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Chapter 13: Q3BSC (page 597)

Notation What do r, \({r_s}\) , \(\rho \), and \({\rho _s}\) denote? Why is the subscript s used? Does the subscript s represent the same standard deviation s introduced in Section 3-2?

Short Answer

Expert verified

The symbols\(r\;{\rm{and}}\;{r_s}\)represent the sample linear correlation coefficient and the sample rank correlation coefficient respectively.

The symbols\(\rho \;{\rm{and}}\;{\rho _s}\)represent denotes the population linear correlation coefficient and the population rank correlation coefficient respectively.

Subscript s is used to differentiate between the linear correlation coefficient and the rank correlation coefficient.

Subscript s does not represent the standard deviation.

Step by step solution

01

Identify the statistical measures for the given notations

r denotes the sample linear correlation coefficient.

\({r_s}\)denotes the sample rank correlation coefficient.

\(\rho \)denotes the population linear correlation coefficient.

\({\rho _s}\) denotes the population rank correlation coefficient.

02

Identify subscript “s”

Subscript “s” is used to differentiate between the two measures, such as:

  • linear correlation coefficient and
  • rank correlation coefficient.

It does not represent standard deviation.

It stands for “Spearman,” which is the surname of the statistician “Charles Spearman,” who proposed the concept of rank correlation.Linear correlation coefficient and rank correlation coefficient are defined using different symbols.

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