Enter your search terms Submit search form
	Web pdp-10.trailing-edge.com

SUBROUTINE TETRA

PURPOSE
   COMPUTE A TETRACHORIC CORRELATION COEFFICIENT BETWEEN TWO
   VARIABLES WHERE DATA IN BOTH VARIABLES HAVE BEEN REDUCED
   ARTIFICIALLY TO TWO CATEGORIES.

USAGE
   CALL TETRA (N,U,V,HU,HV,R,RS,IE)

DESCRIPTION OF PARAMETERS
   N  - NUMBER OF OBSERVATIONS
   U  - INPUT VECTOR OF LENGTH N CONTAINING THE FIRST VARIABLE
	REDUCED TO TWO CATEGORIES
   V  - INPUT VECTOR OF LENGTH N CONTAINING THE SECOND VARIABLE
	REDUCED TO TWO CATEGORIES
   HU - INPUT NUMERICAL CODE INDICATING THE HIGHER CATEGORY OF
	THE FIRST VARIABLE.  IF ANY VALUE OF VARIABLE U IS
	EQUAL TO OR GREATER THAN HU, IT WILL BE CLASSIFIED AS
	THE HIGHER CATEGORY, OTHERWISE AS THE LOWER CATEGORY.
   HV - SAME AS HU EXCEPT THAT HV IS FOR THE SECOND VARIABLE.
   R  - TETRACHORIC CORRELATION COMPUTED
   RS - STANDARD ERROR OF TETRACHORIC CORRELATION COMPUTED
   IE - ERROR CODE
	0 - NO ERROR
	1 - UNABLE TO COMPUTE A TETRACHORIC CORRELATION DUE TO
	    THE FACT THAT AT LEAST ONE CELL SHOWS ZERO FRE-
	    QUENCY IN THE 2X2 CONTINGENCY TABLE CONSTRUCTED
	    FROM INPUT DATA.  IN THIS CASE, R AND RS ARE SET
	    TO 10**75.	(SEE GUILFORD, 1956)
	2 - THE ROOT SOLVER GIVES MULTIPLE ROOTS, OR NO ROOTS,
	    R, IN THE INTERVAL (-1,1) INCLUSIVE. R AND RS ARE
	    SET TO 10**75.
	3 - UNABLE TO COMPUTE A SATISFACTORY VALUE OF TETRA-
	    CHORIC CORRELATION USING NEWTON-RAPHSON METHOD OF
	    APPROXIMATION TO THE ROOT OF THE EQUATION.	R AND
	    RS ARE SET TO 10**75.  SEE SUBROUTINE POLRT ERROR
	    INDICATORS.
	4 - HIGH ORDER COEFFICIENT OF THE POLYNOMIAL IS ZERO.
	    SEE SUBROUTINE POLRT ERROR INDICATORS.

REMARKS
   VALUES OF VARIABLES U AND V MUST BE NUMERICAL, AND
   ALPHABETIC AND SPECIAL CHARACTERS MUST NOT BE USED.
   FOR A DEPENDABLE RESULT FOR TETRACHORIC CORRELATION,
   IT IS RECOMMENDED THAT N BE AT LEAST 200 OR GREATER.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NDTRI
   POLRT--THIS POLYNOMIAL ROOT ROUTINE WAS SELECTED BECAUSE OF
	  ITS SMALL STORAGE REQUIREMENT.  OTHER SSP ROUTINES
	  WHICH COULD REPLACE POLRT ARE PRQD AND PRBM.	THEIR
	  USE WOULD REQUIRE MODIFICATION OF TETRA.

METHOD
   REFER TO J. P. GUILFORD, 'FUNDAMENTAL STATISTICS IN PSYCHO-
   LOGY AND EDUCATION', MCGRAW-HILL, NEW YORK, 1956, CHAPTER 13
   AND W. P. ELDERTON, 'FREQUENCY CURVES AND CORRELATION' 4-TH
   ED., CAMBRIDGE UNIVERSITY PRESS, 1953, CHAPTER 9.