5 COMMON X(), F(), E(), E2(), F2()
10 CLS
20 PRINT "          STATISTICAL ECOLOGY:  A PRIMER ON METHODS AND COMPUTING "
30 PRINT
40 PRINT "           I N T E R A C T I V E    B A S I C    P R O G R A M  "
50 PRINT
60 PRINT "                        N E G B I N O M . B A S                   "
70 PRINT
80 PRINT "         -----------------------------------------------------------"
90 PRINT "         CHI-SQUARE TEST (GOODNESS-OF-FIT) FOR AGREEMENT WITH A"
100 PRINT "                    NEGATIVE BINOMINAL DISTRIBUTION            "
110 PRINT "         -----------------------------------------------------------"
120 PRINT
130 PRINT "                          This Test is Based On:        ": PRINT
140 PRINT "          OBSERVED data: # Sampling Units with 0,1,2...r individuals"
150 PRINT "          EXPECTED data: # Sampling Units with 0,1,2,..r individuals"
160 PRINT "                         based on NEGATIVE BIONOMINAL Probabilities"
165 PRINT "         -----------------------------------------------------------"
170 PRINT "          NOTE: The TOTAL number of sampling units should be > 40"
180 PRINT "         -----------------------------------------------------------"
190 FOR I = 1 TO 3: PRINT : NEXT I
200 PRINT "PRESS ANY KEY TO CONTINUE"
210 IF INKEY$ = "" THEN 210
220 CLS
230 DEF FNF (VAR) = LOG(VAR) / LOG(10)
240 DIM X(100), F(100), E(100), E2(101), F2(101)
250 PRINT "- - - - - - - - - -PART I. DATA ENTRY- - - - - - - - - - ": PRINT ""
260 PRINT "This program requires data TABULATED in the form"
270 PRINT "   of a FREQUENCY DISTRIBUTION - for example: ": PRINT ""
280 PRINT "                x =               Fx = Frequency       "
290 PRINT "        Number of Individuals  (Number of Sampling Units"
300 PRINT "          PER Sampling Unit     Containing x individuals)"
310 PRINT "                  0                119               "
320 PRINT "                  1                 62               "
330 PRINT "                  2                  6               "
340 PRINT "                  3                  2               ": PRINT
350 PRINT "To use this program, first enter the LARGEST frequency class"
360 PRINT "  i.e., x INDIVIDUALS per SU, that occurs in your data set (in the"
370 INPUT "  above example, x = 3).  Largest x or FREQUENCY CLASS  = "; CLASSES
380 PRINT : PRINT "Next, INPUT your OBSERVED FREQUENCY DATA             "
390 PRINT
400 PRINT " __x__,__F(x)__"
410 FOR I = 1 TO CLASSES + 1: X(I) = I - 1
420 PRINT "  "; I - 1; : INPUT "     ", F(I)
430 NEXT I
440 X(CLASSES + 2) = 0: F(CLASSES + 2) = 0
450 REM CALCULATE TOTAL NUMBER OF SAMPLING UNITS IN DATA SET (N),
460 REM   TOTAL NUMBER OF INDIVIDUALS (S1), & SUMS OF SQUARES (S2)
470    N = 0: S1 = 0: S2 = 0
480 FOR I = 1 TO CLASSES + 2
490    N = N + F(I): REM TOTAL NUMBER OF SAMPLING UNITS
500   S1 = S1 + (X(I) * F(I)): REM TOTAL NUMBER OF INDIVIDUALS
510   S2 = S2 + ((X(I) * X(I)) * F(I)): REM SUMS OF SQS OF INDIVIDUALS
520 NEXT I
530 REM CALCULATE INDEX OF DISPERSION, GREEN'S INDEX, K OF NEG. BINOM
540    MEAN = S1 / N: REM MEAN
550    VAR = (S2 - (MEAN * S1)) / (N - 1): REM VARIANCE
560    ID = VAR / MEAN: REM INDEX DISP (EQ. 3.6)
570    CS = ID * (N - 1): REM CHI-SQ (EQ. 3.7B)
580    DS = SQR(2 * CS) - SQR(2 * (N - 1) - 1): REM D STATISTIC (EQ. 3.8)
590    GI = (ID - 1) / (S1 - 1): REM GREEN'S INDEX (EQ 3.10)
600 CLS : PRINT "SUMMARY OF YOUR DATA SET:                               "
610 PRINT "TOTAL number of sampling units................ "; N
620 PRINT "TOTAL number of individuals .................. "; S1
630 PRINT "Number of Individuals/Sampling Unit   "
640 PRINT "        MEAN     =     "; MEAN
650 PRINT "        VARIANCE =     "; VAR
660 PRINT "VARIANCE/MEAN ratio (Index of Dispersion) .... "; ID
670 PRINT "        Chi-Square Statistic (Eq.3.7a) ....... "; CS
680 PRINT "        d Statistic (Eq. 3.8) ................ "; DS
690 PRINT "GREEN'S Index ................................ "; GI
700 PRINT : PRINT "PRESS ANY KEY TO CONTINUE"
710 IF INKEY$ = "" THEN 710
720 CLS
730 PRINT "- - - PART II. ESTIMATION OF PARAMETER K OF NEGATIVE BINOMINAL  "
740 PRINT
750 K = MEAN ^ 2 / (VAR - MEAN): REM K ESTI BY EQN 3.5
760 IF MEAN > 4 AND K > 4 THEN GOTO 770 ELSE GOTO 800
770 PRINT " The estimate of k using Eqn 3.5 is "; K
780 PRINT " Since the mean ("; MEAN; ") is also > 4.0, this is the preferred"
790 PRINT "   estimate of parameter k": GOTO 1090
800 PRINT " The estimate of k using Eqn 3.5 is "; K; " and the mean is "; MEAN
810 PRINT " Since BOTH are NOT > 4.0, k will be estimated using EQN 3.4"
820 PRINT : PRINT
830 PRINT " The objective is to choose different ESTIMATED VALUES of parameter"
840 PRINT " k until the RIGHT-HAND-SIDE of EQN 3.4 matches the LEFT-HAND-SIDE."
850 PRINT " At each iteration, select either a LOWER or HIGHER estimated value"
860 PRINT " of k.  NOTE:  When selecting a value for k, use the DIFFERENCE as "
870 PRINT " as a guide;  for LARGE differences, select larger increments for k"
880 PRINT " and for SMALL differences, make small incremental changes in k    "
890 PRINT
900 PRINT "Iteration LEFT H.S.  RIGHT H.S. DIFFERENCE"
910 ITER = 0
920 PRINT "    0      ------   --------    ----------       INITIAL Esti of k ="; K
930 LHS = FNF(N / F(1)): REM LEFT -HAND-SIDE OF EQN 3.4
940 RHS = K * FNF(1 + MEAN / K): REM RIGHT-HAND-SIDE OF EQN 3.4
950 DIFF = LHS - RHS
960 IF ITER = 0 THEN GOTO 970 ELSE GOTO 1010
970 IF DIFF = 0 THEN GOTO 1080
980 IF DIFF > 0 THEN CODE$ = "HIGHER" ELSE CODE$ = " LOWER"
990 ITER = 1
1000 GOTO 1050
1010 DIFF2% = DIFF * 10000!
1020 IF ABS(DIFF2%) = 0 THEN GOTO 1080 ELSE GOTO 1030
1030 ITER = ITER + 1
1040 IF DIFF > 0 THEN CODE$ = "HIGHER" ELSE CODE$ = " LOWER"
1050 PRINT USING "  ###      #.####     #.####     ##.#####"; ITER; LHS; RHS; DIFF;
1060 PRINT " Enter a "; CODE$; : INPUT " Esti of k = ", K
1070 GOTO 940
1080 PRINT : PRINT "** The ESTIMATE OF PARAMETER k using EQN 3.4 is ="; K: PRINT
1090 PRINT " HIT ANY KEY TO CONTINUE"
1100 IF INKEY$ = "" THEN 1100
1110 CLS
1120 PRINT "- - -PART III. COMPUTING THE CHI-SQUARE STATISTIC- - -  ": PRINT ""
1130 PRINT "The CHI-SQ. STATISTIC is based on: OBS FREQS (Fx) & EXP FREQS (Ex)"
1140 PRINT "  As a general rule, no EXPECTED (Ex) value should ever be < 1   "
1150 PRINT "  (Cochran 1954) or, more rigorously, much less than 5 (Poole 1974)"
1160 PRINT "  If your data has many Fx's with only 1 SU (this often happens in"
1170 PRINT "  tails of the distributions),  biased values of CHI-SQ. may result"
1180 PRINT "  and POOLING of Ex's should be done so that no Ex < 5.  Otherwise "
1190 PRINT "  this is not a strict rule and minimum EX values of 1 or 3 may be "
1200 PRINT "  tried.  In cases where POOLING significantly affects the results "
1210 PRINT "  of the test, we recommend the more conservative values.          "
1220 PRINT
1230 INPUT " ENTER MINIMUM VALUE of Ex allowed: ", MINEXPFQ: CLS
1240 PRINT "Your data will be pooled in both the UPPER and LOWER tails of the"
1250 PRINT "FREQUENCY distribution if any Ex value is LESS THAN ", MINEXPFQ
1260 PRINT
1270 REM CALCULATE THE EXPECTED NUMBER OF SAMPLING UNITS WITH ZERO INDIVIDUALS
1280    E(1) = ((1 + (MEAN / K)) ^ (-K)) * N
1290 REM CALCULATE THE EXPECTED NUMBER OF SAMPLING UNITS WITH 1,2,etc. INDIVS."
1300 SUMEXP = E(1):  FOR I = 2 TO CLASSES + 1
1310    E(I) = (MEAN / (MEAN + K)) * ((K + I - 1 - 1) / (I - 1)) * E(I - 1)
1320    SUMEXP = E(I) + SUMEXP
1330 NEXT I
1340    E(CLASSES + 2) = N - SUMEXP
1350 REM CHECK FOR EXPECTED FREQUENCIES <1 AND COMBINE (UPPER & LOWER TAILS)
1360 REM LOWER TAIL
1370 KK = 0:   E2(1) = 0: F2(1) = 0
1380      E2(1) = E(1 + KK) + E2(1)
1390      F2(1) = F(1 + KK) + F2(1)
1400      IF E2(1) > MINEXPFQ THEN GOTO 1420
1410      KK = KK + 1:  GOTO 1380
1420 FOR I = 2 TO CLASSES + 2 - KK
1430     E2(I) = E(KK + I)
1440     F2(I) = F(KK + I)
1450 NEXT I
1460 REM UPPER TAIL
1470 JMAX = CLASSES + 2 - KK: E2(JMAX) = 0: E2(JMAX + 1) = 0: F2(JMAX) = 0: L = 0: LL = 0
1480      JMAX = JMAX - LL
1490      E2(JMAX) = E(CLASSES + 2 - L) + E2(JMAX + 1)
1500      F2(JMAX) = F(CLASSES + 2 - L) + F2(JMAX + 1)
1510      IF E2(JMAX) > MINEXPFQ AND E2(JMAX - 1) > MINEXPFQ THEN GOTO 1530
1520      L = L + 1:    LL = 1:   GOTO 1480
1530 REM COMPUTE THE CHI-SQUARE VALUES
1540 PRINT "# INDIV/SU     OBS FREQ      EXP FREQ             2    "
1550 PRINT "     (x)         (Fx)          (Ex)        (Fx-Ex) /Ex "
1560 PRINT "----------     --------      --------      ----------- "
1590 CHISQ = 0: LINES = 0
1600 FOR I = 1 TO JMAX: LINES = LINES + 1
1610 IF LINES = 15 THEN INPUT " HIT ENTRY/RETURN KEY to Continue ", DD: LINES = DD
1620      CHISQI = ((F2(I) - E2(I)) ^ 2) / E2(I)
1630      CHISQ = CHISQI + CHISQ
1640 IF I = JMAX THEN PRINT USING ">=  ###"; KK;
1650 IF I = 1 THEN PRINT USING "0 - ###"; KK;
1660 IF I > 1 AND I < JMAX THEN PRINT USING "    ###"; KK;
1670 PRINT USING "         #####"; F2(I);
1680 PRINT USING "        #####.##"; E2(I); CHISQI
1690 KK = KK + 1
1700 NEXT I
1710 REM CALCULATE DEGREES OF FREEDOM FOR NEG. BINOMINAL
1720      DF = JMAX - 2 - 1
1730 PRINT
1740 PRINT "TOTAL CHI-SQUARE = "; CHISQ; "  WITH D.F. = "; DF
1750 FOR I = 1 TO 2: PRINT : NEXT I
1760 PRINT "Hit ANY KEY to Continue"
1770 IF INKEY$ = "" THEN 1770
1780 PRINT "  NO Expected (Ex) value was allowed to be less than ", MINEXPFQ
1790 PRINT "  Would you like to run this analysis again using a DIFFERENT"
1800 PRINT "  MINIMAL allowable size for EXPECTED frequencies? "
1810 INPUT "  ENTER Y OR N..."; A$: IF A$ = "Y" OR A$ = "y" THEN GOTO 1230
1820 END