Yes $HR . . . and I did see this before??
Can't wait until somebody writes a book.
Anyway I also wanted a real backslash \ but used a dash instead.
It was to identify the headings and columns of a table.
Actually it all has to do with a chi-squared test of a contingency table (statistics)
Here is the example if anybody is interested.
## DESCRIPTION
## Statistics
## ENDDESCRIPTION
## KEYWORDS('Statistics','Distribution')
## Tagged by
## DBsubject('Statistics')
## DBchapter('Chi-squared')
## DBsection('Contingency Table')
## Date('April 2012')
## Author('Hedley Pinsent')
## Institution('CNA')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
#
# First comes some stuff that appears at the beginning of every problem
#
DOCUMENT(); # This should be the first executable line in the problem.
loadMacros(
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"unionMacros.pl",
"unionTables.pl",
"PGstatisticsmacros.pl",
);
TEXT($BEGIN_ONE_COLUMN,beginproblem()) ;
# vvvvvvvvvvvvvvvvv Defining Categories
while ($nRows + $nColumns < 5){
$nRows = list_random(2,3,4);
$nColumns = list_random(2,3,4)}
@colourList = ("Red","Green","Yellow","Blue","Orange", "Purple");
@colaList = ("Inca","Pepsi","Coca-Cola","Mountain Dew","Lime","Frosty");
@colaList = @colaList[NchooseK(6,$nRows)];
@colourList = @colourList[NchooseK(6,$nColumns)];
# ^^^^^^^^^^^^^^^^^ Defining Categories
## Constructing Differences vvvvvvvvvvvvvvvvvvvvvv
foreach $irow (0..$nRows -1){
foreach $icol (0..$nColumns -1){
$D[$irow*$nColumns + $icol] = 0;# Differences = zeros
}
}
#adjust below to get balance between reject and do not reject
$tries = random(1,5,1);
foreach $i (0..$tries){
$diff = list_random(1,2,3,4,5, -5,-4,-3,-2,-1);
@colPair = NchooseK($nColumns, 2);
@rowPair = NchooseK($nRows, 2);
$D[$rowPair[0]*$nColumns + $colPair[0]] += $diff;
$D[$rowPair[0]*$nColumns + $colPair[1]] -= $diff;
$D[$rowPair[1]*$nColumns + $colPair[1]] += $diff;
$D[$rowPair[1]*$nColumns + $colPair[0]] -= $diff;
}
## Constructing Differences ^^^^^^^^^^^^^^^^^^^^^^
# Assigning Values (Expected/Observed) vvvvvvvvvvvvvvvvvvvvvvv
$base = random (1,3,1);
foreach $irow (0..$nRows -1){$rowFact[$irow]= list_random(4,5,6,7,8,9)}
foreach $icol (0..$nColumns -1){$colFact[$icol]= list_random(4,5,6,7,8,9)}
foreach $irow (0..$nRows -1){
foreach $icol (0..$nColumns -1){
$E[$irow*$nColumns + $icol] = $base*$rowFact[$irow]*$colFact[$icol];# Expected
$O[$irow*$nColumns + $icol] = $E[$irow*$nColumns + $icol]+$D[$irow*$nColumns + $icol];# Observed
}
}
# Assigning Values (Expected/Observed)^^^^^^^^^^^^^^^^^^^^^^
##Calculating chi-squared vvvvvvvvvvvvvvvvvvvvvvvvv
$CALC = 0;
foreach $k (0.. $nRows * $nColumns -1){$CALC =$CALC + ($D[$k]**2) / $E[$k]}
##Calculating chi-squared ^^^^^^^^^^^^^^^^^^^^^^^^
##Constructing the data table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
$datatable = BeginTable(spacing => 3);
$datatable .= AlignedRow(["Cola-Colour",@colourList]);
foreach $i (0..$nRows-1) {
foreach $j (0.. $nColumns -1) {
@row [$j] = $O[$i *$nColumns + $j];
}
$datatable .= AlignedRow([$colaList[$i],@row])
}
$datatable .= EndTable();
##Constructing the data table ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
BEGIN_TEXT
Follows is a contingency table for colour preference and cola preference. $BR
For example $O[0 *$nColumns + 0] people in the survey preferred the colour $colourList[0] and their favourite beverage was $colaList[0] $PAR
$datatable
END_TEXT
##Constructing the answer table vvvvvvvvvvvvvvvvvvvvvvvvvvvvv
$answertable = BeginTable(spacing => 3);
$answertable .= AlignedRow(["Cola-Colour",@colourList, "Totals"]);
foreach $i (0..$nRows-1) {
$rowTotal = 0;
foreach $j (0.. $nColumns -1) {
$name = $i . "and". $j;
@answerRule[$j] = NAMED_ANS_RULE($name,6);
push @namedCmp , $name=>num_cmp( $E[$i *$nColumns + $j] ) ;
$rowTotal = $rowTotal + $E[$i *$nColumns + $j] ;
$colTotal[$j] = $colTotal[$j]+ $E[$i *$nColumns + $j];
}
$name = "rowTotal". $i;
@answerRule[$nColumns] = NAMED_ANS_RULE($name,6);
push @namedCmp , $name=>num_cmp( $rowTotal ) ;
$answertable .= AlignedRow([$colaList[$i],@answerRule]);
}
# Last row
foreach $k (0..$nColumns-1 ){
$name = "colTotal".$k;
@answerRule[$k] = NAMED_ANS_RULE($name,6);
push @namedCmp , $name=>num_cmp( $colTotal[$k] ) ;
}
$grandTotal = 0;
foreach $k (0..$nColumns - 1){$grandTotal += $colTotal[$k]}
$name = "grand";
$answerRule[$nColumns] = NAMED_ANS_RULE($name,6);
push @namedCmp , $name=>num_cmp( $grandTotal ) ;
$answertable .= AlignedRow(["Totals",@answerRule]);
$answertable .= EndTable();
##Constructing the answer table ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
BEGIN_TEXT
For the above table calculate the row totals, column totals grand total, and the expected values. $BR Enter these values in the appropriate spaces below.$PAR
$answertable
END_TEXT
## Setting up significance test vvvvvvvvvvvvvvvvvvvvvvvvvvv
$alpha = list_random(0.01,0.05);
$df = ($nColumns -1)*($nRows - 1);
$CRIT = chisqrdistr ($df,$alpha);
##Setting up significance test ^^^^^^^^^^^^^^^^^^^^^^^^^^^
$mcnull = new_multiple_choice();
$mcnull->qa(
"",
"There is no relationship"
);
$mcnull->extra(
"There is a relationship"
);
$mcalt = new_multiple_choice();
$mcalt->qa(
"",
"There is a relationship"
);
$mcalt->extra(
"There is no relationship"
);
##SETTING UP THE TABLE
@r1 = ("\(H_0\)", $mcnull->print_a()) ;
@r2 = ("\(H_1\)",$mcalt->print_a());
$mcTestStatistic = new_multiple_choice();
$mcTestStatistic->qa(
"The test statistic is",
"\( \chi^2 \)"
);
$mcTestStatistic->extra(
"\( z \)",
"\( t \)","\( F \)",
);
# Test Statistics choices
$mctestEQ = new_multiple_choice();
$mctestEQ->qa(
"", "\( \gt \)"
);
$mctestEQ->extra("\( \lt or \gt \)". " -/+",
"\( \lt \)"
);
@r3 = ("We reject if: ", $mcTestStatistic->print_a() ,$mctestEQ->print_a(),NAMED_ANS_RULE("CRIT",6));
$mcAR = new_multiple_choice();
## this is a two-tailed test
if( abs($CALC) >$CRIT ){$mcAR->qa(
"We",
"reject"
);
$mcAR->extra(
"do not reject"
);}
else{$mcAR->qa(
"We",
"do not reject"
);
$mcAR->extra(
"reject"
);}
BEGIN_TEXT
$HR
At a $alpha significance level test whether there is a relationship between favourite colour and farourite cola.
$PAR
$PAR
\{begintable(4)\}
\{row( @r1)\}
\{row( @r2)\}
\{endtable()\}
$PAR
$PAR
\(\alpha \) = \{NAMED_ANS_RULE("alpha",6)\} $PERCENT $BR
$BR
\{begintable(4)\}
\{row( @r3)\}
\{endtable()\}
$PAR
The value of the test statistic is \{NAMED_ANS_RULE("Ftest",6)\} $PAR
\{$mcAR->print_q()\}
\{$mcAR->print_a()\}
END_TEXT
##contingency table check vvvvvvvvvvvvvvvvvv
NAMED_ANS(@namedCmp);
##contingency table check ^^^^^^^^^^^^^^^^^^
#CHECKING FIRST ROW H0
ANS( radio_cmp( $mcnull->correct_ans() ) );
#CHECKING SECOND ROW H1
ANS( radio_cmp( $mcalt->correct_ans() ) );
#checking alpha in percent
NAMED_ANS(alpha=>num_cmp( 100 * $alpha, mode=>"arith", reltol=>.01));
#CHECKING THIRD ROW
ANS( radio_cmp( $mcTestStatistic->correct_ans() ) );
ANS( radio_cmp( $mctestEQ->correct_ans() ) );
NAMED_ANS(CRIT=>num_cmp( $CRIT, mode=>"arith", reltol=>2));
#CHECKING FORTH ROW
NAMED_ANS(Ftest=>num_cmp( $CALC, mode=>"arith", reltol=>2));
ANS( radio_cmp( $mcAR->correct_ans() ) );
TEXT($END_ONE_COLUMN);
ENDDOCUMENT(); # This should be the last executable line in the problem.