5 August 2020: Looking for assistance on a review of the calculation of my work on Kendall's W and Tau. This method made more logical sense in that its heavily used for survey responses. I also converted the categories of the numbers to ratings of 1(highest score) to 5 (lowest score). I ran this through JASP as well, and over all it looks like this is statistically insignificant.
Attached file Tab on is the survey with some quick calculations below, and Tab two is the Kendall's W work for the 11 events I'm focusing on.
Answered Kindly by the four below. I will have to give it some thought what way I plan to go based off suggestions below.
Research question: What Impact Does Triathlon Training Have on the Service Member Passing a Military Annual Fitness Exam?
Having just finished Research 202 I'm doing extracurricular research, and I'm wanting to understand, or rather, gain better familiarity with writing/working on projects. I have already completed, what I feel was a thorough, literature review on the topic. I had drafted/disseminated a survey to my target population (N=1,693), and by the close of the survey I have only n=15 respondents. All 14 respondents consider themselves Triathletes, and 1 considered non-triathlete. Therefore, I do not have enough participants to compare group 1 to group 2. I Think I could switch to a qualitative study, but before I change up a lot of work I'm wondering a couple questions.
What would the way forward be?
Is there a statistical Test for a singular group?
I also looked at Crossfit in literature Review, should a cross examination of a similar study be performed? (Since there is now experimentation, and the surveys is asking for averages of Fitness test Scores).
Logan Innes ,
Awesome stuff! I just completed work with graduation rates in police academies. The analysis would be similar, in short you absolutely can do a single group test. I do not know all the information you have though, so this may or may not work. However, if you have information on their training (i.e. what type or triathlete training, their times on events, etc) you can run a logistic regression analysis. Basically, you just need to include some form of independent variable or variables and then have the liklihood to pass as the dependent variable. Happy to chat if you have more questions, best wishes!
Also here is a link that would be helpful for you if you can go this route. https://statistics.laerd.com/spss-tutorials/binomial-logistic-regression-using-spss-statistics.php
If you compute the mean and standard deviation for each relevant variable in the 14 triathletes you can immediately get the confidence intervals at 95% (in the case of non gaussia variable you can use IQR as surrogate, see https://en.wikipedia.org/wiki/Interquartile_range .
and check if your single non triathlete is within the confidence interval or not.
If you have too many variables and fear of chance correlation, you can simply compute the distances (euclidean distances is oK) between all the 14 triathletes on the entire set of variables, so obtaining 14X13/2 distinct pairwise distances between triathletes couples, compute mean and standard deviation of these 91 numbers (distinct distances) and then compute the 14 distances of the nontriathlet from all the triathletes and check if the mean of these 14 distances is within or outside the confidence interval of the 91 distances between triathletes.
There are several one-sample statistics both parametric and non-parametric that can be used. With single sample statistics it depends on what variables you have access to and what your actually trying to examine. The one-sample t-test for example will allow you to compare the mean score of your group to a population mean. In your case I'm not certain this would be a viable option - but without knowing what data you currently have it's difficult to provide a more concrete solution.
You can use a nonparametric statistics approach with the combination of the Delphi technique with the Kendall's test, where the coefficient of concordance (W) is obtained. For more details, please check the method used in the following article for the group of participants data analysis.
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