-analysis/
Here is a general introduction to the methodology:
- 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/
- https://odajournal.com/2017/04/18/what-is-optimal-data-analysis/
And here is the state-of-the-art:
- https://odajournal.com/2020/06/28/what-is-novometric-data-analysis/
With a sample size of 14, it will be almost impossible to produce significant results with any statistic, because your standard error and confidence intervals (or non-parametric equivalents) will be be too large.
It is a very small sample size given to the number of variables you have and the test that you would like to consider. I agree with David, that it will be almost impossible to produce significant results. I suggest, add more samples.
The sample size is small. You can use (1) Kendall rank correlation or (2) Spearman rank correlation. For Spearman rank correlation data must be at least ordinal and the scores on one variable must be monotonically related to the other variable.
For more details about the non-parametric test for your statistical analysis go to following link:
https://www.statisticssolutions.com/correlation-pearson-kendall-spearman/#:~:text=Spearman%20rank%20correlation%3A%20Spearman%20rank%20correlation%20is%20a,measure%20the%20degree%20of%20association%20between%20two%20variables.
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