It allows researchers to evaluate the strength and direction of relationships between variables like dose and response, plasma level and toxicity, or compliance and formulation type.
However, it is crucial to remember that correlation does not imply causation. He is credited with crafting the first histogram.
When plotted, the values are scattered randomly. A Pearson correlation coefficient (r) calculated here would likely be close to +1, indicating a strong positive correlation.
This helps establish that higher doses are linearly associated with greater therapeutic responses—useful for dose-response studies and Phase II clinical trials.
Example 2: Correlation Between Plasma Drug Concentration and Adverse Effects
Suppose a pharmacovigilance team analyzes plasma concentration of a drug (in µg/mL) and the intensity of adverse drug reactions (scored from 1 to 10).
Plasma Conc.
Karl Pearson’s Correlation Coefficient
Learn the step-by-step process of finding the correlation coefficient in statistics.
Problem Statement
Find the Karl Pearson’s coefficient of correlation between \(X\) and \(Y\) for the given data:
The Karl Pearson’s coefficient of correlation is approximately 0.946, indicating a strong positive correlation between \(X\) and \(Y\).
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Karl Pearsons Coefficient of Correlation
Definition and Formula:
Karl Pearson’s coefficient of correlation (commonly denoted as r) is the most widely used method to quantify the linear relationship between two continuous variables.
Correlation 1: age ~ intelligence Correlation 2: body mass index ~ shoe size
These are nonoverlapping correlations because no variable is part of both correlations.
Definition of Correlation
Karl Pearsons Coefficient of Correlation: Correlation is a statistical technique used to measure and describe the strength and direction of a relationship between two quantitative variables. To do so, you can download the cocor package from here or r-project.org.
He was the first to introduce the probability value, or p-value, which has since become a core tool of testing hypotheses in statistical studies in a wide variety of fields.
Just as important, Pearson developed novel tools for visualizing statistical studies. While correlation can indicate an association, further experimental studies are required to determine cause-effect relationships.
Using correlation analysis wisely helps pharmaceutical scientists and healthcare providers make informed, data-driven decisions to improve drug safety, efficacy, and patient adherence.
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Karl Pearson: Creator of Correlation
Karl Pearson is widely viewed as the founder of modern statistics.
In this case, r might be around -0.98, indicating a strong negative correlation.
This kind of data is critical in pharmaceutical product development where minimizing pill burden (e.g., developing extended-release or combination formulations) can improve adherence.
Example 4: No Correlation – Age and Drug Absorption Rate
In a study of drug absorption rates across age groups, researchers found that there is no consistent trend between age and absorption rate for a specific drug due to compensatory physiological mechanisms.
Here you find an overview of all implemented tests.
You can integrate the R code generated by this web interface in your own R script. In 1925, he decried the prospect of Jewish immigration to Britain, describing Jews as “inferior physically and mentally.”
Pearson died in 1936, just as Nazi Germany began to implement a genocide largely premised on eugenics ideology.
Alternatively, you can type one of the following commands in the R console to install:
# alternative repository install.packages("cocor", lib="/my/own/R-packages/", repo="http://comparingcorrelations.org/repo")
The cocor package also includes a GUI extension for the R front-end RKWard, which you can use instead of this web interface.
Are the two correlations overlapping, i.e., do they have one variable in common?
The two correlations are
Overlapping:
Nonoverlapping:
Correlation 1: age ~ intelligence Correlation 2: age ~ shoe size
These are overlapping correlations because the same variable (age)is part of both correlations.
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The calculations rely on the tests implemented in the package cocor for the R programming language. It provides a numerical value ranging from -1 to +1, indicating the direction and strength of the correlation.
The formula for Karl Pearson’s correlation coefficient is:
Where:
Xi and yi are the individual sample points
xˉbar is the mean of the x-values
yˉbar is the mean of the y-values
Alternatively, for computational ease, this formula can also be used:
Interpretation of r values:
r Value
Interpretation
+1
Perfect positive correlation
0 to +0.75
Moderate to strong positive
0
No linear correlation
-0.75 to 0
Moderate to strong negative
-1
Perfect negative correlation
3.
That is, just because two variables are correlated does not mean one causes the other.
2. In addition to discovering numerous statistical concepts, he pushed to create statistics as a distinct discipline, founding the first ever university statistics department and the first academic journal focused on the field.
It’s a strikingly simple concept but one that makes it much, much easier for somebody to understand the significance of data.
Pearson also played a big role in developing statistical hypothesis testing and statistical decision theory, both of which are major components of modern statistical research. He was an atheist who vehemently criticized Christianity as well as a socialist and anti-monarchist who refused recognitions from the British Crown, including a knighthood.
A vision for statistics
Although Pearson contributed to a number of fields, his most notable work came in statistics.
Pharmaceutical Examples of Correlation
Example 1: Correlation Between Dose and Therapeutic Response
A pharmacologist investigates the relationship between the dose of a drug (in mg) and the corresponding reduction in systolic blood pressure (in mmHg) in five patients.
Dose (mg)
Reduction in SBP (mmHg)
50
8
100
14
150
20
200
25
250
30
From this dataset, it is evident that as the dose increases, the reduction in blood pressure also increases.
He believed not only in a hierarchy of races throughout the world, but also that it was preferable to eliminate or displace “inferior” races than for them to coexist alongside the “superior” race.
He also worried, like his mentor Francis Galton, that people in the professional classes in Britain weren’t reproducing as rapidly as those of “lower stock” and believed this could lead to genetic decline.
Beginning with his days as a student, Pearson voraciously pursued knowledge in every field, including literature, mathematics, philosophy, and the natural sciences.
“I rush from science to philosophy, and from philosophy to our old friends the poets; and then, over-wearied by too much idealism, I fancy I become practical in returning to science,” he wrote in his first book, The New Werther, a work of fiction written in the form of letters by a young man in Germany in search of a new philosophy.
Pearson was a devoted skeptic of many of the institutions governing British society during his life.
It helps determine whether, and to what degree, a change in one variable is associated with a change in another.
In simpler terms, correlation answers the question: “When one variable changes, does the other tend to change as well—and if so, how strongly and in which direction?”
Correlation can be positive, negative, or zero:
A positive correlation indicates that as one variable increases, the other also increases.
A negative correlation indicates that as one variable increases, the other decreases.
A zero correlation means there is no linear relationship between the variables.