## DESCRIPTION
## Match each of the following chi2 terms with their corresponding definitions.
## ENDDESCRIPTION
## KEYWORDS('chi2 terms','definitions')
## DBsubject('Biostatistics')
## DBchapter('')
## DBsection('')
## Date('2026-07-12')
## Author('Neil R. Voss')
## Institution('Roosevelt University')

DOCUMENT();

loadMacros(
    'PGstandard.pl',
    'PGML.pl',
    'PGchoicemacros.pl',
    'parserPopUp.pl',
    'parserUtils.pl',
    'PGgraders.pl',
    'PGcourse.pl'
);
our @ALPHABET = ('A' .. 'Z');

# ================================
# Full matching data
# ================================
%match_data = (
  'critical value' => [
    'found in a table for a given degrees of freedom and <span style="color: #8601af; font-weight:700;">level of significance, &alpha;</span>',
    'the boundary of how extreme a test statistic we need to <span style="color: #4d8426; font-weight:700;">support</span>the <span style="color: #0247fe; font-weight:700;">null hypothesis, H<sub>0</sub></span>',
    'the cutoff used to compare against the observed <span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> test statistic',
  ],
  'chi-square (&chi;&sup2;) test statistic' => [
    'if this value is large, then there is stronger evidence to <span style="color: #4d8426; font-weight:700;">support</span>the <span style="color: #cf4b03; font-weight:700;">alternative hypothesis, H<sub>a</sub></span>',
    'the bigger this number, the smaller the <span style="color: #c21460; font-weight:700;">p-value</span>',
    'the sum of the normalized square difference between observed and expected data',
    'a measure of the discrepancy between the observed and expected data sets',
  ],
  'level of significance, &alpha;' => [
    'the statistical cutoff of the result for the <span style="color: #0247fe; font-weight:700;">null hypothesis, H<sub>0</sub></span> to be <span style="color: #4d8426; font-weight:700;">supported</span> or not',
    'a constant probability that provides a cutoff for falsification of the <span style="color: #0247fe; font-weight:700;">null hypothesis, H<sub>0</sub></span>',
    'the fixed probability for whether or NOT the <span style="color: #0247fe; font-weight:700;">null hypothesis, H<sub>0</sub></span> can be <span style="color: #4d8426; font-weight:700;">supported</span>',
    'a fixed probability cutoff whether the <span style="color: #0247fe; font-weight:700;">null hypothesis, H<sub>0</sub></span> can be or cannot be <span style="color: #4d8426; font-weight:700;">supported</span>',
    'standard cutoff probability used to determine statistic significance',
    'biologists use a probability of 0.05 (5%) for this value',
  ],
  'p-value' => [
    'the probability of getting a result that is either the same or more extreme than the actual observations',
    'if this value is small, then there is stronger evidence to <span style="color: #4d8426; font-weight:700;">support</span>the <span style="color: #cf4b03; font-weight:700;">alternative hypothesis, H<sub>a</sub></span>',
    'the smaller this number, the bigger the <span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> test statistic',
    'a small value suggests the observed data are NOT consistent with the <span style="color: #0247fe; font-weight:700;">null hypothesis, H<sub>0</sub></span>',
  ],
  'null hypothesis, H<sub>0</sub>' => [
    'we attempt to find evidence against this hypothesis in our <span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> test',
    'we want to <span style="color: #eb1601; font-weight:700;">faill to support</span>this hypothesis in our <span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> test',
    'this hypothesis makes it easier to calculate the expected values',
  ],
  'alternative hypothesis, H<sub>a</sub>' => [
    'we are attempting to <span style="color: #4d8426; font-weight:700;">support</span>this hypothesis indirectly by using the <span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> test',
    'if the <span style="color: #0247fe; font-weight:700;">null hypothesis, H<sub>0</sub></span> cannot be <span style="color: #4d8426; font-weight:700;">supported</span> , then this opposing hypothesis is <span style="color: #4d8426; font-weight:700;">supported</span>',
    'this hypothesis represents a deviation or bias from the expected pattern',
    'for this hypothesis, the expected values are often impossible to calculate',
    'we aim to <span style="color: #4d8426; font-weight:700;">support</span>this hypothesis in our <span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> test',
  ],
  'degrees of freedom' => [
    'usually one less than the number of observed categories (rows in the table)',
    'represents how many independent values can vary after constraints are applied',
    'in most <span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> tests, it is the number of observed categories (rows in the table) minus one',
    'this number determines which row of the <span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> <span style="color: #4424d6; font-weight:700;">critical value</span> table you should use',
  ],
);

# -------------------------------
# Select N random keys
# -------------------------------
my $n = 5;
@all_keys = PGsort(sub { $_[0] lt $_[1] }, keys %match_data);
my $local_seed = (defined($problemSeed) && $problemSeed ne '') ? $problemSeed : 1;
my $local_random = new PGrandom($local_seed);

my @indices = (0 .. $#all_keys);
my @shuffled = ();
while (@indices) {
  my $pick = $local_random->random(0, $#indices, 1);
  push @shuffled, splice(@indices, $pick, 1);
}
my @selected_keys = @all_keys[@shuffled[0..$n-1]];

# -------------------------------
# Build question/answer pairs
# -------------------------------
# Each entry: [prompt, choice]
@q_and_a = ();
foreach my $key (@selected_keys) {
  my $values_ref = $match_data{$key};
  my $i = $local_random->random(0, $#$values_ref, 1);
  my $value = $values_ref->[$i];
  push @q_and_a, [ $value, $key ];
}

# -------------------------------
# Randomize the questions
# -------------------------------
my @q_indices = (0 .. $#q_and_a);
my @q_shuffled = ();
while (@q_indices) {
  my $pick = $local_random->random(0, $#q_indices, 1);
  push @q_shuffled, $q_and_a[splice(@q_indices, $pick, 1)];
}
@q_and_a = @q_shuffled;

# -------------------------------
# Sort the choices alphabetically
# -------------------------------
@answers = ();
push(@answers, (map { $_->[1] } @q_and_a));
@answers_sorted = PGsort(sub { $_[0] lt $_[1] }, @answers);

# -------------------------------
# HTML-safe answer labels
# -------------------------------
%answer_html = (
  'critical value' => '<span style="color: #4424d6; font-weight:700;">critical value</span>',
  'chi-square (&chi;&sup2;) test statistic' => '<span style="color: #aa6701; font-weight:700;">chi-square (&chi;&sup2;)</span> test statistic',
  'level of significance, &alpha;' => '<span style="color: #8601af; font-weight:700;">level of significance, &alpha;</span>',
  'p-value' => '<span style="color: #c21460; font-weight:700;">p-value</span>',
  'null hypothesis, H<sub>0</sub>' => '<span style="color: #0247fe; font-weight:700;">null hypothesis, H<sub>0</sub></span>',
  'alternative hypothesis, H<sub>a</sub>' => '<span style="color: #cf4b03; font-weight:700;">alternative hypothesis, H<sub>a</sub></span>',
  'degrees of freedom' => '<span style="color: #687f19; font-weight:700;">degrees of freedom</span>',
);

@answers_sorted_html = map { $answer_html{$_} || $_ } @answers_sorted;

# -------------------------------
# Create answer index lookup
# -------------------------------
our %answer_index;
for (my $i = 0; $i <= $#answers_sorted; $i++) {
  $answer_index{$answers_sorted[$i]} = $i;
}

# -------------------------------
# PopUp/DropDown compatibility
# -------------------------------
sub make_popup {
  return defined &DropDown ? DropDown(@_) : PopUp(@_);
}

# -------------------------------
# Create popup objects (blank default)
# -------------------------------
my @answer_letters = @ALPHABET[0 .. $#answers_sorted];
my @answer_letters_with_blank = ('', @answer_letters);
@answer_dropdowns =
  map { make_popup([ @answer_letters_with_blank ], $answer_index{$q_and_a[$_][1]} + 1 ) }
  0 .. $#q_and_a;

# -------------------------------
# Render the question
# -------------------------------
HEADER_TEXT(<<END_STYLE);
<style>
.pgml-bold { font-weight: 700; }
.two-column {
    display: flex;
	flex-wrap: wrap;
	gap: 2rem;
	align-items: center;
	justify-content: space-evenly;
}
</style>
END_STYLE

$question_text = 'Match each of the following chi-square (&chi;&sup2;) terms with their corresponding definitions.';
$note_text = 'Note: Each choice will be used exactly once.';

BEGIN_PGML
[$question_text]*
[$note_text]*

[@ MODES(HTML => '<div class="two-column"><div>') @]*
[@ join(
    "\n\n",
    map {
        '[_]{$answer_dropdowns[' . $_ . ']} '
            . '*' . ($_ + 1) . '.* '
            . '[$q_and_a[' . $_ . '][0]]*'
    } 0 .. $#q_and_a
) @]**
[@ MODES(HTML => '</div><div class="right-col">') @]*
[@ join(
    "\n\n",
    map {
        chr(65 + $_) . '\\.' . ' ' . '[$answers_sorted_html[' . $_ . ']]*'
    } 0 .. $#answers_sorted
) @]**
[@ MODES(HTML => '</div></div>') @]*
END_PGML

# -------------------------------
# Dynamic Partial Credit Based on $n
# -------------------------------
$showPartialCorrectAnswers = 0;
my @thresholds;
my @scores;
for (my $i = 1; $i <= $n; $i++) {
  push @thresholds, $i;
  push @scores, sprintf("%.2f", $i / $n);
}

install_problem_grader(~~&custom_problem_grader_fluid);
$ENV{grader_numright} = [@thresholds];
$ENV{grader_scores}   = [@scores];
$ENV{grader_message} = 'You can earn partial credit.';

# -------------------------------
# Solution
# -------------------------------
$answer_list = join(', ', map { ($_ + 1) . '-' . $ALPHABET[$answer_index{$q_and_a[$_][1]}] } 0 .. $#q_and_a);
BEGIN_PGML_SOLUTION
The correct answers are: [$answer_list].
END_PGML_SOLUTION

ENDDOCUMENT();