Program written, modified, or edited at StatSoft, Inc.}

{SELECT TEST TYPE - let's the user select the particular sample parameter to test}
{The menu items in this dialog are:
1. TEST FOR MEAN WITH UNKNOWN VARIANCE (BASED ON T DISTRIBUTION)
2. TEST FOR MEAN WITH KNOWN VARIANCE (BASED ON Z DISTRIBUTION)
3. TEST FOR VARIANCE
4. TEST FOR PROPORTION
5. TEST FOR CORRELATION}
choice:=DisplayButtonBox ('One-sample-tests for aggregated data', 'Test for mean (SD
unknown)|Test for mean (SD known)|Test for variance|Test for proportion|Test for
correlation');

{Every test has it's own pair of arrays: test# (for input parameters) and results# (for
output parameters) where # is the number of the menu item as listed above}


{1. TEST FOR MEAN WITH UNKNOWN VARIANCE}
{1.1. Specify input parameters for test and check validity of input}
If choice = 1 then begin
Dim Test1(4);
Testspecs1:
If DisplayNumericInputBox ('Enter the parameters for the test:', 'Mean for Null
Hypothesis H0:|Sample mean:|Sample standard deviation:|Sample size:', Test1) = 0 then
abort;
If (test1(3)<0) OR (test1(4)<=0) OR (test1(4)-trunc(test1(4))<>0) then begin
Error1:=DisplayMessageBox (MB_RETRYCANCEL, 'Invalid parameter(s)!', 'Try again or abort
program');
If Error1 = IDRETRY then Goto Testspecs1 else abort;
end;

{1.2. Specify significance level for tests and confidence limits}
If DisplayNumericInputBox ('Enter significance level:', 'Alpha: (between 0.0 and 1.0):',
alpha) = 0 then abort;
If (alpha<=0) OR (alpha>=1) then begin
Error1:=DisplayMessageBox (MB_RETRYCANCEL, 'Invalid significance level!', 'Try again or
abort program.');
If Error1 = IDRETRY then Goto Testspecs1 else abort;
end;

{1.3. Compute test statistic, confidence limits, etc. and assign values to results
array}
hypmean:=test1(1);
mean:=test1(2);
stddev:=test1(3);
size:=test1(4);
sterr:=stddev/sqrt(size);
statistic:=((mean-hypmean)/(stddev/sqrt(size)));
nu:=size-1;
abstat:=abs(statistic);
plevelb:=2*(1-istudent(abstat, nu));
plevell:=istudent (statistic, nu);
plevelu:=1-istudent (statistic, nu);
tcl1:=VStudent ((alpha/2), nu);
tcu1:=VStudent ((1-alpha/2),nu);
tcl2:=VStudent (alpha, nu);
tcu2:=VStudent ((1-alpha), nu);
If (statistic>tcl1) and (statistic<tcu1) then bothsides$:='Accpt H0' else
bothsides$:='Rejct H0';
If (statistic<tcl2) then leftside$:='Rejct H0' else leftside$:='Accpt H0';
If (statistic>tcu2) then rightside$:='Rejct H0' else rightside$:='Accpt H0';
LCL:=mean+tcl1*sterr;
UCL:=mean+tcu1*sterr;

Dim Results1 (12);
Results1(1):=hypmean;
Results1(2):=Mean;
Results1(3):=LCL;
Results1(4):=UCL;
Results1(5):=statistic;
Results1(6):=nu;
Results1(7):=plevelb;
Results1(8):=plevell;
Results1(9):=plevelu;


{1.4. Create output table (Scrollsheet), specify title, and assign parameters from
results array}
Scroll:=NewScrollsheet (1, 12, Results1, "One-sample t test for mean (variance
unknown)|Significance tests and confidence limits are based on|Student's t
distribution", 'Test results', ?ColumnNames$);
ScrollsheetSetColumnName (Scroll, 1, 'HO', 'mean');
ScrollsheetSetColumnName (Scroll, 2, 'Sample', 'mean');
cflevel$:=str(100-(alpha*100),5,2)+'%';
ScrollsheetSetColumnName (Scroll, 3, 'LCL', '-'+cflevel$);
ScrollsheetSetColumnName (Scroll, 4, 'UCL', '+'+cflevel$);
ScrollsheetSetColumnName (Scroll, 5, ?Name1$, 't-value');
ScrollsheetSetColumnName (Scroll, 6,?Name1$, 'df');
ScrollsheetSetColumnName (Scroll, 7,'2-sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 8, 'le. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 9, 'ri. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 10, '2-sided', 'test');
ScrollsheetSetColumnName (Scroll, 11, '1-sided', 'left');
ScrollsheetSetColumnName (Scroll, 12, '1-sided', 'right');
ScrollsheetSetTextValue (Scroll, 1, 10, bothsides$);
ScrollsheetSetTextValue (Scroll, 1, 11, leftside$);
ScrollsheetSetTextValue (Scroll, 1, 12, rightside$);

{1.5. End of compound instruction for first menu item - see first line of code in
section 1.1.}
end;


{2. TEST FOR MEAN WITH KNOWN VARIANCE}
{2.1. Specify input parameters for test and check validity of input}
If choice = 2 then begin
Dim Test2(4);
Testspecs2:
If DisplayNumericInputBox ('Enter the parameters for the test:', 'Mean for Null
Hypothesis H0:|Sample mean:|Standard deviation:|Sample size:', Test2) = 0 then abort;
If (test2(3)<0) OR (test2(4)<=0) OR (test2(4)-trunc(test2(4))<>0) then begin
Error1:=DisplayMessageBox (MB_RETRYCANCEL, 'Invalid parameter(s)!', 'Try again or abort
program');
If Error1 = IDRETRY then Goto Testspecs2 else abort;
end;

{2.2. Specify significance level for tests and confidence limits}
If DisplayNumericInputBox ('Enter significance level:', 'Alpha: (between 0.0 and 1.0):',
alpha) = 0 then abort;
If (alpha<=0) OR (alpha>=1) then begin
Error1:=DisplayMessageBox (MB_RETRYCANCEL, 'Invalid significance level!', 'Try again or
abort program.');
If Error1 = IDRETRY then Goto Testspecs3 else abort;
end;

{2.3. Compute test statistic, confidence limits, etc. and assign values to results
array}
hypmean:=test2(1);
mean:=test2(2);
stddev:=test2(3);
size:=test2(4);
sterr:=stddev/sqrt(size);

statistic:=((mean-hypmean)/(stddev/sqrt(size)));
abstat:=abs(statistic);
plevelb:=2*(1-inormal(abstat, 0,1));
plevell:=inormal (statistic, 0,1);
plevelu:=1-inormal (statistic, 0,1);
zcl1:=VNormal ((alpha/2), 0,1);
zcu1:=VNormal ((1-alpha/2),0,1);
zcl2:=VNormal (alpha, 0,1);
zcu2:=VNormal ((1-alpha), 0,1);
If (statistic>zcl1) and (statistic<zcu1) then bothsides$:='Accpt H0' else
bothsides$:='Rejct H0';
If (statistic<zcl2) then leftside$:='Rejct H0' else leftside$:='Accpt H0';
If (statistic>zcu2) then rightside$:='Rejct H0' else rightside$:='Accpt H0';
LCL:=mean+zcl1*sterr;
UCL:=mean+zcu1*sterr;

Dim Results2 (11);
Results2(1):=hypmean;
Results2(2):=Mean;
Results2(3):=LCL;
Results2(4):=UCL;
Results2(5):=statistic;
Results2(6):=plevelb;
Results2(7):=plevell;
Results2(8):=plevelu;

{2.4. Create output table (Scrollsheet), specify title, and assign parameters from
results array}
Scroll:=NewScrollsheet (1, 11, Results2, "One-sample t test for mean (variance
known)|Significance tests and confidence limits are based on the|normal distribution",
'Test results', ?ColumnNames$);
ScrollsheetSetColumnName (Scroll, 1, 'HO', 'mean');
ScrollsheetSetColumnName (Scroll, 2, 'Sample', 'mean');
cflevel$:=str(100-(alpha*100),5,2)+'%';
ScrollsheetSetColumnName (Scroll, 3, 'LCL', '-'+cflevel$);
ScrollsheetSetColumnName (Scroll, 4, 'UCL', '+'+cflevel$);
ScrollsheetSetColumnName (Scroll, 5, ?Name1$, 'z-score');
ScrollsheetSetColumnName (Scroll, 6,'2-sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 7, 'le. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 8, 'ri. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 9, '2-sided', 'test');
ScrollsheetSetColumnName (Scroll, 10, '1-sided', 'left');
ScrollsheetSetColumnName (Scroll, 11, '1-sided', 'right');
ScrollsheetSetTextValue (Scroll, 1, 9, bothsides$);
ScrollsheetSetTextValue (Scroll, 1, 10, leftside$);
ScrollsheetSetTextValue (Scroll, 1, 11, rightside$);

{2.5. End of compound instruction for second menu item - see first line of code in
section 2.1.}
End;



{3. TEST FOR VARIANCE}
{3.1. Specify input parameters for test, significance level, and check validity of
input}
If choice = 3 then begin
Dim Test3(4);
Testspecs3:
If DisplayNumericInputBox ('Enter the parameters for the test:', 'Variance for Null
Hypothesis H0:|Sample variance:|Sample size:|Significance level alpha (between 0.0 and
1.0):', Test3) = 0 then abort;
If (test3(1)<=0) OR (test3(2)<=0) OR (test3(3)<=0)  OR (test3(3)-trunc(test3(3))<>0)
then begin
Error1:=DisplayMessageBox (MB_RETRYCANCEL, 'Invalid parameter(s)!', 'Try again or abort
program');
If Error1 = IDRETRY then Goto Testspecs3 else abort;
end;
If (test3(4)<=0) OR (test3(4)>=1) then begin
Error1:=DisplayMessageBox (MB_RETRYCANCEL, 'Invalid significance level!', 'Try again or
abort program.');
If Error1 = IDRETRY then Goto Testspecs3 else abort;
end;

{3.2. Compute test statistic, confidence limits, etc. and assign values to results
array}
hypvariance:=test3(1);
variance:=test3(2);
size:=test3(3);
alpha:=test3(4);
statistic:=((size-1)*variance)/hypvariance;
nu:=size-1;
abstat:=abs(statistic);
plevelb:=(ichi2(statistic, nu))/2 +(1-ichi2(statistic, nu))/2;
plevell:=ichi2 (statistic, nu);
plevelu:=1-ichi2 (statistic, nu);
cscl1:=VChi2 ((alpha/2), nu);
cscu1:=VChi2 ((1-alpha/2),nu);
cscl2:=VChi2 (alpha, nu);
cscu2:=VChi2 ((1-alpha), nu);
If (statistic>cscl1) and (statistic<cscu1) then bothsides$:='Accpt H0' else
bothsides$:='Rejct H0';
If (statistic<cscl2) then leftside$:='Rejct H0' else leftside$:='Accpt H0';
If (statistic>cscu2) then rightside$:='Rejct H0' else rightside$:='Accpt H0';
LCL:=((size-1)*variance)/cscu1;
UCL:=((size-1)*variance)/cscl1;

Dim Results3 (12);
Results3(1):=hypvariance;
Results3(2):=variance;
Results3(3):=LCL;
Results3(4):=UCL;
Results3(5):=statistic;
Results3(6):=nu;
Results3(8):=plevell;
Results3(9):=plevelu;

{3.3. Create output table (Scrollsheet), specify title, and assign parameters from
results array}
Scroll:=NewScrollsheet (1, 12, Results3, "One-sample Chi-Square test for
variance|Significance tests and confidence limits are based on the|Chi-square
distribution", 'Test results', ?ColumnNames$);
ScrollsheetSetColumnName (Scroll, 1, 'HO', 'variance');
ScrollsheetSetColumnName (Scroll, 2, 'Sample', 'variance');
cflevel$:=str(100-(alpha*100),5,2)+'%';
ScrollsheetSetColumnName (Scroll, 3, 'LCL', '-'+cflevel$);
ScrollsheetSetColumnName (Scroll, 4, 'UCL', '+'+cflevel$);
ScrollsheetSetColumnName (Scroll, 5, ?Name1$, 'Chi2');
ScrollsheetSetColumnName (Scroll, 6,?Name1$, 'df');
ScrollsheetSetColumnName (Scroll, 7,'2-sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 8, 'le. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 9, 'ri. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 10, '2-sided', 'test');
ScrollsheetSetColumnName (Scroll, 11, '1-sided', 'left');
ScrollsheetSetColumnName (Scroll, 12, '1-sided', 'right');
ScrollsheetSetTextValue (Scroll, 1, 10, bothsides$);
ScrollsheetSetTextValue (Scroll, 1, 11, leftside$);
ScrollsheetSetTextValue (Scroll, 1, 12, rightside$);
ScrollsheetSetTextValue (Scroll, 1, 7, 'n/a');

{3.4. End of compound instruction for third menu item - see first line of code in
section 3.1.}
end;


{4. TEST FOR PROPORTION}
{4.1. Specify input parameters for test and check validity of input}
If choice = 4 then begin
Dim Test4(4);
Testspecs4:
If DisplayNumericInputBox ('Enter the parameters for the test:', 'Proportion for Null
Hypothesis H0 (between 0.0 and 1.0):|Sample proportion (between 0.0 and 1.0):|Sample
size:|Significance level alpha (between 0.0 and 1.0):', Test4) = 0 then abort;
If (test4(1)<=0) OR (test4(1)>=1) OR (test4(2)<=0) OR (test4(2)>=1) OR (test4(1)<=0) OR
(test4(4)>=1) OR (test4(4)<=0) OR (test4(3)-trunc(test4(3))<>0) then begin
Error1:=DisplayMessageBox (MB_RETRYCANCEL, 'Invalid parameter(s)!', 'Try again or abort
program.');
If Error1 = IDRETRY then Goto Testspecs4 else abort;
end;

{4.2. Compute test statistic, confidence limits, etc. and assign values to results
array}
hypp:=test4(1);
p:=test4(2);
size:=test4(3);
alpha:=test4(4);
If size*p*(1-p) < 9 then DisplayMessageBox (MB_OK, 'Warning!', 'The condition for the
normal approximation is not met. You should interpret the following results very
carefully.'); {Normal approximation only valid when this condition is met}
sigmap:=sqrt((hypp*(1-hypp))/(size-1));
statistic:=(p-hypp)/sqrt((hypp*(1-hypp))/size);
abstat:=abs(statistic);
plevelb:=2*(1-inormal(abstat, 0,1));
plevell:=inormal (statistic, 0,1);
plevelu:=1-inormal (statistic, 0,1);
zcl1:=VNormal ((alpha/2), 0,1);
zcu1:=VNormal ((1-alpha/2),0,1);
zcl2:=VNormal (alpha, 0,1);
zcu2:=VNormal ((1-alpha), 0,1);
If (statistic>zcl1) and (statistic<zcu1) then bothsides$:='Accpt H0' else
bothsides$:='Rejct H0';
If (statistic<zcl2) then leftside$:='Rejct H0' else leftside$:='Accpt H0';
If (statistic>zcu2) then rightside$:='Rejct H0' else rightside$:='Accpt H0';
LCL:=p+zcl1*sigmap;
UCL:=p+zcu1*sigmap;
If LCL < 0 then LCL:=0;

Dim Results4 (11);
Results4(1):=hypp;
Results4(2):=p;
Results4(3):=LCL;
Results4(4):=UCL;
Results4(5):=statistic;
Results4(6):=plevelb;
Results4(7):=plevell;
Results4(8):=plevelu;

{4.3. Create output table (Scrollsheet), specify title, and assign parameters from
results array}
Scroll:=NewScrollsheet (1, 11, Results4, "One-sample test for proportion|Significance
tests and confidence limits are based on the|normal distribution (approximation!)",
'Test results', ?ColumnNames$);
ScrollsheetSetColumnName (Scroll, 1, 'HO', 'proport.');
ScrollsheetSetColumnName (Scroll, 2, 'Sample', 'proport.');
cflevel$:=str(100-(alpha*100),5,2)+'%';
ScrollsheetSetColumnName (Scroll, 3, 'LCL', '-'+cflevel$);
ScrollsheetSetColumnName (Scroll, 4, 'UCL', '+'+cflevel$);
ScrollsheetSetColumnName (Scroll, 5, ?Name1$, 'z-score');
ScrollsheetSetColumnName (Scroll, 6,'2-sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 7, 'le. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 8, 'ri. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 9, '2-sided', 'test');
ScrollsheetSetColumnName (Scroll, 10, '1-sided', 'left');
ScrollsheetSetColumnName (Scroll, 11, '1-sided', 'right');
ScrollsheetSetTextValue (Scroll, 1, 9, bothsides$);
ScrollsheetSetTextValue (Scroll, 1, 10, leftside$);
ScrollsheetSetTextValue (Scroll, 1, 11, rightside$);

{4.4. End of compound instruction for fourth menu item - see first line of code in
section 4.1.}
end;

{5. TEST FOR CORRELATION}
{5.1. Specify input parameters for test and check validity of input}
If choice = 5 then begin
Dim Test5(4);
Testspecs5:
If DisplayNumericInputBox ('Enter the parameters for the test:', 'Correlation for Null
Hypothesis H0 (between -1.0 and 1.0):|Sample correlation (between -1.0 and 1.0):|Sample
size:|Significance level alpha (between 0.0 and 1.0):', Test5) = 0 then abort;
If (test5(1)<=-1) OR (test5(1)>=1) OR (test5(2)<=-1) OR (test5(2)>=1) OR (test5(3)<=0)
OR (test5(3)-trunc(test5(3))<>0) OR (test5(4)>=1) OR (test5(4)<=0) then begin
Error1:=DisplayMessageBox (MB_RETRYCANCEL, 'Invalid parameter(s)!', 'Try again or abort
program.');
If Error1 = IDRETRY then Goto Testspecs5 else abort;
end;

{5.2. Compute test statistic, confidence limits, etc. and assign values to results
array}
hypr:=test5(1);
r:=test5(2);
size:=test5(3);
alpha:=test5(4);
Fisherz1:=(1/2)*log((1+r)/(1-r));
Fisherz2:=(1/2)*log((1+hypr)/(1-hypr));
sigmaz:=1/sqrt(size-3);
statistic:=(Fisherz1-Fisherz2)*sqrt(size-3);
abstat:=abs(statistic);
plevelb:=2*(1-inormal(abstat, 0,1));
plevell:=inormal (statistic, 0,1);
plevelu:=1-inormal (statistic, 0,1);
zcl1:=VNormal ((alpha/2), 0,1);
zcu1:=VNormal ((1-alpha/2),0,1);
zcl2:=VNormal (alpha, 0,1);
zcu2:=VNormal ((1-alpha), 0,1);
If (statistic>zcl1) and (statistic<zcu1) then bothsides$:='Accpt H0' else
bothsides$:='Rejct H0';
If (statistic<zcl2) then leftside$:='Rejct H0' else leftside$:='Accpt H0';
If (statistic>zcu2) then rightside$:='Rejct H0' else rightside$:='Accpt H0';
LL:=Fisherz1+zcl1*sigmaz;
UL:=Fisherz1+zcu1*sigmaz;
LCL:=tanh(LL);
UCL:=tanh(UL);

Dim Results5 (11);
Results5(1):=hypR;
Results5(2):=R;
Results5(3):=LCL;
Results5(4):=UCL;
Results5(5):=statistic;
Results5(6):=plevelb;
Results5(7):=plevell;
Results5(8):=plevelu;

{5.3. Create output table (Scrollsheet), specify title, and assign parameters from
results array}
Scroll:=NewScrollsheet (1, 11, Results5, "One-sample test for correlation|Significance
tests and confidence limits are based on the|std. normal distribution (via Fisher's z
transformation)", 'Test results', ?ColumnNames$);
ScrollsheetSetColumnName (Scroll, 1, 'HO', 'corr.');
ScrollsheetSetColumnName (Scroll, 2, 'Sample', 'corr.');
cflevel$:=str(100-(alpha*100),5,2)+'%';
ScrollsheetSetColumnName (Scroll, 3, 'LCL', '-'+cflevel$);
ScrollsheetSetColumnName (Scroll, 4, 'UCL', '+'+cflevel$);
ScrollsheetSetColumnName (Scroll, 5, ?Name1$, 'z-score');
ScrollsheetSetColumnName (Scroll, 6,'2-sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 7, 'le. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 8, 'ri. sided', 'p-level');
ScrollsheetSetColumnName (Scroll, 9, '2-sided', 'test');
ScrollsheetSetColumnName (Scroll, 10, '1-sided', 'left');
ScrollsheetSetColumnName (Scroll, 11, '1-sided', 'right');
ScrollsheetSetTextValue (Scroll, 1, 9, bothsides$);
ScrollsheetSetTextValue (Scroll, 1, 10, leftside$);
ScrollsheetSetTextValue (Scroll, 1, 11, rightside$);

{5.4. End of compound instruction for fifth menu item - see first line of code in
section 5.1.}
end;

{END OF OVERALL PROGRAM CODE}

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