Which statistical method should I use? (Sports Biomechanics)

[Boden]

Hi everyone!

I'm currently writing my thesis and was wondering which statistical method is best suited for my research question. We're investigating if different anthropometrical and neuromuscular characteristics of a runner (such as leg length, muscle strength, independent variables) can explain the biomechanical difference while running in two different running shoes. So to clarify, we've studied the difference in running mechanics while running in two different shoes and now we want to examine if any of these independent variables can explain the difference.

We've been discussing both multiple regressionanalysis as well as ancova and repeated measures mixed model ancova, with the independent variable as a covariate. I'm just afraid that ancova for instance doesn't really answer the question "explain the difference" and that we can really see how much the different variables affect one another in conjuction with the outcome variable.

PS: We have a very small sample size of 8 runners.

Appreciate all the help I can get, and just let me know if I need to clarify anything further.

 

[Karabiner]

Why don't you just calculate the biomechanical difference and use this as dependent variable?

Is it possible to collapse characteristics of the runner into one or two variables? If you use
several predictor variables in an analysis with just n=8, you will almost certainly produce
overfitting and non-reproducable results. If you analyse the characteristics separately,
then there is the issue of multiple testing and increased risk of type1 error (and one cannot
do a correction for that here, since it would further reduce the already very low statistical
power).

With kind regards

Karabiner

 

[Boden]

Thanks for your answer Karabiner.

For the multiple regression analysis, of course, the difference between the biomechanical variable would be used as a dependent variable.

What I am thinking about is which statistical method should be used, for instance, for the hypothesis: Shoe 2 induces greater ankle plantarflexor moment (dependent biomechanical variable) than Shoe 1 in runners with greater calf muscle strength and leg stiffness (neuromuscular independent variables).

My theory is that multiple different independent variables might explain the difference we're seeing in runners while running in shoe 2. This difference doesn't seem to be unison however, with some runners not showing any difference between the two shoes.

Is the multiple regression analysis enough to answer this question, or is there any other statistical method more suited for it?

Regards,
Sebastian

 

[Karabiner]

What I am thinking about is which statistical method should be used, for instance, for the hypothesis: Shoe 2 induces greater ankle plantarflexor moment (dependent biomechanical variable) than Shoe 1 in runners with greater calf muscle strength and leg stiffness (neuromuscular independent variables).

Either 2 simple regressions of the difference between ankle plantarflexor moment shoe1 - shoe2 on calf muscle strength, and on leg stiffness., respectively.

Or, a multiple regression of the difference between ankle plantarflexor moment shoe1 - shoe2 on both variables (calf muscle strength & leg stiffness).

With kind regards

Karabiner

 

[Boden]

My thoughts as well. Thank you so much Karabiner.

Two more questions, if you don't mind.
What would be the difference between an Ancova looking at the difference between shoe 1 and 2 with calf muscle strength as a covariate compared to a simple regression with the difference between the two shoes as an dependent variable and calf muscle strength as independent?
Is it that if there is a difference, then you can see it with both but that simple regression also tells you how strong that relationship is, and therefore is the more preferable method?

Lastly, there's many ways to perform a multiple regression analysis. Would a standard model be preferable in this case? I would think so partly because of the question in hand. We don't really know yet if there is any relationship, so we are interested in the overall result and how they uniquely contribute to that relationship. At the same time, if there is a relationship, we're also interested in the best combination, and therefore stepwise. How would you do it?

Regards,
Sebastian

 

[Karabiner]

Two more questions, if you don't mind.
What would be the difference between an Ancova looking at the difference between shoe 1 and 2 with calf muscle strength as a covariate compared to a simple regression with the difference between the two shoes as an dependent variable and calf muscle strength as independent?

With ANCOVA you mean a repeated-measures ANOVA with an additional interval scaled predictor?
That should give you the same resuts as the simple regression (the interaction effect in the RM-ANCOVA
is the effect of the predictor on the differnece variable in regression).

At the same time, if there is a relationship, we're also interested in the best combination, and therefore stepwise. How would you do it?

You should build a model which is theoretically meaningful, and include the according variables.
Do not use stepwise variable selection. It easily produces artefacts and overfitted models which
cannot be generalized.

But since you only have n=8 observations, the discussion s a bit arbitrary. Any model containing
more than 1 predictor may already be considerd overfitted.

With kind regards

Karabiner

 

[Boden]

Really appreciate your answers Karabiner. Thank you!

Regarding stepwise regression;
One of the assumptions when doing a regression analysis is multicollinearity. If I would do my analysis, observe a strong relationship between to independent variables and remove one of these variables, would this be by definition a stepwise regression? Just to make it clear.

Edit: Would perhaps an PCA (principal component analysis) with a OPLS (orthogonal partial least squares) be a better option considering the small sample size?

Thanks again Karabiner.

Regards,
Sebastian

 

[Karabiner]

Multiple regression, PCA etc. look like trying here to draw curls on a bald head.
For PCA see for example https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1156&context=pare

Maybe it is better to accept that one cannot do awfully much with a small sample size of n=8.

With kind regards

Karabiner