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Fixed issue #6391 Quartile calculations seem to be wrong. They really…
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… were. The limit/offset functions weren't working properly, and the method was calculating quartiles based on sum values, which is just wrong. Corrected methodology and database call, although the database call should probably be improved later.
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@jcleeland
jcleeland committed Jul 26, 2012
1 parent a6b43b4 commit dabf358
Showing 1 changed file with 79 additions and 46 deletions.
125 changes: 79 additions & 46 deletions application/helpers/admin/statistics_helper.php
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Original file line number Diff line number Diff line change
Expand Up @@ -1091,10 +1091,24 @@ function buildOutputList($rt, $language, $surveyid, $outputType, $sql) {

//no more comment from Mazi regarding the calculation

/* IMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT */
/* IF YOU DON'T UNDERSTAND WHAT QUARTILES ARE DO NOT MODIFY THIS CODE */
/* Quartiles and Median values are NOT related to average, and the sum is irrelevent */

// Calculating only makes sense with more than one result
if ($medcount>1)
{
//1ST QUARTILE (Q1)
/* L=(1/4)(n+1), U=(3/4)(n+1) */
/* Minitab linear interpolation between the two
closest data points. Minitab would let L = 2.5 and find the value half way between the
2nd and 3rd data points. In our example, that would be (4+9)/2 =
6.5. Similarly, the upper quartile value would be half way between
the 7th and 8th data points, which would be (49+64)/2 = 56.5. If L
were 2.25, Minitab would find the value one fourth of the way
between the 2nd and 3rd data points and if L were 2.75, Minitab
would find the value three fourths of the way between the 2nd and
3rd data points. */
$q1=(1/4)*($medcount+1);
$q1b=(int)((1/4)*($medcount+1));
$q1c=$q1b-1;
Expand All @@ -1104,36 +1118,31 @@ function buildOutputList($rt, $language, $surveyid, $outputType, $sql) {
// fix if there are too few values to evaluate.
if ($q1c<0) {$q1c=0;}

if ($q1 != $q1b)
if ($q1 != $q1b) //The value will be between two of the individual results
{
//ODD NUMBER
$query = $querystarter . " ORDER BY ".Yii::app()->db->quoteColumnName($fieldname)."*1 ";
$result=Yii::app()->db->createCommand($query)->limit(2, $q1c)->query();

foreach ($result->readAll() as $row)
$result = Yii::app()->db->createCommand($query)->query();
$i=0;
foreach ($result as $row)
{
if ($total == 0) {$total=$total-$row[$fieldname];}

else {$total=$total+$row[$fieldname];}

$lastnumber=$row[$fieldname];
if($row[$fieldname]) {$i++;}
if($i==$q1c) {$secondlastnumber=$row[$fieldname];}
if($i==$q1b) {$lastnumber=$row[$fieldname];}
}

$q1total=$lastnumber-((1-$q1diff)*$total);

if ($q1total < $minimum) {$q1total=$minimum;}
$q1total=$lastnumber-((1-$q1diff)*$secondlastnumber);
//if ($q3total < $maximum) {$q1total=$maximum;} //What the? If the 3rd quartiel is higher than the highest, then make the 1st quartile the highest? This makes no sense!

$showem[]=array($statlang->gT("1st quartile (Q1)"), $q1total);
}
else
{
//EVEN NUMBER
$query = $querystarter . " ORDER BY ".Yii::app()->db->quoteColumnName($fieldname)."*1 ";
$result=Yii::app()->db->createCommand($query)->limit(1, $q1c)->query();
$query = $querystarter . " ORDER BY ".Yii::app()->db->quoteColumnName($fieldname)."*1";
$result = Yii::app()->db->createCommand($query)->query();

foreach ($result->readAll() as $row)
foreach ($result as $row)
{
$showem[]=array($statlang->gT("1st quartile (Q1)"), $row[$fieldname]);
if($row[$fieldname]) {$i++;}
if($i==$q1b) {$showem[]=array($statlang->gT("1st quartile (Q1)"), $row[$fieldname]);}
}
}

Expand All @@ -1150,61 +1159,78 @@ function buildOutputList($rt, $language, $surveyid, $outputType, $sql) {
{
//remainder
$query = $querystarter . " ORDER BY ".Yii::app()->db->quoteColumnName($fieldname)."*1 ";
$result=Yii::app()->db->createCommand($query)->limit(2, $medianc)->query();
$result=Yii::app()->db->createCommand($query)->query();

$i=0;
foreach ($result as $row) {
if($row[$fieldname]) {$i++;}
if($i==$medianc) {$secondlastnumber=$row[$fieldname];}
if($i==$medianb) {$lastnumber=$row[$fieldname];}

foreach ($result->readAll() as $row) {$total=$total+$row[$fieldname];}
}
$mediantotal=$lastnumber-((1-$mediandiff)*$secondlastnumber);
//if ($q3total < $maximum) {$q1total=$maximum;} //What the? If the 3rd quartiel is higher than the highest, then make the 1st quartile the highest? This makes no sense!

$showem[]=array($statlang->gT("2nd quartile (Median)"), $mediantotal);

$showem[]=array($statlang->gT("2nd quartile (Median)"), $total/2);
}

else
{
//EVEN NUMBER
$query = $querystarter . " ORDER BY ".Yii::app()->db->quoteColumnName($fieldname)."*1 ";
$result = Yii::app()->db->createCommand($query)->limit(1, $medianc-1)->query();
$query = $querystarter . " ORDER BY ".Yii::app()->db->quoteColumnName($fieldname)."*1";
$result = Yii::app()->db->createCommand($query)->query();

foreach ($result->readAll() as $row)
foreach ($result as $row)
{
$showem[]=array($statlang->gT("Median value"), $row[$fieldname]);
if($row[$fieldname]) {$i++;}
if($i==$medianb) {$showem[]=array($statlang->gT("2nd quartile (Median)"), $row[$fieldname]);}
}
}

$total=0;


//3RD QUARTILE (Q3)
$q3=(3/4)*($medcount+1);
$q3b=(int)((3/4)*($medcount+1));
$q3c=$q3b-1;
/* L=(1/4)(n+1), U=(3/4)(n+1) */
/* Minitab linear interpolation between the two
closest data points. Minitab would let L = 2.5 and find the value half way between the
2nd and 3rd data points. In our example, that would be (4+9)/2 =
6.5. Similarly, the upper quartile value would be half way between
the 7th and 8th data points, which would be (49+64)/2 = 56.5. If L
were 2.25, Minitab would find the value one fourth of the way
between the 2nd and 3rd data points and if L were 2.75, Minitab
would find the value three fourths of the way between the 2nd and
3rd data points. */
$q3=(3/4)*($medcount+1); //Find the 75th percentile according to count of items
$q3b=(int)((3/4)*($medcount+1)); //The int version of $q3
$q3c=$q3b-1; //The number before the int version of $q3
$q3diff=$q3-$q3b;

if ($q3 != $q3b)
if ($q3 != $q3b) //The value will be between two of the individual results
{
$query = $querystarter . " ORDER BY ".Yii::app()->db->quoteColumnName($fieldname)."*1 ";
$result = Yii::app()->db->createCommand($query)->limit(2,$q3c)->query();

foreach ($result->readAll() as $row)
$result = Yii::app()->db->createCommand($query)->query();
$i=0;
foreach ($result as $row)
{
if ($total == 0) {$total=$total-$row[$fieldname];}

else {$total=$total+$row[$fieldname];}

$lastnumber=$row[$fieldname];
if($row[$fieldname]) {$i++;}
if($i==$q3c) {$secondlastnumber=$row[$fieldname];}
if($i==$q3b) {$lastnumber=$row[$fieldname];}
}
$q3total=$lastnumber-((1-$q3diff)*$total);

if ($q3total < $maximum) {$q1total=$maximum;}
$q3total=$lastnumber-((1-$q3diff)*$secondlastnumber);
//if ($q3total < $maximum) {$q1total=$maximum;} //What the? If the 3rd quartiel is higher than the highest, then make the 1st quartile the highest? This makes no sense!

$showem[]=array($statlang->gT("3rd quartile (Q3)"), $q3total);
}
else
{
$query = $querystarter . " ORDER BY ".Yii::app()->db->quoteColumnName($fieldname)."*1";
$result = Yii::app()->db->createCommand($query)->limit(1, $q3c);
$result = Yii::app()->db->createCommand($query)->query();

foreach ($result->queryAll() as $row)
foreach ($result as $row)
{
$showem[]=array($statlang->gT("3rd quartile (Q3)"), $row[$fieldname]);
if($row[$fieldname]) {$i++;}
if($i==$q3b) {$showem[]=array($statlang->gT("3rd quartile (Q3)"), $row[$fieldname]);}
}
}

Expand Down Expand Up @@ -1281,7 +1307,14 @@ function buildOutputList($rt, $language, $surveyid, $outputType, $sql) {
."\t\t\t".sprintf($statlang->gT("Q1 and Q3 calculated using %s"), "<a href='http://mathforum.org/library/drmath/view/60969.html' target='_blank'>".$statlang->gT("minitab method")."</a>")
."</font>\n"
."\t\t</td>\n"
."\t</tr>\n</table>\n";
."\t</tr>\n";
$statisticsoutput .= "\t<tr>\n"
."\t\t<td align='center' colspan='4'>
<input type='button' class='statisticsbrowsebutton' value='"
.$statlang->gT("Browse")."' id='$fieldname' /></td>\n</tr>";
$statisticsoutput .= "<tr><td class='statisticsbrowsecolumn' colspan='3' style='display: none'>
<div class='statisticsbrowsecolumn' id='columnlist_{$fieldname}'></div></td></tr>";
$statisticsoutput .= "</table>\n";

break;
default:
Expand Down

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