I’ve run 14 sets of experiments using DOE > Response Surface (Box Behnken). Based on the results, the p-values for my factors are not below 0.05, which suggests they are not statistically significant. However, according to the literature, these parameters should be significant. My p-values are 0.06, 0.47, and 1.24 for each factor.
Can I still include the statistical graphs from Minitab in my report, or should I change the range of my parameters? Also, I’m not sure if I need to adjust the response surface model.
Thank you in advance.
The p-value can't be greater than 1. Are you looking at the right output ?
Could you attach the diagnostic plots? It would be much easier to analyze. Based on what you’ve written, we can only confirm that the value of 0.06 might indicate a trend, while the rest do not appear to be statistically significant, but that's what you already know.
The normal probability plot is, in my opinion, too S-shaped. Also, the residual histogram is clearly bimodal. The AICc at this level also indicates overfitting or lack-of-fit. All of these issues suggest that the problem is deeper. The main assumption of regression analysis is that the data are normally distributed, which is not the case in your design.
Could you perhaps share exactly what you are measuring? What terms did you include in the model, and is it linear, 2FI, or quadratic?
I am immobilizing biomolecules on surface of a polymer. the concentration of the biomolecule in the solution, time of exposure, and concentration of a modifier are my parameters. I defined a range based on literature. Then, I check the elemental percentage changes on the surface with XPS. I am unsure if XPS is a correct method for characterization.
Could you please share the literature proving these specific parameters are indeed significant? Thank you.
I'm not very familiar with these models...
But I suspect the main issue is that have only 14 observations and 3 factor you're trying to test. This is the nature of p-values: the more observations you have, the more likely you will get a significant p-value. The fact that your r-squared is 0.79 suggests that there's something meaningful to this model. Are you able to tease out the r-squared contribution of each factor ?
1) You might consider not including one of these factors.
1b) Or at least starting with simple correlations or something to see if these factors individually are related to your outcome variable.
2) As to whether you can still present the plot. If you think these are factors that have been shown to be meaningful for your dependent variable i the past, I think it makes sense to. Sometimes for these kinds of things, variables with p-values of 0.10 or so are included anyway. I would focus less on p-values and more on the overall model that's produced. Are you able to get a p-value for the model as a whole ?
Your sample size is too small to produce reliable results. What you have produced cannot be interpreted with confidence,
I appreciate your time and help!
Dear Jakub Jagielski We looked through the literature, and most of them set a value for these parameters which gives us a range and we tried to consider that in our experiment.
Dear Sal Mangiafico I thought the higher the Rsq, the better! And at least it should be over 0.9. The model is quadratic so in the final equation we have A, B, C, A*A,..., A*B,... and the p-values get worse along. If I should avoid a parameter maybe I need to consider only a linear part of the equation. So it would be like: Y=aA+bB+cC!
Dear Kelvyn Jones I'm unsure if I learned what you meant with sample size. Do you mean we need more than 14 experiments to see the significance of parameters? Or it is regarding each sample that I measure with XPS? If it is the former, do we have a guide that how many sets are safe to have reliable p-value? If it is the latter, I am thinking of correlating a few experiments from XPS with another technique, to see if XPS is a proper characterization method here.
Yes, a higher r-square indicates a better model fit. What constitutes a good r-square depends on the field and the specific study. But in the real world, an r-squared of 0.79 is pretty damned good. But this doesn't translate to an analytical chemistry lab.
Yes, you could use a simpler model. I don't know if something like lasso would be appropriate for what you want to do, but that's a modern method. Less modern methods are adding or subtracting the terms stepwise either by p-value or r-square or some other criterion.
I don't know if either of these methods are appropriate for what you're doing, or if you should just stick to your original model, and report what you have.
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