How are these three coefficients related mathematically? What ...

[newyorker26]

How are these three coefficients related mathematically?
 
  What will be an ideal response?

Question 2

How do the Pearson's r, the Spearman Rho and the Phi coefficients differ?
 
  What will be an ideal response?

[polinasid]

Answer to Question 1

Spearman rho and the phi coefficient are derived from the Pearson r. They are simpler versions of the Pearson.

Answer to Question 2

Each is appropriate for a particular type of variable and level of measurement. For example, the Pearson is used with continuous variables measured on an interval or ratio scale; the Spearman rho is used with rank order data measured with an ordinal scale;, and phi is used when both variables are true dichotomies (nominal data).