FRACTION Subcommand (RANK command)

FRACTION specifies the way to compute a proportion estimate P for the NORMAL and PROPORTION rank functions.

  • FRACTION can be used only with function subcommands NORMAL or PROPORTION. If it is used with other function subcommands, FRACTION is ignored and a warning message is displayed.
  • Only one formula can be specified for each RANK procedure. If more than one is specified, an error results.

In the following formulas, r is the rank and w is the sum of case weights.

BLOM. Blom’s transformation, defined by the formula (r – 3/8) / (w + 1/4). 1 This is the default.

RANKIT. The formula is (r – 1/2) / w. 2

TUKEY. Tukey’s transformation, defined by the formula (r – 1/3) / (w + 1/3). 3

VW. Van der Waerden’s transformation, defined by the formula r / (w +1). 4

Example

RANK VARIABLES=MORTGAGE VALUE /FRACTION=BLOM
  /NORMAL INTO MORTNORM VALNORM.
  • RANK generates new variables MORTNORM and VALNORM. MORTNORM contains normal scores for MORTGAGE, and VALNORM contains normal scores for VALUE.
1 Blom, G. 1958. Statistical estimates and transformed beta variables. New York: John Wiley and Sons.
2 Chambers, J. M., W. S. Cleveland, B. Kleiner, and P. A. Tukey. 1983. Graphical methods for data analysis. Boston: Duxbury Press.
3 Tukey, J. W. 1962. The future of data analysis. Annals of Mathematical Statistics, 33:22, 1-67.
4 Lehmann, E. L. 1975. Nonparametrics: Statistical methods based on ranks. San Francisco: Holden-Day.