I am hoping to find a correlation between some samples of routine blood tests taken on the first day of arrival at the hospital for some pacients with community-acquired pneumonia and the number of antibiotics empirically chosen (mono therapy, bi therapy, and multiple antibiotics).
PEARSON CORRELATION COEFFICIENT is appropriate when X = quantitative and Y = quantitative. When you have a mix of quantitative and ordinal (1st, 2nd, 3rd, 4th, ... etc.), the correct correlation to use is biserial correlation coefficient. See figure.
Here, your blood test is quantitative, and the arrival time (first arrival) is ordinal data. The second level of test, i.e. blood test and pneumonia and types of antibiotic treatment is quantitative (blood test) and nominal ( type of disease acquired or type of treatment regime used). The proper correlation here is point biserial, i.e. Y = blood test and X = type of treatment or type of disease).
Pearson correlation used between scale variables , while when your data consist of scale variable and the other was ordinal variable you can use Spearman correlation or Kendal correlation which both depend on ranks not on values its self .
other situation , if your data has normal distribution and scale in this case you can use Pearson , but if your data has not normal distributed you must use Spearman .
Good Luck
The number of medications is a counted scale, so it will follow a distribution that may be modelled with either Poisson (with robust variance for overdispersion) or negative binomial (likewise).
A correlation won't tell you much. Correlations are almost always uninterpretable in terms of clinical practice or patient outcomes. You need a measure of effect size. This is easier to get from a regression model.
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