<span id="mailbox-conversation"><div><div>Does that then mean that for a rule to really be considered as interesting, it needs both a lift above 1 and a p-value below 0.05? Or could a rule with a lift above 1 and an insignificant p-value still be of value?</div></div></span><div class="mailbox_signature">
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<div style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 13px; line-height: normal; background-color: rgb(255, 255, 255);">Aron Lindberg</div>
<div style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 13px; line-height: normal; background-color: rgb(255, 255, 255);"><br></div>
<div style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 13px; line-height: normal; background-color: rgb(255, 255, 255);">Doctoral Candidate, Information Systems</div>
<div style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 13px; line-height: normal; background-color: rgb(255, 255, 255);">Weatherhead School of Management </div>
<div style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 13px; line-height: normal; background-color: rgb(255, 255, 255);">Case Western Reserve University</div>
<div style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 13px; line-height: normal; background-color: rgb(255, 255, 255);">aronlindberg.github.io</div>
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<br><br><div class="gmail_quote"><p>On Thu, Mar 12, 2015 at 12:42 AM, Gilbert Ritschard <span dir="ltr"><<a href="mailto:Gilbert.Ritschard@unige.ch" target="_blank">Gilbert.Ritschard@unige.ch</a>></span> wrote:<br></p><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div lang="EN-US">
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<p class="MsoNormal"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Lift and implication strength are not equivalent, and can well differ as you have observed.<p></p></span></p>
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<p class="MsoNormal"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Lift measures whether the chance to observe the conclusion increases when the condition holds, why the implication strength measures whether the number of counter-examples
 decreases when the condition holds. A significant p-value means that the latter decrease is significant.<p></p></span></p>
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<p class="MsoNormal"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Best.<p></p></span></p>
<p class="MsoNormal"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Gilbert<p></p></span></p>
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<p class="MsoNormal"><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> traminer-users-bounces@lists.r-forge.r-project.org [mailto:traminer-users-bounces@lists.r-forge.r-project.org]
<b>On Behalf Of </b>Aron Lindberg<br><b>Sent:</b> Thursday, March 12, 2015 02:18<br><b>To:</b> Users questions<br><b>Cc:</b> Users questions<br><b>Subject:</b> Re: [Traminer-users] p-values for sequential association rules?<p></p></span></p>
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<p class="MsoNormal">Thanks Gilbert,</p>
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<p class="MsoNormal">That’s very helpful! How do I mesh this with the interpretation of the lift? For example, I have many rules where the lift is below 1 (and then based on assessing the lift is of no interest), but where the p-value is significant. I also
 have cases which show the reverse scenario, lift > 1, but insignificant p-values. Is it the case that the lift is similar to a coefficient, and then there is some error around it, thus sometimes causing large lift values to be insignificant?</p>
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<p class="MsoNormal">Best,</p>
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<p class="MsoNormal">Aron</p>
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<p class="MsoNormal" style="background:white"><span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>Aron Lindberg<p></p></span></p>
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<p class="MsoNormal" style="background:white"><span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>Doctoral Candidate, Information Systems<p></p></span></p>
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<p class="MsoNormal" style="background:white"><span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>Weatherhead School of Management <p></p></span></p>
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<p class="MsoNormal" style="background:white"><span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>Case Western Reserve University<p></p></span></p>
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<p class="MsoNormal" style="background:white"><span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>aronlindberg.github.io<p></p></span></p>
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<p>On Wed, Mar 11, 2015 at 3:09 PM, Gilbert Ritschard <<a href="mailto:Gilbert.Ritschard@unige.ch">Gilbert.Ritschard@unige.ch</a>> wrote:</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Hi Aron,<p></p></span></p>
<p><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'> <p></p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>The p-value is that of the implication strength (ImplicStat). This criteria is a z value. The lower
 ImplicStat (greater negative value), the greater the implication strength of the rule. Your first two rules have an implication strength of about -1, and P(Z<-1) is about .16 for a normal distribution. Likewise, for the 3^rd rule, you have an implicative
 strength of .08, and P(Z<.08) = .53. When the p-value is less than .05, the rule has a significant implicative strength.<p></p></span></p>
<p><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'> <p></p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>For more explanation see for example,
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style='font-family:"Calibri",sans-serif'>Ritschard, G., V. Pisetta and D.A. Zighed (2008), Inducing and evaluating classification trees with statistical implicative criteria,
 in R. Gras, E. Suzuki, F. Guillet and F. Spagnolo (eds), <i>Statistical Implicative Analysis: Theory and Applications</i>, Series Studies in Computational Intelligence, Vol. 127. Berlin: Springer, 397-420.
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style='font-family:"Calibri",sans-serif'>Preprint:
<a href="http://mephisto.unige.ch/pub/publications/gr/ritsch-pisetta-zighed_bookGras_final_plain.pdf">
http://mephisto.unige.ch/pub/publications/gr/ritsch-pisetta-zighed_bookGras_final_plain.pdf</a>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style='font-family:"Calibri",sans-serif'>Best,<p></p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style='font-family:"Calibri",sans-serif'>Gilbert
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>
<a href="mailto:traminer-users-bounces@lists.r-forge.r-project.org">traminer-users-bounces@lists.r-forge.r-project.org</a> [<a href="mailto:traminer-users-bounces@lists.r-forge.r-project.org">mailto:traminer-users-bounces@lists.r-forge.r-project.org</a>]
<b>On Behalf Of </b>Aron Lindberg<br><b>Sent:</b> Wednesday, March 11, 2015 16:29<br><b>To:</b> <a href="mailto:traminer-users@lists.r-forge.r-project.org">traminer-users@lists.r-forge.r-project.org</a><br><b>Subject:</b> [Traminer-users] p-values for sequential association rules?<p></p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Hi,</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">When running sequential association rules I get several values in the output:</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">         Rules Support      Conf      Lift Standardlift   JMeasure ImplicStat   p.value</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">1 (I1) => (I2)      15 0.7142857 0.7482993   -1.1607143 0.45894146 -0.9770084 0.1642825</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">2 (I2) => (I1)      17 0.8095238 0.8480726   -0.4404762 0.20127953 -0.9770084 0.1642825</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">3 (I2) => (I3)      17 0.8095238 0.9373434    0.5193644 0.01626898  0.0805823 0.5321129</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">From here I understand what support, confidence, and lift are:</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><a href="http://stackoverflow.com/questions/27947556/traminerseqerules-help-page">http://stackoverflow.com/questions/27947556/traminerseqerules-help-page</a></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">However, what does the p-value mean? It seems to be highly and negatively correlated with the confidence, but at the same time I have many sequences with combinations high support,
 confidence, and lift that still are insignificant.</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Hence: what does the p-value pertain to? Can the rules be meaningfully interpreted even with the p-value is insignificant?</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Best,</p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">ARon</p>
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<span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>Aron Lindberg<p></p></span></p>
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<span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>Doctoral Candidate, Information Systems<p></p></span></p>
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<span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>Weatherhead School of Management <p></p></span></p>
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<span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>Case Western Reserve University<p></p></span></p>
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<span style='font-size:10.0pt;font-family:"Helvetica",sans-serif;color:black'>aronlindberg.github.io<p></p></span></p>
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