**************************************************************;
* ShellfishMantel.sas -- Compute Mantel's test of spatial *;
* correlation for the pipis and cockles shellfish data *;
* reported in Manly 2001:224. *;
* *;
* Data: Manly, B.F.J. 2001. Statistics for Environmental *;
* Science and Management. Chapman & Hall, Boca Raton, p.224. *;
* *;
* Barry Moser, Dept. Experimental Statistics, Louisiana *;
* State University, Baton Rouge, LA 70803-5606. *;
* Date: 03/02/2001 *;
**************************************************************;
Options PS=55 LS=80 PageNo=1 NoDate FullSTimer
FORMCHAR='|----|+|---+=|-/\<>*';
GOptions Transparency NoBorder NoPrompt
VSize=6 in HSize=6 in
HText=1 FText=Swiss HTitle=1 FTitle=Swiss;
Title1 "Pipis (Paphies australis) Shellfish Spatial Correlation";
Data Pipis;
Input LowWaterDistance @;
Do BeachDistance=0 To 200 By 20;
Input Count @;
Quadrat+1;
Output;
End;
Label LowWaterDistance="Distance From Low Water (m)"
BeachDistance="Distance Along Beach (m)"
Count="Counts of Pipis (Paphies australis)"
Quadrat="Sampling Quadrat ID";
Datalines;
0 1 0 4 0 0 0 3 0 2 0 0
10 0 0 0 0 104 0 0 0 1 0 0
20 7 24 0 0 240 0 0 103 1 0 0
30 20 0 0 0 0 0 3 250 7 0 0
40 20 0 2 4 0 222 0 174 4 0 58
50 0 0 11 0 0 126 0 62 7 6 29
60 0 0 7 0 0 0 0 0 23 7 29
70 0 0 0 0 89 0 0 7 8 0 30
;
Proc Print Data=Pipis;
Id Quadrat;
Run;
Title2 "Map of the Data";
Proc Plot Data=Pipis;
Plot LowWaterDistance*BeachDistance=" " $ Count / Box
VRef=5 15 25 35 45 55 65
HRef=10 30 50 70 90 110 130 150 170 190;
Run;
Quit;
Title2 "Summary Statistics";
Proc Means Data=Pipis N Mean Var Min Max;
Var Count;
Run;
Title2 "Mantel Test";
%Macro Mantel(Data=_LAST_,X=X,Y=Y,Count=Count,Dist=Stats,Diag=Diagnostics,Reps=999,Seed=0);
/*
* Mantel Randomization Test for Spatial Correlation.
* Generate the distance information and absolute
* differences between response counts. There will
* be n(n-1)/2 distances and differences. Then compute
* correlation between the distances and differences
* and between inverse distances and differences.
* Test by randomizing the assignment of counts to
* quadrats and recomputing above correlations.
*/
Proc IML;
Start Dist;
Use &Data;
Read All Var{&X &Y} Into X;
Read All Var{&Count} Into Y;
Close &Data;
n=NRow(X);
l=n*(n-1)/2; /* number of different elements needed */
D=J(l,2,0); /* Inter-quadrat Distances and Inverse Distances */
C=J(l,1,0); /* Inter-quadrat abs difference in response */
k=0;
Do i=1 To n-1;
Do j=i+1 To n;
k=k+1;
Diff=X[i,]-X[j,];
D[k,1]=Sqrt(Diff*Diff`); /* Compute Euclidean Distance From Centers */
If D[k,1]>0 Then D[k,2]=1/D[k,1];
C[k]=Abs(Y[i]-Y[j]);
End;
End;
/* If requested, save the observed information for plotting */
%If "&Diag" NE "" %Then
%Do;
Colnames={"AbsDifference" "Distance" "InverseDist"};
CD=C||D;
Create &Diag From CD[Colname=Colnames];
Append From CD;
Close &Diag;
Free CD Colnames;
%End;
/* Now Center Both Vectors About Their Means */
CMean=Sum(C)/l;
C=C-CMean;
D[,1]=D[,1]-(D[+,1]/l);
D[,2]=D[,2]-(D[+,2]/l);
/* Compute correlation between distances and differences in responses */
CpCDpD1=Sqrt((C`*C)*(D[,1]`*D[,1]));
r1=(C`*D[,1])/CpCDpD1;
CpCDpD2=Sqrt((C`*C)*(D[,2]`*D[,2]));
r2=(C`*D[,2])/CpCDpD2;
Finish Dist;
Run Dist;
Start Randomize;
/* Randomly order the counts relative to the distances */
/* and compute correlation again. */
Reps=&Reps;
R=J(Reps,2,0);
Do m=1 To Reps;
U=Uniform(Repeat(&Seed,n,1));
Temp=Y; Y[Rank(U),]=Temp;
k=0;
Do i=1 To n-1;
Do j=i+1 To n;
k=k+1;
C[k]=Abs(Y[i]-Y[j]);
End;
End;
C=C-CMean;
R[m,1]=(C`*D[,1])/CpCDpD1;
R[m,2]=(C`*D[,2])/CpCDpD2;
End;
R=(r1||r2)//R;
p1=(Rank(R[,1])[1])/(Reps+1);
If p1 < 0.5 Then p1=p1*2;
Else p1=2*(1-p1);
p2=(Rank(R[,2])[1])/(Reps+1);
If p2 < 0.5 Then p2=p2*2;
Else p2=2*(1-p2);
Finish;
Run Randomize;
Print "Mantel Randomization Test For Spatial Correlation";
Print "Correlation Between Distances and Response Differences: " r1,
"Probability of more extreme value: " p1;
Print "Correlation Between Inverse Distances and Response Differences: " r2,
"Probability of more extreme value: " p2;
%If "&Dist" NE "" %Then
%Do;
Colnames={"R1" "R2"};
Create &Dist From R[Colname=Colnames];
Append From R;
Close &Dist;
%End;
Quit;
%Mend Mantel;
%Mantel(Data=Pipis,X=LowWaterDistance,Y=BeachDistance,Count=Count,
Reps=9999,Dist=Stats,Diag=Diagnostics);
Title3 "Distributions of Test Statistics";
Proc Chart Data=Stats;
VBar R1 R2;
Run;
Proc Univariate Data=Stats;
Var R1 R2;
Run;
Title3 "Diagnostics";
Proc Plot Data=Diagnostics;
Plot AbsDifference*(Distance InverseDist);
Run;
Quit;
Title1 "Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation";
Data Cockles;
Input LowWaterDistance @;
Do BeachDistance=0 To 200 By 20;
Input Count @;
Quadrat+1;
Output;
End;
Label LowWaterDistance="Distance From Low Water (m)"
BeachDistance="Distance Along Beach (m)"
Count="Counts of Cockles (Austrovenus stutchburyi)"
Quadrat="Sampling Quadrat ID";
Datalines;
0 0 0 1 0 0 0 0 0 0 0 0
10 0 0 0 0 7 0 0 0 0 0 0
20 0 0 0 0 9 0 0 3 6 0 0
30 0 0 0 0 0 0 0 0 0 0 0
40 1 0 0 5 0 0 0 7 0 0 10
50 0 0 0 0 0 7 0 10 1 1 19
60 0 0 0 0 0 0 0 0 0 0 2
70 0 0 0 0 2 0 0 2 0 0 16
;
Proc Print Data=Cockles;
Id Quadrat;
Run;
Title2 "Map of the Data";
Proc Plot Data=Cockles;
Plot LowWaterDistance*BeachDistance=" " $ Count / Box
VRef=5 15 25 35 45 55 65
HRef=10 30 50 70 90 110 130 150 170 190;
Run;
Quit;
Title2 "Summary Statistics";
Proc Means Data=Cockles N Mean Var Min Max;
Var Count;
Run;
%Mantel(Data=Cockles,X=LowWaterDistance,Y=BeachDistance,Count=Count,
Reps=9999,Dist=Stats2,Diag=Diagnostics2);
Title3 "Distributions of Test Statistics";
Proc Chart Data=Stats2;
VBar R1 R2;
Run;
Proc Univariate Data=Stats2;
Var R1 R2;
Run;
Title3 "Diagnostics";
Proc Plot Data=Diagnostics2;
Plot AbsDifference*(Distance InverseDist);
Run;
Quit;
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Quadrat | LowWaterDistance | BeachDistance | Count |
| 1 | 0 | 0 | 1 |
| 2 | 0 | 20 | 0 |
| 3 | 0 | 40 | 4 |
| 4 | 0 | 60 | 0 |
| 5 | 0 | 80 | 0 |
| 6 | 0 | 100 | 0 |
| 7 | 0 | 120 | 3 |
| 8 | 0 | 140 | 0 |
| 9 | 0 | 160 | 2 |
| 10 | 0 | 180 | 0 |
| 11 | 0 | 200 | 0 |
| 12 | 10 | 0 | 0 |
| 13 | 10 | 20 | 0 |
| 14 | 10 | 40 | 0 |
| 15 | 10 | 60 | 0 |
| 16 | 10 | 80 | 104 |
| 17 | 10 | 100 | 0 |
| 18 | 10 | 120 | 0 |
| 19 | 10 | 140 | 0 |
| 20 | 10 | 160 | 1 |
| 21 | 10 | 180 | 0 |
| 22 | 10 | 200 | 0 |
| 23 | 20 | 0 | 7 |
| 24 | 20 | 20 | 24 |
| 25 | 20 | 40 | 0 |
| 26 | 20 | 60 | 0 |
| 27 | 20 | 80 | 240 |
| 28 | 20 | 100 | 0 |
| 29 | 20 | 120 | 0 |
| 30 | 20 | 140 | 103 |
| 31 | 20 | 160 | 1 |
| 32 | 20 | 180 | 0 |
| 33 | 20 | 200 | 0 |
| 34 | 30 | 0 | 20 |
| 35 | 30 | 20 | 0 |
| 36 | 30 | 40 | 0 |
| 37 | 30 | 60 | 0 |
| 38 | 30 | 80 | 0 |
| 39 | 30 | 100 | 0 |
| 40 | 30 | 120 | 3 |
| 41 | 30 | 140 | 250 |
| 42 | 30 | 160 | 7 |
| 43 | 30 | 180 | 0 |
| 44 | 30 | 200 | 0 |
| 45 | 40 | 0 | 20 |
| 46 | 40 | 20 | 0 |
| 47 | 40 | 40 | 2 |
| 48 | 40 | 60 | 4 |
| 49 | 40 | 80 | 0 |
| 50 | 40 | 100 | 222 |
| 51 | 40 | 120 | 0 |
| 52 | 40 | 140 | 174 |
| 53 | 40 | 160 | 4 |
| 54 | 40 | 180 | 0 |
| 55 | 40 | 200 | 58 |
| 56 | 50 | 0 | 0 |
| 57 | 50 | 20 | 0 |
| 58 | 50 | 40 | 11 |
| 59 | 50 | 60 | 0 |
| 60 | 50 | 80 | 0 |
| 61 | 50 | 100 | 126 |
| 62 | 50 | 120 | 0 |
| 63 | 50 | 140 | 62 |
| 64 | 50 | 160 | 7 |
| 65 | 50 | 180 | 6 |
| 66 | 50 | 200 | 29 |
| 67 | 60 | 0 | 0 |
| 68 | 60 | 20 | 0 |
| 69 | 60 | 40 | 7 |
| 70 | 60 | 60 | 0 |
| 71 | 60 | 80 | 0 |
| 72 | 60 | 100 | 0 |
| 73 | 60 | 120 | 0 |
| 74 | 60 | 140 | 0 |
| 75 | 60 | 160 | 23 |
| 76 | 60 | 180 | 7 |
| 77 | 60 | 200 | 29 |
| 78 | 70 | 0 | 0 |
| 79 | 70 | 20 | 0 |
| 80 | 70 | 40 | 0 |
| 81 | 70 | 60 | 0 |
| 82 | 70 | 80 | 89 |
| 83 | 70 | 100 | 0 |
| 84 | 70 | 120 | 0 |
| 85 | 70 | 140 | 7 |
| 86 | 70 | 160 | 8 |
| 87 | 70 | 180 | 0 |
| 88 | 70 | 200 | 30 |
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Map of the Data |
Plot of LowWaterDistance*BeachDistance$Count. Symbol used is ' '.
--+------+------+------+------+------+------+------+------+------+------+--
70 + 0 | 0 | 0 | 0 | 89 | 0 | 0 | 7 | 8 | 0 | 30+
| | | | | | | | | | | |
| | | | | | | | | | | |
|-----+------+------+------+------+------+------+------+------+------+----|
| | | | | | | | | | | |
| | | | | | | | | | | |
60 + 0 | 0 | 7 | 0 | 0 | 0 | 0 | 0 | 23 | 7 | 29+
| | | | | | | | | | | |
D | | | | | | | | | | | |
i |-----+------+------+------+------+------+------+------+------+------+----|
s | | | | | | | | | | | |
t | | | | | | | | | | | |
a 50 + 0 | 0 | 11 | 0 | 0 | 126 | 0 | 62 | 7 | 6 | 29+
n | | | | | | | | | | | |
c | | | | | | | | | | | |
e |-----+------+------+------+------+------+------+------+------+------+----|
| | | | | | | | | | | |
F | | | | | | | | | | | |
r 40 + 20 | 0 | 2 | 4 | 0 | 222 | 0 | 174 | 4 | 0 | 58+
o | | | | | | | | | | | |
m | | | | | | | | | | | |
|-----+------+------+------+------+------+------+------+------+------+----|
L | | | | | | | | | | | |
o | | | | | | | | | | | |
w 30 + 20 | 0 | 0 | 0 | 0 | 0 | 3 | 250 | 7 | 0 | 0 +
| | | | | | | | | | | |
W | | | | | | | | | | | |
a |-----+------+------+------+------+------+------+------+------+------+----|
t | | | | | | | | | | | |
e | | | | | | | | | | | |
r 20 + 7 | 24 | 0 | 0 | 240 | 0 | 0 | 103 | 1 | 0 | 0 +
| | | | | | | | | | | |
( | | | | | | | | | | | |
m |-----+------+------+------+------+------+------+------+------+------+----|
) | | | | | | | | | | | |
| | | | | | | | | | | |
10 + 0 | 0 | 0 | 0 | 104 | 0 | 0 | 0 | 1 | 0 | 0 +
| | | | | | | | | | | |
| | | | | | | | | | | |
|-----+------+------+------+------+------+------+------+------+------+----|
| | | | | | | | | | | |
| | | | | | | | | | | |
0 + 1 | 0 | 4 | 0 | 0 | 0 | 3 | 0 | 2 | 0 | 0 +
--+------+------+------+------+------+------+------+------+------+------+--
0 20 40 60 80 100 120 140 160 180 200
Distance Along Beach (m)
|
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Summary Statistics |
| The MEANS Procedure |
| Analysis Variable : Count Counts of Pipis (Paphies australis) | ||||
| N | Mean | Variance | Minimum | Maximum |
| 88 | 19.2613636 | 2580.70 | 0 | 250.0000000 |
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Mantel Test |
| Mantel Randomization Test For Spatial Correlation |
| R1 | |
| Correlation Between Distances and Response Differences: | -0.108933 |
| P1 | |
| Probability of more extreme value: | 0.0074 |
| R2 | |
| Correlation Between Inverse Distances and Response Differences: | 0.0337107 |
| P2 | |
| Probability of more extreme value: | 0.088 |
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Mantel Test |
| Distributions of Test Statistics |
Frequency
800 + * * *
| * * * *
| * * * *
| * * * *
| * * * * *
700 + * * * * * *
| * * * * * * *
| * * * * * * * *
| * * * * * * * *
| * * * * * * * *
600 + * * * * * * * *
| * * * * * * * *
| * * * * * * * * *
| * * * * * * * * * *
| * * * * * * * * * *
500 + * * * * * * * * * *
| * * * * * * * * * *
| * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * *
400 + * * * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * * * *
| * * * * * * * * * * * * * *
300 + * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * *
200 + * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * *
100 + * * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * * * * * * * * *
------------------------------------------------------------------
- - - - - - - - - - - - -
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1
3 2 1 0 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8
R1 Midpoint
|
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Mantel Test |
| Distributions of Test Statistics |
Frequency
1000 + *
| *
| *
| *
900 + *
| * * *
| * * *
| * * *
800 + * * * * *
| * * * * *
| * * * * * *
| * * * * * * *
700 + * * * * * * * *
| * * * * * * * *
| * * * * * * * *
| * * * * * * * *
600 + * * * * * * * *
| * * * * * * * * *
| * * * * * * * * *
| * * * * * * * * * *
500 + * * * * * * * * * *
| * * * * * * * * * *
| * * * * * * * * * *
| * * * * * * * * * *
400 + * * * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * *
300 + * * * * * * * * * * * * *
| * * * * * * * * * * * * *
| * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * *
200 + * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * *
100 + * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * * * * *
--------------------------------------------------------------
- - - - - - - - - - - - - - - - - -
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 0 1 1 2 2 3 3 4 4 5 5
0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5
R2 Midpoint
|
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Mantel Test |
| Distributions of Test Statistics |
| The UNIVARIATE Procedure |
| Variable: R1 |
| Moments | |||
| N | 10000 | Sum Weights | 10000 |
| Mean | -0.0004284 | Sum Observations | -4.283679 |
| Std Deviation | 0.04770601 | Variance | 0.00227586 |
| Skewness | 0.27246389 | Kurtosis | -0.1482817 |
| Uncorrected SS | 22.7581914 | Corrected SS | 22.7563564 |
| Coeff Variation | -11136.691 | Std Error Mean | 0.00047706 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | -0.00043 | Std Deviation | 0.04771 |
| Median | -0.00235 | Variance | 0.00228 |
| Mode | . | Range | 0.31024 |
| Interquartile Range | 0.06607 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student's t | t | -0.89793 | Pr > |t| | 0.3692 |
| Sign | M | -205 | Pr >= |M| | <.0001 |
| Signed Rank | S | -908028 | Pr >= |S| | 0.0017 |
| Quantiles (Definition 5) | |
| Quantile | Estimate |
| 100% Max | 0.17799602 |
| 99% | 0.11968977 |
| 95% | 0.08326913 |
| 90% | 0.06240257 |
| 75% Q3 | 0.03113203 |
| 50% Median | -0.00235121 |
| 25% Q1 | -0.03493904 |
| 10% | -0.06053032 |
| 5% | -0.07470789 |
| 1% | -0.09736562 |
| 0% Min | -0.13224362 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| -0.132244 | 8878 | 0.161691 | 8365 |
| -0.131305 | 926 | 0.167516 | 3488 |
| -0.127912 | 7389 | 0.167837 | 9550 |
| -0.126169 | 8058 | 0.168583 | 7605 |
| -0.124864 | 1808 | 0.177996 | 8342 |
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Mantel Test |
| Distributions of Test Statistics |
| The UNIVARIATE Procedure |
| Variable: R2 |
| Moments | |||
| N | 10000 | Sum Weights | 10000 |
| Mean | 0.00014652 | Sum Observations | 1.46516842 |
| Std Deviation | 0.02140455 | Variance | 0.00045815 |
| Skewness | -0.3904671 | Kurtosis | 0.02073714 |
| Uncorrected SS | 4.5813039 | Corrected SS | 4.58108923 |
| Coeff Variation | 14608.9345 | Std Error Mean | 0.00021405 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | 0.000147 | Std Deviation | 0.02140 |
| Median | 0.001911 | Variance | 0.0004582 |
| Mode | . | Range | 0.14611 |
| Interquartile Range | 0.02937 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student's t | t | 0.684513 | Pr > |t| | 0.4937 |
| Sign | M | 322 | Pr >= |M| | <.0001 |
| Signed Rank | S | 1141069 | Pr >= |S| | <.0001 |
| Quantiles (Definition 5) | |
| Quantile | Estimate |
| 100% Max | 0.05642139 |
| 99% | 0.04232190 |
| 95% | 0.03272122 |
| 90% | 0.02651513 |
| 75% Q3 | 0.01566508 |
| 50% Median | 0.00191137 |
| 25% Q1 | -0.01370809 |
| 10% | -0.02847577 |
| 5% | -0.03760029 |
| 1% | -0.05611179 |
| 0% Min | -0.08969064 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| -0.0896906 | 3488 | 0.0530875 | 8988 |
| -0.0824566 | 594 | 0.0556685 | 6736 |
| -0.0822273 | 8342 | 0.0557239 | 1389 |
| -0.0797207 | 9550 | 0.0560249 | 9006 |
| -0.0772502 | 7605 | 0.0564214 | 283 |
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Mantel Test |
| Diagnostics |
Plot of AbsDifference*Distance. Legend: A = 1 obs, B = 2 obs, etc.
252 + D E AECC DDC BBC C A DC DA
| C A BAAA A AB A
| A H C AGFABAHAB DBB AF A D
| A A A CAA A AA
| A A A B
| A H E BCEC CDDB FCF DCB
216 + A A BCAA AAA A
| A BA
| B
| A A
| A BA
| A
180 + A A
| D D CDED CEAB BBC CB DC DA
| C A AAA A A A A
AbsDifference | A A B
| B
| A A A A
144 + CA
| A A
| A
| A H D ADDBBBEBB EDC BDABB
| AAB AD C A
| A A B
108 + B
| B M G BNGCCEOBD JCE BJA AAHBA CAA
| A A A BABA ABA D BA A
| A E B DCBBBGAF BC BACBCAAAAAAA
| AA B A CBC BB B
| A B A AAA
72 + A BA A B A
| A A B A
| B G D DDHDBCGBB GDD AFCBA LBA IBA AC DC BC
| C C E A A A A B B AAA A
| B A A A A
| A A A B
36 + A A AA A A B
| A E F CDCDCEI E KEEABHBDCBJDAAALCCBDFEA LDBC ICBA
| B M E BMIGDGKBC FDC BJBBBADCA K AAIBCBAD C
| C M J DGFD EHDC EBC GDB KFAA HAA EFC GE EC
| B H E BGFABAFAA EAB A AA ABA EBA CDC CA CC
| O Z Z YZZZNZZTZ ZWVFGZLLGFZVGECZJCDRTICAKCDA D
0 + Z Z Z ZZZZYZZZZ ZZZGUZWZPMZZNKEZKMIZXRFDZTFH HIBA
---+-----------+-----------+-----------+-----------+-----------+--
0 50 100 150 200 250
Distance
NOTE: 1016 obs hidden.
|
| Pipis (Paphies australis) Shellfish Spatial Correlation |
| Mantel Test |
| Diagnostics |
Plot of AbsDifference*InverseDist. Legend: A = 1 obs, B = 2 obs, etc.
252 + EGDFAEDBCC E A BC C A
| A CA AA A B A A B
| EGFDFCCAF G A AB D D A
| CCB A A A
| BA A A
| IMDGBBCE C B BC D D A
216 + ACABD A A
| C A
| B
| A A
| C A
| A
180 + A A
| EGEGBCDBDE D C AC B B
| A B A A A A A B A
AbsDifference | B A A
| B
| A A A A
144 + CA
| A A
| A
| BIJDFADBD D A AC D D A
| AABBC B A A
| B A A
108 + B
| EMMMIKIECG N B AF G F B
| AAFD A CB A A A
| BEIFFGCCBC D AA B C A
| B DGAAAA A A
| C A B A
72 + A BBB A
| AAAA A
| LPPLKFGCDDH D D AC D C B
| AE BB A A E C A B
| AA A A B
| B A A A
36 + C A B A A
| ZZTPQIHEEDC D C CC B C A
| HZKPJFJFHGI M B AD G F B
| TYRMHEHGBDF G D EE E H C
| JREBEDEBCAF G B AD C E B
| XZZZZZZZZZZ Z Y LT W Y O
0 + ZZZZZZZZZZZ Z Z UZ Z Z Z
---+-----------+-----------+-----------+-----------+-----------+--
0.00 0.02 0.04 0.06 0.08 0.10
InverseDist
NOTE: 1577 obs hidden.
|
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Quadrat | LowWaterDistance | BeachDistance | Count |
| 1 | 0 | 0 | 0 |
| 2 | 0 | 20 | 0 |
| 3 | 0 | 40 | 1 |
| 4 | 0 | 60 | 0 |
| 5 | 0 | 80 | 0 |
| 6 | 0 | 100 | 0 |
| 7 | 0 | 120 | 0 |
| 8 | 0 | 140 | 0 |
| 9 | 0 | 160 | 0 |
| 10 | 0 | 180 | 0 |
| 11 | 0 | 200 | 0 |
| 12 | 10 | 0 | 0 |
| 13 | 10 | 20 | 0 |
| 14 | 10 | 40 | 0 |
| 15 | 10 | 60 | 0 |
| 16 | 10 | 80 | 7 |
| 17 | 10 | 100 | 0 |
| 18 | 10 | 120 | 0 |
| 19 | 10 | 140 | 0 |
| 20 | 10 | 160 | 0 |
| 21 | 10 | 180 | 0 |
| 22 | 10 | 200 | 0 |
| 23 | 20 | 0 | 0 |
| 24 | 20 | 20 | 0 |
| 25 | 20 | 40 | 0 |
| 26 | 20 | 60 | 0 |
| 27 | 20 | 80 | 9 |
| 28 | 20 | 100 | 0 |
| 29 | 20 | 120 | 0 |
| 30 | 20 | 140 | 3 |
| 31 | 20 | 160 | 6 |
| 32 | 20 | 180 | 0 |
| 33 | 20 | 200 | 0 |
| 34 | 30 | 0 | 0 |
| 35 | 30 | 20 | 0 |
| 36 | 30 | 40 | 0 |
| 37 | 30 | 60 | 0 |
| 38 | 30 | 80 | 0 |
| 39 | 30 | 100 | 0 |
| 40 | 30 | 120 | 0 |
| 41 | 30 | 140 | 0 |
| 42 | 30 | 160 | 0 |
| 43 | 30 | 180 | 0 |
| 44 | 30 | 200 | 0 |
| 45 | 40 | 0 | 1 |
| 46 | 40 | 20 | 0 |
| 47 | 40 | 40 | 0 |
| 48 | 40 | 60 | 5 |
| 49 | 40 | 80 | 0 |
| 50 | 40 | 100 | 0 |
| 51 | 40 | 120 | 0 |
| 52 | 40 | 140 | 7 |
| 53 | 40 | 160 | 0 |
| 54 | 40 | 180 | 0 |
| 55 | 40 | 200 | 10 |
| 56 | 50 | 0 | 0 |
| 57 | 50 | 20 | 0 |
| 58 | 50 | 40 | 0 |
| 59 | 50 | 60 | 0 |
| 60 | 50 | 80 | 0 |
| 61 | 50 | 100 | 7 |
| 62 | 50 | 120 | 0 |
| 63 | 50 | 140 | 10 |
| 64 | 50 | 160 | 1 |
| 65 | 50 | 180 | 1 |
| 66 | 50 | 200 | 19 |
| 67 | 60 | 0 | 0 |
| 68 | 60 | 20 | 0 |
| 69 | 60 | 40 | 0 |
| 70 | 60 | 60 | 0 |
| 71 | 60 | 80 | 0 |
| 72 | 60 | 100 | 0 |
| 73 | 60 | 120 | 0 |
| 74 | 60 | 140 | 0 |
| 75 | 60 | 160 | 0 |
| 76 | 60 | 180 | 0 |
| 77 | 60 | 200 | 2 |
| 78 | 70 | 0 | 0 |
| 79 | 70 | 20 | 0 |
| 80 | 70 | 40 | 0 |
| 81 | 70 | 60 | 0 |
| 82 | 70 | 80 | 2 |
| 83 | 70 | 100 | 0 |
| 84 | 70 | 120 | 0 |
| 85 | 70 | 140 | 2 |
| 86 | 70 | 160 | 0 |
| 87 | 70 | 180 | 0 |
| 88 | 70 | 200 | 16 |
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Map of the Data |
Plot of LowWaterDistance*BeachDistance$Count. Symbol used is ' '.
--+------+------+------+------+------+------+------+------+------+------+--
70 + 0 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 0 | 0 | 16+
| | | | | | | | | | | |
| | | | | | | | | | | |
|-----+------+------+------+------+------+------+------+------+------+----|
| | | | | | | | | | | |
| | | | | | | | | | | |
60 + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 +
| | | | | | | | | | | |
D | | | | | | | | | | | |
i |-----+------+------+------+------+------+------+------+------+------+----|
s | | | | | | | | | | | |
t | | | | | | | | | | | |
a 50 + 0 | 0 | 0 | 0 | 0 | 7 | 0 | 10 | 1 | 1 | 19+
n | | | | | | | | | | | |
c | | | | | | | | | | | |
e |-----+------+------+------+------+------+------+------+------+------+----|
| | | | | | | | | | | |
F | | | | | | | | | | | |
r 40 + 1 | 0 | 0 | 5 | 0 | 0 | 0 | 7 | 0 | 0 | 10+
o | | | | | | | | | | | |
m | | | | | | | | | | | |
|-----+------+------+------+------+------+------+------+------+------+----|
L | | | | | | | | | | | |
o | | | | | | | | | | | |
w 30 + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 +
| | | | | | | | | | | |
W | | | | | | | | | | | |
a |-----+------+------+------+------+------+------+------+------+------+----|
t | | | | | | | | | | | |
e | | | | | | | | | | | |
r 20 + 0 | 0 | 0 | 0 | 9 | 0 | 0 | 3 | 6 | 0 | 0 +
| | | | | | | | | | | |
( | | | | | | | | | | | |
m |-----+------+------+------+------+------+------+------+------+------+----|
) | | | | | | | | | | | |
| | | | | | | | | | | |
10 + 0 | 0 | 0 | 0 | 7 | 0 | 0 | 0 | 0 | 0 | 0 +
| | | | | | | | | | | |
| | | | | | | | | | | |
|-----+------+------+------+------+------+------+------+------+------+----|
| | | | | | | | | | | |
| | | | | | | | | | | |
0 + 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 +
--+------+------+------+------+------+------+------+------+------+------+--
0 20 40 60 80 100 120 140 160 180 200
Distance Along Beach (m)
|
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Summary Statistics |
| The MEANS Procedure |
| Analysis Variable : Count Counts of Cockles (Austrovenus stutchburyi) |
||||
| N | Mean | Variance | Minimum | Maximum |
| 88 | 1.2386364 | 11.4481452 | 0 | 19.0000000 |
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Summary Statistics |
| Mantel Randomization Test For Spatial Correlation |
| R1 | |
| Correlation Between Distances and Response Differences: | 0.0680132 |
| P1 | |
| Probability of more extreme value: | 0.176 |
| R2 | |
| Correlation Between Inverse Distances and Response Differences: | -0.031252 |
| P2 | |
| Probability of more extreme value: | 0.1734 |
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Summary Statistics |
| Distributions of Test Statistics |
Frequency
1000 + *
| * *
| * *
| * * * *
900 + * * * *
| * * * *
| * * * *
| * * * * *
800 + * * * * *
| * * * * *
| * * * * *
| * * * * * * *
700 + * * * * * * *
| * * * * * * *
| * * * * * * * *
| * * * * * * * * *
600 + * * * * * * * * *
| * * * * * * * * *
| * * * * * * * * *
| * * * * * * * * * *
500 + * * * * * * * * * *
| * * * * * * * * * *
| * * * * * * * * * *
| * * * * * * * * * * *
400 + * * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * *
300 + * * * * * * * * * * * *
| * * * * * * * * * * * * *
| * * * * * * * * * * * * * *
| * * * * * * * * * * * * * *
200 + * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * *
100 + * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * * * *
------------------------------------------------------------
- - - - - - - - - - - -
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1
3 2 1 0 9 7 6 5 4 3 1 0 0 1 3 4 5 6 7 9 0 1 2 3 5 6 7 8 9
8 6 4 2 0 8 6 4 2 0 8 6 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8
R1 Midpoint
|
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Summary Statistics |
| Distributions of Test Statistics |
Frequency
900 + * * * *
| * * * *
| * * * *
| * * * * *
800 + * * * * *
| * * * * * *
| * * * * * *
| * * * * * *
700 + * * * * * *
| * * * * * * *
| * * * * * * * *
| * * * * * * * *
600 + * * * * * * * *
| * * * * * * * * *
| * * * * * * * * *
| * * * * * * * * *
500 + * * * * * * * * *
| * * * * * * * * * *
| * * * * * * * * * * *
| * * * * * * * * * * *
400 + * * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * *
| * * * * * * * * * * * * *
300 + * * * * * * * * * * * * * *
| * * * * * * * * * * * * * *
| * * * * * * * * * * * * * *
| * * * * * * * * * * * * * *
200 + * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * *
100 + * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * * *
| * * * * * * * * * * * * * * * * * * * * * * * * *
----------------------------------------------------------------
- - - - - - - - - - - - - - - - - - -
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 0 0 1 1 2 2 3 3 4 4 5 5
2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 2 7 2 7 2 7 2 7 2 7 2 7
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
R2 Midpoint
|
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Summary Statistics |
| Distributions of Test Statistics |
| The UNIVARIATE Procedure |
| Variable: R1 |
| Moments | |||
| N | 10000 | Sum Weights | 10000 |
| Mean | 0.00039961 | Sum Observations | 3.99611391 |
| Std Deviation | 0.04757744 | Variance | 0.00226361 |
| Skewness | 0.30637626 | Kurtosis | -0.1084226 |
| Uncorrected SS | 22.6354582 | Corrected SS | 22.6338613 |
| Coeff Variation | 11905.9261 | Std Error Mean | 0.00047577 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | 0.00040 | Std Deviation | 0.04758 |
| Median | -0.00250 | Variance | 0.00226 |
| Mode | . | Range | 0.33837 |
| Interquartile Range | 0.06544 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student's t | t | 0.839918 | Pr > |t| | 0.4010 |
| Sign | M | -199 | Pr >= |M| | <.0001 |
| Signed Rank | S | -530831 | Pr >= |S| | 0.0660 |
| Quantiles (Definition 5) | |
| Quantile | Estimate |
| 100% Max | 0.20009636 |
| 99% | 0.11692679 |
| 95% | 0.08442810 |
| 90% | 0.06416652 |
| 75% Q3 | 0.03182514 |
| 50% Median | -0.00249793 |
| 25% Q1 | -0.03361960 |
| 10% | -0.05885979 |
| 5% | -0.07292817 |
| 1% | -0.09623863 |
| 0% Min | -0.13827759 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| -0.138278 | 3321 | 0.166566 | 2494 |
| -0.126957 | 9044 | 0.172870 | 6653 |
| -0.125498 | 5010 | 0.173063 | 8081 |
| -0.125027 | 1787 | 0.183327 | 4821 |
| -0.125010 | 70 | 0.200096 | 4331 |
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Summary Statistics |
| Distributions of Test Statistics |
| The UNIVARIATE Procedure |
| Variable: R2 |
| Moments | |||
| N | 10000 | Sum Weights | 10000 |
| Mean | -0.0001434 | Sum Observations | -1.4340733 |
| Std Deviation | 0.02152683 | Variance | 0.0004634 |
| Skewness | -0.4122496 | Kurtosis | 0.04857561 |
| Uncorrected SS | 4.63378593 | Corrected SS | 4.63358027 |
| Coeff Variation | -15010.969 | Std Error Mean | 0.00021527 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | -0.00014 | Std Deviation | 0.02153 |
| Median | 0.00143 | Variance | 0.0004634 |
| Mode | . | Range | 0.14837 |
| Interquartile Range | 0.02929 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student's t | t | -0.66618 | Pr > |t| | 0.5053 |
| Sign | M | 243 | Pr >= |M| | <.0001 |
| Signed Rank | S | 837129 | Pr >= |S| | 0.0037 |
| Quantiles (Definition 5) | |
| Quantile | Estimate |
| 100% Max | 0.05786707 |
| 99% | 0.04238399 |
| 95% | 0.03231022 |
| 90% | 0.02628383 |
| 75% Q3 | 0.01536798 |
| 50% Median | 0.00143261 |
| 25% Q1 | -0.01392290 |
| 10% | -0.02907965 |
| 5% | -0.03820256 |
| 1% | -0.05530753 |
| 0% Min | -0.09050039 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| -0.0905004 | 4331 | 0.0531523 | 9546 |
| -0.0896001 | 4821 | 0.0538167 | 1439 |
| -0.0888482 | 3366 | 0.0538493 | 7959 |
| -0.0830993 | 6998 | 0.0565666 | 6203 |
| -0.0822514 | 6653 | 0.0578671 | 70 |
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Summary Statistics |
| Diagnostics |
Plot of AbsDifference*Distance. Legend: A = 1 obs, B = 2 obs, etc.
AbsDifference |
|
19 + C C ACCAAAC A DBB ADAAA D A EAA CCA EBA DC
|
18 + A A A A
|
17 + A A A
|
16 + B ACABABBAD CBBAACABAACB ACAAACBBA CBAB CBAA
|
15 + A A A A
|
14 + A A A A
|
13 + A A
|
12 + A A A
|
11 + A
|
10 + B I G CHHEBDIBB GDE AICB IDA KBA CD EC DC
|
9 + B J D AIEBBDIBB FCC BF AB D A A A A
|
8 + B A BA AA A A
|
7 + D U L FOMJDJYCG PII DPEBCAIDA FA
|
6 + B H D IEBADF A DBD EACA DBA GAA CBB
|
5 + B H H CFFD DIEB BBB DBA ECA DA A
|
4 + A A A BAABA AA A
|
3 + C H D BHF BDHAB DAC AEAAA ECA FAA
|
2 + C K E GNHGDHPCO PHFDCMCFCCGDBCBHBBBDBB DBAA CCA
|
1 + G T P FONJFGUGJ PGFACQDCBARIAAATDAAJKEA HEA CB
|
0 + Z Z Z ZZZZZZZZZ ZZZJYZZZVRZZUOFZRPLZZZJEZVHI OJBA
|
---+-----------+-----------+-----------+-----------+-----------+--
0 50 100 150 200 250
Distance
NOTE: 1533 obs hidden.
|
| Cockles (Austrovenus stutchburyi) Shellfish Spatial Correlation |
| Summary Statistics |
| Diagnostics |
Plot of AbsDifference*InverseDist. Legend: A = 1 obs, B = 2 obs, etc.
AbsDifference |
|
19 + ONFGFCBABAC C A AB B A
|
18 + AA A A
|
17 + A A A
|
16 + OOGGGDCBBBA C A A A
|
15 + B A A
|
14 + AA A A
|
13 + A A
|
12 + AA A
|
11 + A
|
10 + OUNOLFHDEEH H C AF E D B
|
9 + ACFIJDGFDBE I A AC E E B
|
8 + AAB BA A B
|
7 + GRZZNRNJJM O F DH K J D
|
6 + PHIGDDEBBE I AC E C B
|
5 + FIGFBJFBDF F C DD D D B
|
4 + AB BBAB A A A
|
3 + HJHFDFED F H B D D D C
|
2 + OZSYZURGHGH N G BC E F C
|
1 + SZZZXOVJJJN O F DL J J G
|
0 + ZZZZZZZZZZZ Z Z ZZ Z Z Z
|
---+-----------+-----------+-----------+-----------+-----------+--
0.00 0.02 0.04 0.06 0.08 0.10
InverseDist
NOTE: 1998 obs hidden.
|