I have 99 patients divided into subgroups according to the following variables:

  1. Their syntax score (which measures how severe the obstruction in coronary arteries is). Values of this variable are between 10.2 and 41 and are classified into three levels, first 1-22, second 23 - 32, third 33 or above. An increase in the syntax score means worse heart condition.

  2. MPI, which is myocardial performance index. Values of this variable are between 0.25 and 1.2. Increase in MPI also means worse heart condition.

Theoretically there is association between syntax score and MPI, so that increased syntax score should cause increased MPI, but when I did statistical analysis using SPSS there was no significant association.

Note that 35 patients from these 99 have normal coronary arteries so they are excluded from statistical analysis.

I did analysis using correlation, chi-square and ANOVA where I dealt with values in different ways. In correlation, I dealt with both syntax score and MPI as scale (continuous) variables, while in chi-squared, I dealt with both syntax score and MPI as nominal variables. In ANOVA, I dealt with syntax score as nominal variable and MPI as scale variable.

What is the most suitable statistical analysis?

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    $\begingroup$ So you have only 2 variables: Syntax Score, and MPI, and your hypothesis is that syntax causes MPI , and the relationship is positive. Is this correct ? Is each patient measured only once ? What was the Pearson correlation coefficient of the 2 raw variables. $\endgroup$ – Robert Long Apr 9 '19 at 9:14
  • $\begingroup$ yes that was my hypothesis and each patient is measured once. correlation coefficient was like this Correlations syntax score 2 MPI syntax score 2 Pearson Correlation 1 .088 Sig. (2-tailed) .488 N 64 64 MPI Pearson Correlation .088 1 Sig. (2-tailed) .488 N 64 64 $\endgroup$ – bahjat Apr 9 '19 at 9:22
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    $\begingroup$ That's very low and I suspect you may have trouble obtaining meaningful results unless there is marked non-linear association. However, please see my answer for more details. I hope it helps. $\endgroup$ – Robert Long Apr 9 '19 at 9:24
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    $\begingroup$ Let's just spell out that treating these variables as nominal is a terrible idea and just wastes the information in the data. $\endgroup$ – Nick Cox Apr 9 '19 at 9:39
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    $\begingroup$ Poor presentation: please note my extensive editing to make this more readable. Please think up a better title. A large fraction of threads here could have the same title, but it is no use to anyone else in the future searching for threads relevant to them. $\endgroup$ – Nick Cox Apr 9 '19 at 9:51

A good place to start would be plotting the 2 variables against each other.

This may or may not indicate a non-linear relationship. It may also indicate very little relationship at all, which is quite possible, given the low correlation.

Histograms of each variable may also be informative.

Subject to the above I would then consider a simple linear regression, treating each variable as numeric (NOT nominal)

MPI ~ Syntax

Splitting Syntax into 3 categories is probably a bad idea because doing so loses an lot of information and reduces the statistical power to detect an effect, if one exists. If you have done this because you believe the relationship is non-linear then using the raw variable and including one of more non-linear terms is a better idea, such as

MPI ~ Syntax + Syntax^2

It may be necessary to rescale Syntax since it is on a quite different scale to MPI

You have mentioned in comments that the Pearson correlation coefficient is 0.088. This is very low, and unless there is a non-linear association, I suspect you will struggle to obtain useful results with these data

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    $\begingroup$ (+1). I would add even more emphasis to plotting the data. $\endgroup$ – Nick Cox Apr 9 '19 at 9:39
  • $\begingroup$ @bahjat does this answer your question ? If so, please consider marking it as the accepted answer, if not, perhaps I can help further ? $\endgroup$ – Robert Long Apr 14 '19 at 17:08

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