Hello,
I am measuring stress and strain on tissues in two different conditions and want to see the differences in the stress-strain curve. Since the nature of measurement introduces error during repeated measurement in both stress and strain there is both X and Y error for measurements and I obtain a graph like the one attached below. My question is what would be the correct statistical test to compare the two curves? and how can this be done using graphpad. One of the issue is that the X values are not same for both curves so ANOVA with one-on-one comparison becomes difficult as for the same X value I do not have corresponding Y values.
See if you can linearize the relationships. I'd guess that log(Y) vs. X will be linear. You may then use Deming regression. I don't know if there is a method to directly test a difference (in slopes, I assume) of two Deming models, but it's possible to bootstrap confidence intervals for then slopes that could be used for an inference about the difference.
I am quite sure that this is beyond Graphpads possibilities. I know that this is possible in R (https://cran.r-project.org/web/packages/deming/index.html).
Jochen Wilhelm, does the approach you are suggesting entail bootstrapping a CI for the difference between the two slopes? Or does it entail bootstrapping a CI for each slope separately, and then seeing if they overlap or not? If it is the latter, I would be worried about the issue described in this CMAJ article:
If we're so different, why do we keep overlapping? When 1 plus 1 doesn't make 2.
Rory Wolfe, James Hanley
CMAJ Jan 2002, 166 (1) 65-66;
https://www.cmaj.ca/content/166/1/65
The context is much simpler in that article, but I think the general principle still applies.
Cheers,
Bruce
Dear Bruce Weaver , I am not aware of a possibility to bootstrap the difference directly and I am aware of the problems you mention. It would certainly be best to bootstrap the difference directly. Maybe there is someone around pointing us to a better solution?
A. Linear
1- Look at an example in GraphPad software. As you can see, the X's are different in some cases.
2- Select the Compare option in the settings window.
3- The linear regression model (along with 95% confidence intervals) related to each of the e and s groups has been drawn.
4- You can see the parameters and results of the linear regression model obtained for each of the e&s groups.
5- Comparison of betas (tangent theta) is done in this sheet.
B. Nonlinear
6- Look at the data for a nonlinear example. (This is just an example).
7- Choose one of the nonlinear models that suits your data.
8- Try to compare the non-linear curves obtained from each of the E and S groups. There are other options here. For example, comparing two specific parameters with each other.
9- In this sheet, you can see the result of comparing two curves with each other. You have a certain P value.
10- You can see the non-linear graphs for each group. Again, I stress that this is just an example and you can test it on your own data.
Abolfazl Ghoodjani - where is considered that the x-values are also uncertain (error in y and x) ?
Kapish Gupta - I missed the point that you have repeated measures. That simplifies the issue: for each series you can fit an individual Deming regression line. For each individual you get a slope. The two groups of slope estimates can be compared using a t-test.
Dear Jochen Wilhelm , thank you very much for your attention.
In this case, the user can use the images I have attached in the Format Data Table window.
Just to note: "plotting errors on x-values" does not necessarily mean that errors in x are considered in the regression model.
Jochen Wilhelm Yes, You are right. I tested it now. The GraphPad software does not involve the Err. Bar in the regression model and uses them only to draw the graph. Thank you very much.
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