Introduction

The correlation coefficient is a statistical measure that quantifies the degree to which two variables are linearly related. It ranges from -1 to 1, with the following interpretations:

  • Positive Correlation ( 0< r <1 ): As one variable increases, the other tends to increase.
  • Negative Correlation ( −1< r <0 ): As one variable increases, the other tends to decrease.
  • No Correlation ( r = 0 ): There is no linear relationship between the two variables.

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It provides a way to quantify the extent to which each data point in a distribution differs from the mean of the distribution. The standard deviation is always non-negative, and a lower standard deviation indicates that the data points tend to be close to the mean, while a higher standard deviation indicates that the data points are spread out over a wider range.

In Meta-Analysis, it is sometimes useful to convert standard deviation values into correlation coefficients to better understand the relationship between variables. This article explains the concept and provides a practical example along with the formula used for this conversion.

Variables Definitions

  1. Baseline SD: This represents the standard deviation of a set of data before any treatment or intervention. It is a measure of the amount of variation in the initial dataset.
  2. Post-Treatment SD: This is the standard deviation of the same set of data after a treatment or intervention has been applied. It measures the amount of variation in the dataset following the treatment.
  3. SD Change: The difference between the baseline standard deviation and the post-treatment standard deviation. It indicates how much the standard deviation has changed due to the treatment.
  4. Correlation Coefficient (CC): The result of the conversion, representing the strength and direction of the linear relationship between the two variables. The correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
  5. Conversion Formula

The conversion from standard deviation to correlation coefficient is done using the following formula:

This formula is derived from the relationship between correlation coefficients and standard deviations.

Formula Reference - Cochrane Handbook