The Fechner correlation coefficient, also known as the rank correlation coefficient, is used to estimate the degree of relationship between two variables. Here are some formulas related to this coefficient:
- Fechner correlation coefficient (r):
[
r = 1 – \frac{6 \sum d_i^2}{n(n^2 – 1)}
]
where:
- (d_i) is the difference between the ranks for each pair of observations,
- (n) — total number of observations.
- Calculation of ranks:
- Assign ranks to each value in the sample. If there are identical values, assign them the average rank.
- Sum of squared differences of ranks:
[
\sum d_i^2 = \sum (R_1 – R_2)^2
]
where (R_1) and (R_2) are the ranks of the two variables. - Significance check:
- To test the significance of the correlation coefficient, you can use tables of critical values or perform significance tests.