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<title>Ask Ghassem - Recent questions tagged normal-distribution</title>
<link>https://ask.ghassem.com/tag/normal-distribution</link>
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<item>
<title>Using aggregate data to generate observation-level data statistically sound?</title>
<link>https://ask.ghassem.com/644/using-aggregate-generate-observation-level-statistically</link>
<description>&lt;p&gt;Context: In the realm of Paid Search Marketing. Current reporting does not provide event level data only aggregate totals with different segments.&amp;nbsp; Want to compare distributions/test statistical significance of A/B test results.&amp;nbsp; Did not want to assume that data followed normal distribution or know STDEV&amp;nbsp;for data so came with this approach.&amp;nbsp;&lt;/p&gt;

&lt;p&gt;My Question: I am going to use the average &quot;CPA&quot; or &quot;CTR&quot; for a date range, and generate an observation for each conversion based off the average for a time range.&amp;nbsp; Is this statistically sound way if I want to generate raw data? Would I have wonky distributions because of the multiple averages?&amp;nbsp; Just want a gutcheck if I&#039;m completely off base.&amp;nbsp;&amp;nbsp;&lt;/p&gt;

&lt;p&gt;My Aggregate data looks like below:&lt;/p&gt;

&lt;table border=&quot;1&quot; cellpadding=&quot;1&quot; style=&quot;width:500px&quot;&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th scope=&quot;col&quot;&gt;Day&lt;/th&gt;
&lt;th scope=&quot;col&quot;&gt;Cost&lt;/th&gt;
&lt;th scope=&quot;col&quot;&gt;Acquisition&lt;/th&gt;
&lt;th scope=&quot;col&quot;&gt;CPA or CTR&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp;1&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 40&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 2&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;$20&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp;2&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 75&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 3&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;$25&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;

&lt;p&gt;Observation data I generate looks like below:&lt;/p&gt;

&lt;table border=&quot;1&quot; cellpadding=&quot;1&quot; style=&quot;width:500px&quot;&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th scope=&quot;col&quot;&gt;Day&lt;/th&gt;
&lt;th scope=&quot;col&quot;&gt;Acquisition&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;1&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;$20&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;1&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;$20&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;2&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;$25&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;2&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;$25&amp;nbsp;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;2&lt;/td&gt;
&lt;td&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;$25&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;

&lt;p&gt;I really appreciate your help with this question! An important project to me at work.&amp;nbsp;&amp;nbsp;&lt;/p&gt;</description>
<category>general</category>
<guid isPermaLink="true">https://ask.ghassem.com/644/using-aggregate-generate-observation-level-statistically</guid>
<pubDate>Tue, 11 Jun 2019 22:04:01 +0000</pubDate>
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<item>
<title>Computing the Confidence Interval for a Difference Between Two Means</title>
<link>https://ask.ghassem.com/546/computing-the-confidence-interval-difference-between-means</link>
<description></description>
<category>Statistics</category>
<guid isPermaLink="true">https://ask.ghassem.com/546/computing-the-confidence-interval-difference-between-means</guid>
<pubDate>Fri, 07 Dec 2018 23:02:45 +0000</pubDate>
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<item>
<title>What is degree of Freedom while calculating confidence interval?</title>
<link>https://ask.ghassem.com/544/what-degree-freedom-while-calculating-confidence-interval</link>
<description></description>
<category>Statistics</category>
<guid isPermaLink="true">https://ask.ghassem.com/544/what-degree-freedom-while-calculating-confidence-interval</guid>
<pubDate>Fri, 07 Dec 2018 22:27:27 +0000</pubDate>
</item>
<item>
<title>What is the T Distribution?</title>
<link>https://ask.ghassem.com/534/what-is-the-t-distribution</link>
<description></description>
<category>Statistics</category>
<guid isPermaLink="true">https://ask.ghassem.com/534/what-is-the-t-distribution</guid>
<pubDate>Fri, 30 Nov 2018 21:22:02 +0000</pubDate>
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<title>Probability for the data items within mean +- 1, +-2, +-3 standard deviation?</title>
<link>https://ask.ghassem.com/529/probability-for-data-items-within-mean-standard-deviation</link>
<description></description>
<category>Statistics</category>
<guid isPermaLink="true">https://ask.ghassem.com/529/probability-for-data-items-within-mean-standard-deviation</guid>
<pubDate>Fri, 30 Nov 2018 21:15:35 +0000</pubDate>
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<item>
<title>What will be probability for the data items within mean +- 1, +-2, +-3 standard deviation?</title>
<link>https://ask.ghassem.com/520/what-will-probability-data-items-within-standard-deviation</link>
<description></description>
<category>general</category>
<guid isPermaLink="true">https://ask.ghassem.com/520/what-will-probability-data-items-within-standard-deviation</guid>
<pubDate>Wed, 14 Nov 2018 15:10:15 +0000</pubDate>
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<item>
<title>How much percentage of data items are consumed within mean +-1 , +-2, +-3 standard deviation?</title>
<link>https://ask.ghassem.com/518/much-percentage-items-consumed-within-standard-deviation</link>
<description></description>
<category>general</category>
<guid isPermaLink="true">https://ask.ghassem.com/518/much-percentage-items-consumed-within-standard-deviation</guid>
<pubDate>Wed, 14 Nov 2018 15:04:52 +0000</pubDate>
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<item>
<title>What is the mean and standard deviation of a standard normal distribution?</title>
<link>https://ask.ghassem.com/330/what-mean-standard-deviation-standard-normal-distribution</link>
<description></description>
<category>Statistics</category>
<guid isPermaLink="true">https://ask.ghassem.com/330/what-mean-standard-deviation-standard-normal-distribution</guid>
<pubDate>Fri, 12 Oct 2018 01:39:12 +0000</pubDate>
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<item>
<title>How to calculate normal distribution?</title>
<link>https://ask.ghassem.com/532/how-to-calculate-normal-distribution</link>
<description></description>
<category>Statistics</category>
<guid isPermaLink="true">https://ask.ghassem.com/532/how-to-calculate-normal-distribution</guid>
<pubDate>Sat, 01 Sep 2018 20:20:01 +0000</pubDate>
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