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	<id>http://practicalstats.labanca.net/index.php?action=history&amp;feed=atom&amp;title=Normal_Curve_Equivalent_scores</id>
	<title>Normal Curve Equivalent scores - Revision history</title>
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	<updated>2026-09-25T00:18:35Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>http://practicalstats.labanca.net/index.php?title=Normal_Curve_Equivalent_scores&amp;diff=40&amp;oldid=prev</id>
		<title>Admin at 00:11, 29 August 2019</title>
		<link rel="alternate" type="text/html" href="http://practicalstats.labanca.net/index.php?title=Normal_Curve_Equivalent_scores&amp;diff=40&amp;oldid=prev"/>
		<updated>2019-08-29T00:11:29Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 00:11, 29 August 2019&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Rationale for NCE scores ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Rationale for NCE scores ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Because percentile ranks are considered ordinal level data, there are limits to the mathematical manipulations and &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;statiscal &lt;/del&gt;&amp;#039;&amp;#039;&amp;#039;analyses&amp;#039;&amp;#039;&amp;#039; that can take place.&amp;#160; However, this limitation can be overcome by converting data into normalized standard scores instead of percentile rank.&amp;#160; The common normalized standard score used in educational research is the normal curve equivalent (NCE) score.&amp;#160; &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Because percentile ranks are considered ordinal level data, there are limits to the mathematical manipulations and &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;statistical &lt;/ins&gt;&amp;#039;&amp;#039;&amp;#039;analyses&amp;#039;&amp;#039;&amp;#039; that can take place.&amp;#160; However, this limitation can be overcome by converting data into normalized standard scores instead of percentile rank.&amp;#160; The common normalized standard score used in educational research is the normal curve equivalent (NCE) score.&amp;#160; &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;contributed by Frank LaBanca, EdD&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;contributed by Frank LaBanca, EdD&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot; &gt;Line 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Description of NCE scores ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Description of NCE scores ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The NCE scores are on a scale of 1 to 99 with a mean of 50 and a standard deviation of 21.38.&amp;#160; For the purposes of educational research the standard deviation is usually calculated using a value of 21.&amp;#160; An NCE value of 1 corresponds with 1st percentile, 50 with 50th percentile, and 99 with 99th percentile.&amp;#160; Other NCE scores are mathematically modeled and do not correspond with the exact percentile, because of variations of area under the normal curve.&amp;#160; The NCE is considered an (equally-appearing) interval scale.&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The NCE scores are on a scale of 1 to 99 with a mean of 50 and a standard deviation of 21.38.&amp;#160; For the purposes of educational research&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;the standard deviation is usually calculated using a value of 21.&amp;#160; An NCE value of 1 corresponds with 1st percentile, 50 with 50th percentile, and 99 with 99th percentile.&amp;#160; Other NCE scores are mathematically modeled and do not correspond with the exact percentile, because of variations of area under the normal curve.&amp;#160; The NCE is considered an (equally-appearing) interval scale.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;contributed by Frank LaBanca, EdD&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;contributed by Frank LaBanca, EdD&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Admin</name></author>
		
	</entry>
	<entry>
		<id>http://practicalstats.labanca.net/index.php?title=Normal_Curve_Equivalent_scores&amp;diff=39&amp;oldid=prev</id>
		<title>Admin: Created page with &quot;== Rationale for NCE scores == Because percentile ranks are considered ordinal level data, there are limits to the mathematical manipulations and statiscal &#039;&#039;&#039;analyses&#039;&#039;&#039; that...&quot;</title>
		<link rel="alternate" type="text/html" href="http://practicalstats.labanca.net/index.php?title=Normal_Curve_Equivalent_scores&amp;diff=39&amp;oldid=prev"/>
		<updated>2019-08-29T00:11:01Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;== Rationale for NCE scores == Because percentile ranks are considered ordinal level data, there are limits to the mathematical manipulations and statiscal &amp;#039;&amp;#039;&amp;#039;analyses&amp;#039;&amp;#039;&amp;#039; that...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;== Rationale for NCE scores ==&lt;br /&gt;
Because percentile ranks are considered ordinal level data, there are limits to the mathematical manipulations and statiscal &amp;#039;&amp;#039;&amp;#039;analyses&amp;#039;&amp;#039;&amp;#039; that can take place.  However, this limitation can be overcome by converting data into normalized standard scores instead of percentile rank.  The common normalized standard score used in educational research is the normal curve equivalent (NCE) score.  &lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;contributed by Frank LaBanca, EdD&amp;#039;&amp;#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Description of NCE scores ==&lt;br /&gt;
&lt;br /&gt;
The NCE scores are on a scale of 1 to 99 with a mean of 50 and a standard deviation of 21.38.  For the purposes of educational research the standard deviation is usually calculated using a value of 21.  An NCE value of 1 corresponds with 1st percentile, 50 with 50th percentile, and 99 with 99th percentile.  Other NCE scores are mathematically modeled and do not correspond with the exact percentile, because of variations of area under the normal curve.  The NCE is considered an (equally-appearing) interval scale.&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;contributed by Frank LaBanca, EdD&amp;#039;&amp;#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Computing NCE scores ==&lt;br /&gt;
&lt;br /&gt;
1. Convert ordinal data to a z score&lt;br /&gt;
&lt;br /&gt;
2. Convert z score to NCE score using the formula below&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;contributed by Frank LaBanca, EdD&amp;#039;&amp;#039;&lt;br /&gt;
&lt;br /&gt;
== NCE formula ==&lt;br /&gt;
&lt;br /&gt;
X&amp;#039;=(s&amp;#039;)(z) + X(mean)&amp;#039;&lt;br /&gt;
&lt;br /&gt;
NCE score = standard deviation (21) x z score + 50&lt;br /&gt;
&lt;br /&gt;
Remember: the NCE score is a standard score with a mean of 50 and standard deviation of 21.  NCE scores can range from 1 to 99 and are equally-appearing interval data.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;contributed by Frank LaBanca, EdD; modified by Chris Longo &amp;amp; Chris Ruggiero&amp;#039;&amp;#039;&lt;/div&gt;</summary>
		<author><name>Admin</name></author>
		
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