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 "                        P O I S S O N . B A S                   "
70 PRINT
80 PRINT "         --------------------------------------------------------"
90 PRINT "         CHI-SQUARE TEST (GOODNESS-OF-FIT) FOR AGREEMENT WITH A"
100 PRINT "                          POISSON SERIES                       "
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 POISSON probabilities           "
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 DIM X(100), F(100), E(100), E2(101), F2(101)
240 PRINT "- - - - - - - - - -PART I. DATA ENTRY- - - - - - - - - - ": PRINT ""
250 PRINT "This program requires data TABULATED in the form"
260 PRINT "   of a FREQUENCY DISTRIBUTION - for example: ": PRINT ""
270 PRINT "                x =               F(x) = Frequency       "
280 PRINT "        Number of Individuals  (Number of Sampling Units"
290 PRINT "          PER Sampling Unit     Containing x individuals)"
300 PRINT "                  0                  1               "
310 PRINT "                  1                  1               "
320 PRINT "                  2                  1               "
330 PRINT "                  3                  3               "
340 PRINT "                  4                  2               "
350 PRINT "                  5                  2               ": PRINT
360 PRINT "To use this program, first enter the LARGEST frequency class"
370 PRINT "  i.e., x individuals per SU, that occurs in YOUR data set (in the "
380 INPUT "  above example, x = 5).  Largest x or FREQUENCY CLASS  = "; CLASSES
390 PRINT "Next, INPUT your OBSERVED FREQUENCY DATA             "
400 PRINT
410 PRINT " __x__,__F(x)__"
420 FOR I = 1 TO CLASSES + 1: X(I) = I - 1
430 PRINT "  "; I - 1; : INPUT "     ", F(I)
440 NEXT I
450 X(CLASSES + 2) = 0: F(CLASSES + 2) = 0
460 REM CALCULATE TOTAL NUMBER OF SAMPLING UNITS IN DATA SET (N),
470 REM   TOTAL NUMBER OF INDIVIDUALS (S1), & SUMS OF SQUARES (S2)
480    N = 0: S1 = 0: S2 = 0
490 FOR I = 1 TO CLASSES + 2
500    N = N + F(I): REM TOTAL NUMBER OF SAMPLING UNITS
510   S1 = S1 + (X(I) * F(I)): REM TOTAL NUMBER OF INDIVIDUALS
520   S2 = S2 + ((X(I) * X(I)) * F(I)): REM SUMS OF SQS OF INDIVIDUALS
530 NEXT I
540 REM CALCULATE INDEX OF DISPERSION, GREEN'S INDEX, CHI-SQ VALUE
550    MEAN = S1 / N: REM MEAN
560    VAR = (S2 - (MEAN * S1)) / (N - 1): REM VARIANCE
570    ID = VAR / MEAN: REM INDEX DISP.(EQ 3.6)
580    CS = ID * (N - 1): REM CHI-SQ (EQ 3.7B)
590    DS = SQR(2 * CS) - SQR(2 * (N - 1) - 1): REM D STATISTIC (EQ 3.8)
600    GI = (ID - 1) / (S1 - 1): REM GREEN'S INDEX (EQ 3.10)
610 CLS : PRINT "SUMMARY OF YOUR DATA SET:                               "
620 PRINT "TOTAL number of sampling units................ "; N
630 PRINT "TOTAL number of individuals .................. "; S1
640 PRINT "Number of Individuals/Sampling Unit   "
650 PRINT "        MEAN     =     "; MEAN
660 PRINT "        VARIANCE =     "; VAR
670 PRINT "VARIANCE/MEAN ratio (Index of Dispersion)..... "; ID
680 PRINT "        Chi-Square Statistic (Eq.3.7a) ....... "; CS
690 PRINT "        d Statistic (Eq. 3.8)................. "; DS
700 PRINT "GREEN'S Index ................................ "; GI
710 PRINT
720 PRINT "PRESS ANY KEY TO CONTINUE"
730 IF INKEY$ = "" THEN 730
740 CLS
750 PRINT "- - -PART II. COMPUTING THE CHI-SQUARE STATISTIC- - -  ": PRINT ""
760 PRINT "The CHI-SQ. STATISTIC is based on: OBS FREQS (Fx) & EXP FREQS (Ex)"
770 PRINT "  As a general rule, no EXPECTED (Ex) value should ever be < 1   "
780 PRINT "  (Cochran 1954) or, more rigorously, much less than 5 (Poole 1974)"
790 PRINT "  If your data has many Fx's with only 1 SU (this often happens in"
800 PRINT "  tails of the distributions),  biased values of CHI-SQ. may result"
810 PRINT "  and POOLING of Ex's should be done so that no Ex < 5.  Otherwise "
820 PRINT "  this is not a strict rule and minimum EX values of 1 or 3 may be "
830 PRINT "  tried.  In cases where POOLING significantly affects the results "
840 PRINT "  of the test, we recommend the more conservative values.          "
850 PRINT : PRINT
860 INPUT "ENTER MINIMUM VALUE of Ex allowed: ", MINEXPFQ: CLS
870 PRINT " Your data will be pooled in both the UPPER and LOWER tails of the"
880 PRINT " FREQUENCY distribution if any Ex value is LESS THAN ", MINEXPFQ
890 PRINT
900 REM CALCULATE THE EXPECTED NUMBER OF SAMPLING UNITS WITH ZERO INDIVIDUALS
910    E(1) = (EXP(-MEAN)) * N
920 REM CALCULATE THE EXPECTED NUMBER OF SAMPLING UNITS WITH 1,2,etc. INDIVS."
930 SUMEXP = E(1):  FOR I = 2 TO CLASSES + 1
940    E(I) = (MEAN * E(I - 1)) / (I - 1)
950    SUMEXP = E(I) + SUMEXP
960 NEXT I
970    E(CLASSES + 2) = N - SUMEXP
980 REM CHECK FOR EXPECTED FREQUENCIES <1 AND COMBINE (UPPER & LOWER TAILS)
990 REM LOWER TAIL
1000 K = 0:    E2(1) = 0: F2(1) = 0
1010      E2(1) = E(1 + K) + E2(1)
1020      F2(1) = F(1 + K) + F2(1)
1030      IF E2(1) > MINEXPFQ THEN GOTO 1050
1040      K = K + 1:    GOTO 1010
1050 FOR I = 2 TO CLASSES + 2 - K
1060     E2(I) = E(K + I)
1070     F2(I) = F(K + I)
1080 NEXT I
1090 REM UPPER TAIL
1100 JMAX = CLASSES + 2 - K: E2(JMAX) = 0: E2(JMAX + 1) = 0: F2(JMAX) = 0: L = 0: LL = 0
1110      JMAX = JMAX - LL
1120      E2(JMAX) = E(CLASSES + 2 - L) + E2(JMAX + 1)
1130      F2(JMAX) = F(CLASSES + 2 - L) + F2(JMAX + 1)
1140      IF E2(JMAX) > MINEXPFQ AND E2(JMAX - 1) > MINEXPFQ THEN GOTO 1160
1150      L = L + 1:    LL = 1:   GOTO 1110
1160 REM COMPUTE THE CHI-SQUARE VALUES
1170 PRINT "# INDIV/SU     OBS FREQ      EXP FREQ             2    "
1180 PRINT "     (x)         (Fx)          (Ex)        (Fx-Ex) /Ex "
1190 PRINT "----------     --------      --------      ----------- "
1200 CHISQ = 0: LINES = 0
1210 FOR I = 1 TO JMAX: LINES = LINES + 1
1220 IF LINES = 17 THEN INPUT " HIT ENTRY/RETURN KEY TO CONTINUE ", DD: LINES = DD
1230      CHISQI = ((F2(I) - E2(I)) ^ 2) / E2(I)
1240      CHISQ = CHISQI + CHISQ
1250 IF I > 1 AND I < JMAX THEN GOTO 1290 ELSE GOTO 1260
1260 IF I = 1 THEN PRINT USING "0 - ###"; K;
1270 IF I = JMAX THEN PRINT USING ">=  ###"; K;
1280 GOTO 1300
1290 PRINT USING "    ###"; K;
1300 PRINT USING "         #####"; F2(I);
1310 PRINT USING "        #####.##"; E2(I); CHISQI
1320 K = K + 1
1330 NEXT I
1340 REM CALCULATE DEGREES OF FREEDOM
1350      DF = JMAX - 2
1360 PRINT " "
1370 PRINT "TOTAL CHI-SQUARE = "; CHISQ; "  WITH D.F. = "; DF
1380 PRINT : PRINT "PRESS ANY KEY TO CONTINUE"
1390 IF INKEY$ = "" THEN 1390
1400 PRINT "  NO Expected (Ex) value was allowed to be less than ", MINEXPFQ
1410 PRINT "  Would you like to run this analysis again using a DIFFERENT"
1420 PRINT "  MINIMAL allowable size for EXPECTED frequencies? "
1430 INPUT "  ENTER Y OR N..."; A$: IF A$ = "Y" OR A$ = "y" THEN GOTO 860
1440 END