What is a positive correlation

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 SX and SY 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

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