http://wiki.zcubes.com/index.php?action=history&feed=atom&title=Manuals%2Fcalci%2FBartlett%27sTest 2026-04-27T21:18:58Z Revision history for this page on the wiki MediaWiki 1.35.2 http://wiki.zcubes.com/index.php?title=Manuals/calci/Bartlett%27sTest&diff=209980&oldid=prev 2018-05-08T09:48:56Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:48, 8 May 2018</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l96" >Line 96:</td> <td colspan="2" class="diff-lineno">Line 96:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>|RESULT || THE P-VALUE IS LESSER THAN THE B-CRITICAL VALUE, SO THE VARIANCES ARE JUDGED TO BE EQUAL.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>|RESULT || THE P-VALUE IS LESSER THAN THE B-CRITICAL VALUE, SO THE VARIANCES ARE JUDGED TO BE EQUAL.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>|}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>|}</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;">== See Also ==</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;">*[[Manuals/calci/ANOVASINGLEFACTOR| ANOVASINGLEFACTOR]]</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>*[[Z_API_Functions | List of Main Z Functions]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>*[[Z_API_Functions | List of Main Z Functions]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>*[[ Z3 |  Z3 home ]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>*[[ Z3 |  Z3 home ]]</div></td></tr> </table>

Jayaram http://wiki.zcubes.com/index.php?title=Manuals/calci/Bartlett%27sTest&diff=209979&oldid=prev 2018-05-08T09:43:19Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:43, 8 May 2018</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6" >Line 6:</td> <td colspan="2" class="diff-lineno">Line 6:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>==Description==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>==Description==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>* Bartlett's test is used to test if k samples are from populations with equal variances.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>* Bartlett's test is used to test if k samples are from populations with equal variances.</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;">* Also called Bartlett's test for homogeneity of variances. It is used to test if variances are equal for all samples.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>* Bartlett's test is sensitive to departures from normality.  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>* Bartlett's test is sensitive to departures from normality.  </div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;">* It is used when you’re fairly certain your data comes from a normal distribution.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>* That is, if the samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>* That is, if the samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>   &lt;math&gt;B=\frac{df_WlnMS_W-\sum_{j}df_jln s_j^2}{1+\frac{1}{3(k-1)}(\sum_{j}\frac{1}{df_j}-\frac{1}{df_W})}&lt;/math&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>   &lt;math&gt;B=\frac{df_WlnMS_W-\sum_{j}df_jln s_j^2}{1+\frac{1}{3(k-1)}(\sum_{j}\frac{1}{df_j}-\frac{1}{df_W})}&lt;/math&gt;</div></td></tr> </table>

Jayaram http://wiki.zcubes.com/index.php?title=Manuals/calci/Bartlett%27sTest&diff=208080&oldid=prev 2017-05-10T05:20:04Z

<p>Created page with &quot;&lt;div style=&quot;font-size:25px&quot;&gt;&#039;&#039;&#039;BARTLETTSTEST(DataRange,ConfidenceLevel,NewTableFlag)&#039;&#039;&#039;&lt;/div&gt;&lt;br/&gt; *&lt;math&gt;DataRange&lt;/math&gt; is the array of x values. *&lt;math&gt;ConfidenceLevel&lt;/ma...&quot;</p> <p><b>New page</b></p><div>&lt;div style=&quot;font-size:25px&quot;&gt;'''BARTLETTSTEST(DataRange,ConfidenceLevel,NewTableFlag)'''&lt;/div&gt;&lt;br/&gt;<br /> *&lt;math&gt;DataRange&lt;/math&gt; is the array of x values.<br /> *&lt;math&gt;ConfidenceLevel&lt;/math&gt; is the value from 0 to 1.<br /> *&lt;math&gt;NewTableFlag&lt;/math&gt; is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.<br /> <br /> ==Description==<br /> * Bartlett's test is used to test if k samples are from populations with equal variances.<br /> * Bartlett's test is sensitive to departures from normality. <br /> * That is, if the samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality.<br /> &lt;math&gt;B=\frac{df_WlnMS_W-\sum_{j}df_jln s_j^2}{1+\frac{1}{3(k-1)}(\sum_{j}\frac{1}{df_j}-\frac{1}{df_W})}&lt;/math&gt;<br /> * B is the Bartlett's test static.<br /> * &lt;math&gt;MS_W&lt;/math&gt; is the pooled variance across all groups.<br /> <br /> ==Result==<br /> * If p-value is greater than BCriticl value, reject the null hypothesis.<br /> * Else retain null hypothesis.<br /> <br /> ==Example==<br /> {| class=&quot;wikitable&quot;<br /> |+Spreadsheet<br /> |-<br /> ! !! A !! B !!C !!D <br /> |-<br /> ! 1<br /> | 51 || 82 || 79 || 85 <br /> |-<br /> ! 2<br /> | 87 || 91 || 84 || 80 <br /> |-<br /> !3<br /> | 50 || 92 || 74 || 65 <br /> |-<br /> !4<br /> | 48 || 80 || 98 || 71<br /> |-<br /> !5<br /> | 79 || 52 || 63 || 67<br /> |-<br /> !6<br /> | 61 || 79 || 83 || 51<br /> |-<br /> !7<br /> | 53 || 73 || 85 || 63<br /> |-<br /> !8<br /> |54 || 74 || 58 || 93<br /> |}<br /> =BARTLETTSTEST([A1:A8,B1:B8,C1:C8,D1:D8],0.05,true)<br /> {| class=&quot;wikitable&quot;<br /> |+BARTLETT'S TEST<br /> |-<br /> ! !!DATA-0!!DATA-1!! DATA-2!!DATA-3<br /> |-<br /> |MEAN||60.375||77.875||78||71.875<br /> |-<br /> |VARIANCE || 214.26785714285714 || 157.55357142857142 || 164.57142857142858 || 181.55357142857142<br /> |-<br /> |LNVARIANCE || 5.367226901229239 || 5.059765536486956 || 5.1033446922005234 || 5.201550769540011<br /> |-<br /> |COUNT || 8 || 8 || 8 || 8<br /> |-<br /> |DF || 7 || 7 || 7 || 7<br /> |-<br /> |1/DF || 0.14285714285714285 || 0.14285714285714285 || 0.14285714285714285 || 0.14285714285714285<br /> |}<br /> {| class=&quot;wikitable&quot;<br /> |+ERROR<br /> |-<br /> ! !! SAMPLE DATA<br /> |-<br /> |DF || 28<br /> |-<br /> | 1/DF || 0.03571428571428571<br /> |-<br /> |VARIANCE || 179.48660714285714<br /> |-<br /> |LNVARIANCE || 5.19010059312721<br /> |}<br /> {| class=&quot;wikitable&quot;<br /> |+RESULTS<br /> |-<br /> ! !! DATA<br /> |-<br /> |B-NUMERATOR || 0.19960131136474502<br /> |-<br /> |B-DENOMINATOR || 1.0595238095238095<br /> |-<br /> |B || 0.18838775454650092<br /> |-<br /> |P-VALUE || 0.979441777737987<br /> |-<br /> |B-CRITICAL || 7.810299999999978<br /> |-<br /> |RESULT || THE P-VALUE IS LESSER THAN THE B-CRITICAL VALUE, SO THE VARIANCES ARE JUDGED TO BE EQUAL.<br /> |}<br /> <br /> *[[Z_API_Functions | List of Main Z Functions]]<br /> <br /> *[[ Z3 | Z3 home ]]</div>

Jayaram