# Methods and formulas for correlation coefficients for Cross Tabulation and Chi-Square

Select the method or formula of your choice.

## Pearson's r

Pearson's correlation is a measure of linear relationship between two variables, which ranges from +1 to -1. A correlation of +1 indicates a perfect positive linear relationship between variables.

The data are converted to ordinal data by taking the data values and coding as equally-spaced integers. For example, the series 4, 7, 20, is analyzed as 1, 2, 3, and thus, the series 4, 7, 7, 20, is analyzed as 1, 2, 2, 3.
###### Note

This is different from the Spearman statistic which analyzes the same sequence of 4, 7, 7, 20 as 1, 2.5, 2.5, 3.

### Notation

TermDescription
ni+ number of observations in the ith row
n+j number of observations in the jth column
nij observations in the cell corresponding to the ith row and jth column
n++ total number of observations

## Spearman's rho

Spearman's rho is a measure of the linear relationship between two variables. Spearman's differs from Pearson's correlation only because the computations are done after the numbers are converted to ranks.

### Formula

If i = 1, then:

If i = 2, 3,..., r, then:

If j = 1, then:

If j = 2, 3,..., c, then:

### Notation

TermDescription
c number of columns
r number of rows
ni+ number of observations in the ith row
n+j number of observations in the jth column
nij observations in the cell corresponding to the ith row and jth column
n++ total number of observations
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