"correlation analysis with" is correct and usable in written English.
You can use it when you are looking to analyze the relationship between two or more variables. For example, "We conducted a correlation analysis with demographic and economic data to determine the impact of taxes."
Diameters of proximal tubules and cysts were correlated (Pearson correlation analysis) with proliferation index.
Bivariate correlations were calculated by Pearson's correlation analysis with p < 0.05 regarded as significant.
A set of experiments were conducted based on correlation analysis with 120 students of these four factors and learning performance.
To test Hypothesis 6, we built a mere factor score for the competence test and conducted a bivariate correlation analysis with the constructs in our identity survey.
The relationships between ammonia-oxidizing communities and environmental factors were examined using Pearson's correlation analysis with the PASW 19.0 software (IBM SPSS Inc., Chicago, USA).
Colocalization quantification was performed as previously described [18] using intensity correlation analysis with the following modifications.
Correlations were calculated by Pearson correlation analysis with one-sided significance calculated by Cronbach's Alpha.
Copy number was extracted on a gene-by-gene basis to perform Pearson correlation analysis with expression.
The dietary similarity matrix (hereafter DSM) was then compared to MSI using matrix correlation analysis with Mantel's test for significance.
We repeated the correlation analysis with the asymmetric substitution matrices from orthologues and obtained essentially the same results.
Furthermore, correlation analysis with amygdala's activation when listening to negative music with eyes closed showed co-activation with the LC and the VPFC.
