# What is a positive correlation

**StATS :** What is a correlation? (Pearson correlation)

A correlation is a number between -1 and +1 that measures the degree of association between two variables (call them X and Y). A positive value for the correlation implies a positive association (large values of X tend to be associated with large values of Y and small values of X tend to be associated with small values of Y). A negative value for the correlation implies a negative or inverse association (large values of X tend to be associated with small values of Y and vice versa).

**The formula for the Pearson correlation**

Suppose we have two variables X and Y, with means XBAR and YBAR respectively and standard deviations S_{X} and S_{Y} respectively. The correlation is computed as

There are some short cuts, but in general the formula is tedious and we will let the computer do all this work.

**When will a correlation be positive?**

Suppose that an X value was above average, and that the associated Y value was also above average. Then the product

would be the product of two positive numbers which would be positive. If the X value and the Y value were both below average, then the product above would be of two negative numbers, which would also be positive.

Therefore, a positive correlation is evidence of a general tendency that large values of X are associated with large values of Y and small values of X are associated with small values of Y.

**When will a correlation be negative?**

Suppose that an X value was above average, and that the associated Y value was instead below average. Then the product

would be the product of a positive and a negative number which would make the product negative. If the X value was below average and the Y value was above average, then the product above would be also be negative.

Therefore, a negative correlation is evidence of a general tendency that large values of X are associated with small values of Y and small values of X are associated with large values of Y.

Let's compute a correlation coefficient between the 1 minute APGAR scores (X), and the 5 minute APGAR scores (Y). Here's a table

showing some of the intermediate calcuations.

**Interpretation of the correlation coefficient.**

The correlation coefficient measures the strength of a linear relationship between two variables.

The correlation coefficient is always between -1 and +1. The closer the correlation is to +/-1, the closer to a perfect linear relationship. Here is how I tend to interpret correlations.

- -1.0 to -0.7 strong negative association.
- -0.7 to -0.3 weak negative association.
- -0.3 to +0.3 little or no association.
- +0.3 to +0.7 weak positive association.
- +0.7 to +1.0 strong positive association.

This rule, of course, is somewhat arbitrary. For some situations, I mught move the cut-off values closer to 0 (e.g. 0,.2 and 0.6) and for other situations, I might move the cutoff values closer to 1 (e.g. 0.4 and 0.8).

**Example of a strong positive association.**

The correlation between blood viscosity and packed cell volume is 0.88.

Notice that small volumes tend to have low viscosity and large volumes tend to have high viscosity.

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**Example of a weak positive association.**

The correlation between blood viscosity and fibrogen is 0.46.

Notice that there is also a tendency for small fibrogen values to have low viscosity and for large fibrogen values to have high viscosity. This tendency, however, is less pronounced than in the previous example.

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**Example of little or no association.**

The correlation between blood viscosity and plasma protein is -0.10.

Low levels of protein are associated with both high and low viscosities. High levels of protein are also associated with both high and low viscosities.

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**Correlation matrix.**

When you have more than two variables, you can arrange the correlations between every pair into a matrix.

At the bottom of this page is an example using the blood viscosity data.

To create this table, select ANALYZE | CORRELATE | BIVARIATE from the SPSS menu.

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**Rounding helps a correlation matrix.**

At the bottom of the page is the same correlation matrix, multiplied by 100 and rounded to two significant digits.

We also removed some of the extraneous information.

- - Correlation Coefficients - -

Source: www.pmean.com

Category: Forex