# Correlation

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### USMLE® Step 2 style questions USMLE

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A researcher is studying the association between mean maternal body mass index (BMI) before pregnancy and mean childhood BMI at four years of age. Analysis of the results reveals a correlation coefficient of 0.35 and p-value of 0.03. Which of the following conclusions can be drawn from this analysis?

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### Transcript

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#### Contributors

Correlation is a statistical technique that shows whether two quantitative variables are related, and also how strongly they’re related.

For example, let’s say you want to figure out if drinking more soda is correlated with having a higher body mass index or BMI.

So, you ask 100 people how many sugary beverages they drink in a week and then check each person’s height and weight to calculate their BMI.

You could plot these measurements or data points on a scatterplot, with the number of beverages on the x-axis and BMI on the y-axis, and where each data point represents one individual.

Typically, a trendline is drawn to best represent the pattern of data points on the plot, with roughly half the points above the line and half the points below the line.

Now, a positive correlation means that BMI increases as the number of beverages increases, and, if the two variables have a perfect positive correlation, then the trendline will pass through every single data point.

Now imagine that there’s a negative correlation. That means that the BMI decreases as the number of beverages increases, and, with a perfect negative correlation, the trendline also passes through every data point.

Finally, if there’s no correlation, then the data points will be randomly spread out all over the scatterplot, and the trendline will be flat with no positive or negative direction.

To figure out how strongly two variables are correlated, we can use the Pearson’s correlation test, which is a parametric test that measures how close or spread out the data points are from the trendline.

The Pearson’s correlation test calculates a correlation coefficient, which is a number that represents how well the two variables are correlated, and usually it’s written with a lowercase r.

The correlation coefficient can range from negative 1 - which represents perfect negative correlation - to positive 1 - which represents perfect positive correlation.

A correlation coefficient of 0 means that there’s no correlation between the two variables.

Now, there are four key assumptions that are used in a Pearson’s correlation test, and an acronym for these assumptions is L-I-N-E, or LINE.

First, the relationship between the two variables has to be Linear, which means that the trendline drawn to represent the data points is a straight line.

Relationships that have a different type of curve, like in an exponential relationship or a U-shaped relationship, will have a low correlation coefficient because a straight trendline doesn’t match the shape of the data points.

The second assumption is that each individual in the sample was recruited Independently from other individuals in the sample.

In other words, no individuals influenced whether or not any other individual was included in the study.

For example, if one person agrees to be in the study only if their friend can also be included in the study, then these two individuals would not be independent of each other and the second assumption would not be met.

### Summary

A correlation is a statistical measure that quantifies the degree of relationship between two variables. In other words, it shows how closely two things are related. A correlation coefficient can range from -1 to 1, with a value of 1 indicating a perfect positive correlation and a value of -1 indicating a perfect negative correlation.

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