Hi all,
I would like to see how strongly the exhausted isoflurane correlates with the coronary sinus isoflurane level. Basically, I hypothesised that we could use exhausted isoflurane to predict the level of isoflurane in coronary sinus blood during cardiopulmonary bypass.
By doing a normal correlation on spss, my correlation coefficient is 0.68, p
Dear Ka Ting
You can attempt the quadratic regression treating one dependent variable. If you have theoretical basis for the curvilinear or no relationship pattern, then also u can go for curvilinear regression. It will be better than correlation coefficient, as CC measures the linear relationship between two variables.
Dear Rajiv,
Thank you very much for your advice.
I am not sure how to confirm does the curvilinear relationship really present on my graph?
I judge it on the scatter plot based on my bare eyes. I have run the quadratic on one dependent variable as you said this morning and it seems not much different.
I just wonder would there be any way that i could sure whether is there any curvilinear relatioonship on my scatter plot?
Many thanks for your time.
Ka
Replace X and Y with your own variable names in the following SPSS syntax:
* Fit quadratic function using REGRESSION procedure.
COMPUTE Xsq = X**2.
REGRESSION
/DEPENDENT Y
/METHOD=ENTER X Xsq.
* Fit quadratic function using UNIANOVA procedure.
UNIANOVA Y WITH X /DESIGN=X X*X.
* Rsq value is show below the ANOVA summary table.
HTH.
Looking at the graph, it's difficult to know what kind of model is best.
You _could_ make it a linear model, or a quadratic model.
But I suspect these models don't fit particularly well. One problem is that, using Artery as the x-axis, the variance around x = 0.25 is tiny, and the variance around x = 1.25 is huge.
What to do? One of the following:
1) It looks to me like like switching the x- and y- axes would make the data more applicable for a general linear model.
2) Here's what the data say to me: When artery is low, vein is low. When artery is high, vein is anywhere from slightly higher to very high. Because of spread of the data, you might try a Cate-Nelson approach. See: http://rcompanion.org/rcompanion/h_02.html . This just divides bi-variate into groups of low-low and high-high, but is really useful when the data spread out in an L shape.
4) Switch the x- and y- axes and use a linear- plateau model. See the section called "Examples of linear plateau and quadratic plateau models" in this book: http://rcompanion.org/documents/RHandbookProgramEvaluation.pdf
3) Use a nonparametric correlation, and leave it at that. Kendall or Spearman correlation.
I have tried to use curvilinear quadratic regression, but it seems that it didnt have much improvement to the formula. The R2 changes is very subtle/minimal after using the quadratic approach.
Hence, i questioned myself whether will that scatter plot is actually a linear relationship instead of curvilinear relationship.
What do you think?
Many thanks
Dear Ka Ting Ng,
In case of curve linear relationship is suspected, take the logarithm transformation of the y data. If correlation improves after the transformation means there exist a curve linear relationship. If the change in correlation is not much, then you can proceed for further analysis and interpretation assuming that there exist a linear relationship.
Dear Ramnath Takiar,
Thank you so much for your suggestion.
That is a very sensible way to try.
Have a nice day.
Yours sincerely,
Ka
Dear Ramnath,
Should I use logarithm transformation for both x- and y-axis data?
I have run a normality test on both variables. X-variable is non-normal distributed, Y-variable is normal distributed.
I have transformed Y-data as you suggested. Parametric value (increased from 0.67 to 0.80); whilst non parametric no changes (remained as 0.68).
1. Just out my curiosity, which correlation result should I take? Presumably is non-parametric one as my variables are one non-normal and one normal distributed.?
2. Should I also transformed both variables?
Many thanks for your time.
Yours sincerely,
Ka
I think by parametric value, you mean correlation. Right. OK. As per your description, your aim is to predict y given x, so it can be only done by parametric approach. Find out the regression coefficient, intercept, thus the regression equation for prediction. By doing x transformation, if correlation improves, you can do so. I am eager to know what is the sample size in your project? If r = 0.8, it is quite good for a model and prediction purposes. It is generally argued that a parametric test is often more powerful than a non-parametric test. So, if normality assumption is violated to a less extent then one should not bother.
I suggest you to find out the prediction values of y and see how much they differ from their original values. If it is within 5 to 10% fine or In case the average value of the differences is below 10%, it is fine. Please, do this and inform me then I can suggest you further.
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