Comparison between (3rd-order polynomial) regressions.

Thank you, Luca, but I don't understand your answer.

Please explain!

Raffy

I know there are Ciba-Geigy tables to compare coefficients sets from couples of polynomial regression equations.

One of the approaches might be to use bootstrapping to estimate uncertainty in the equation parameters (maybe you already have), and then using appropriate statistics to test for the difference in the parameters between child-adult. Works fine with small polynomials where it is easy to give meaning to parameters (e.g. intercept, etc.). You'll have 4 parameters for every equation, and two conditions. Please consider normalising the dependent data (as you did with the time-to-exhaustion) before doing the comparison and the fitting, otherwise you might end up with significant differences only due to the magnitude of the responses rather than to the actual underlying MPF-driving mechanism. Not sure it's the best approach out there, but it make sense to me.

Hope this helps!

Let me rephrase your question and see if I have proper understanding. In your dataset you have MPF as a function of the normailzed time-to-exaustion (TTE), and of the group(G) of subjects. We can reshape tabulated values to supplement models through interactions.

Here three approaches:

1) you could consider a longitudinal analysis with TTE as longitudinal factor, and perform model comparison through log-likelihood ratio. have a look at: https://www.mathworks.com/help/stats/longitudinal-analysis.html

2) Your test model is MPF ~ TTE^3 * G. This model expands to MPF = c0 + c1* TTE + c2 *G + c3*TTE*G + c4*TTE^2 + c5*TTE^2*G etc...

Once you fit this model, you would be able to get for each coefficient its value, standard, error, z-score, pval, confidence interval, etc...

Have a look at https://www.statsmodels.org/stable/mixed_linear.html

In this way you would be checking e.g. the 'base' effect for each coefficient for the standard group, and the effect on that coefficient for the other group of subjects.

2 bis) The model can be adjusted to suppress specific coefficients and obtain something less generic.

Let's say we are sure that groupwise differences are only bound to the third power of TTE e.g. MPF = c0 + c1* TTE + c2*TTE^2 + c3*TTE^3 + c4**TTE^3*G.

3) you could build your models, then contrast them with Wald test. Have a look at https://www.statsmodels.org/dev/examples/notebooks/generated/contrasts.html

Depending on the design matrix of your dataset you may end up in some limitations but an appropriately built mixed-model would probably help.

PM me if needed.

I had the same problem with intraclass correlation coefficient. You can use this (is in spanish). https://mathcracker.com/es/calculadora-comparar-correlaciones-muestrales#results

References - Comparing Correlated Correlation Coefficients - Meng el tal 1992

Current Research and Statistical Practices in Sport Science and a Need for Change - Bernards et al 2017