Wildl. Soc. Bull. 17:549-550, 1989

                             WILDLIFE SOFTWARE
                                     
                 TESTING FOR DIFFERENCES AMONG SURVIVAL OR
                   RECOVERY RATES USING PROGRAM CONTRAST
                                     
JOHN R. SAUER, Patuxent Wildlife Research Center, U.S. Fish and Wildlife Service,
     Laurel, MD  20708

JAMES E. HINES, Patuxent Wildlife Research Center, U.S. Fish and Wildlife Service,
     Laurel, MD 20708

     Sauer and Williams (1989) described generalized statistical procedures for
multiple comparisons of parameter estimates that have associated variances and
covariances. Although of general applicability, they discussed the use of the method
with regard to comparison of survival or recovery rates. Their method uses a
Chi-square statistic to test the composite hypothesis

Ho: sl = s2 = s3 = . . . = sn,   (1)

where si (i = 1, . . ., n) are the rates to be tested. This procedure generalizes the
Z-test discussed by Brownie et al. (1985), which tests a simple hypothesis of form:

Ho: c1s1 + c2s2 + c3s3 + . . .+ cnsn = 0 (2)
                                                      n=1
The cl, c2, . . ., cn are constants with the constraint  S  ci = 0, dividing the rates 
                                                      i=1
into 2 groups which can then be tested with the Z-test. 
     CONTRAST is a FORTRAN program that implements the Sauer and Williams (1989)
procedure. Input data for CONTRAST are the rate estimates i (here denoted by s, as
we assume that most applications of the procedure will analyze survival rates), along
with associated variances vr(i) and covariances cv(i, j). Data can either be
entered interactively or stored in a separate input file. Output from the program is
both displayed on the screen and printed to disk.
     CONTRAST first prompts for entry of data or an input filename, then computes
the Chi-square test statistic for hypothesis (1). The user is then prompted to either
specify a contrast, which defines a simple hypothesis (2) or to specify groups (Nò2)
of rates to be tested. If a contrast is selected, a Chi-square test that is equivalent
to the Brownie et al. (1985) Z-test is calculated. If more than 2 groups are selected,
group means, variances, and covariances are calculated, and a Chi-square statistic
is calculated for this composite hypothesis of equal group means. See Sauer and
Williams (1989) for a discussion of the multiple comparison procedures. The program
source code executable code, user documentation, and test data are available on the
southeastern software and message exchange (SESAME), and a detailed user's manual for
the program is available from the authors.
     CONTRAST was written using the Ryan McFarland FORTRAN compiler (and the 8087
emulator library), so a math coprocessor is not required. The program should run on
all IBMPC compatible computers. Size of the program depends upon the maximum number
of survival rates. The program presently uses <256K of memory and is set up to compare
ó50 estimates of survival rates. Maximum number of survival rates can be decreased or
increased by changing the 'IDIM = 50' statements in the code to 'IDIM = XX', XX being
the number of survival rates.

                             LITERATURE CITED
                                     
BROWNIE, C., D. R. ANDERSON, K. P. BURNHAM, AND D. S. ROBSON. 1985. Statistical
     inference from band recovery data - a handbook. Second ed. U.S. Fish and Wildl.
     Serv. Resour. Publ. 156. 305pp.
SAUER, J. R., AND B. K. WILLIAMS. 1989. Generalized procedures for testing hypotheses
     about survival or recovery rates. J. Wildl. Manage. 53:137-142.

Received 27 March 1989.
Accepted 30 August 1989.