Hallo, dies ist ein Test.

PWD: /www/data-lst1/unixsoft/unixsoft/kaempfer/.public_html

Running in File Mode
Relative path: ./../../../../../server/data/WWW/sv/../wilcoxon.shtml
Real path: /www/data-lst3/signal/hochmuth/.public_html/wilcoxon.shtml
Zurück

<HTML>
<HEAD>
<LINK rel='stylesheet' type='text/css' href='./css/hu.css'>
<LINK rel='stylesheet' type='text/css' href='https://www2.hu-berlin.de/hu/css/hu.css'>
<LINK rel='stylesheet' type='text/css' href='./css/olaf.css'>
<TITLE>Wilcoxontafel</TITLE>
</HEAD>
<BODY>
<H2>Tafelwerte f&uuml;r die Tests von Wilcoxon, Mann und Whitney</H2>
<HR>

Wenn die errechnete Testgr&ouml;&szlig;e U &le; Tafelwert, dann
wird die Nullhypothese &#132;beide Verteilungen sind gleich&#147;
abgelehnt.
 
 
<TABLE border="1" bordercolor='gray' cellspacing="0" cellpadding="4">
 <TR>
 <TH colspan="13" align='middle'>&alpha; = 0,05 bzw. alpha = 0,05 (einseitiger Test)</TH>
 </TR>
 <TR>
 <TD align="right" bgcolor='#e0e0e0'>N2</TD>
 <TD align="right" bgcolor='#e0e0e0'> 9</TD>
 <TD align="right" bgcolor='#e0e0e0'>10</TD>
 <TD align="right" bgcolor='#e0e0e0'>11</TD>
 <TD align="right" bgcolor='#e0e0e0'>12</TD>
 <TD align="right" bgcolor='#e0e0e0'>13</TD>
 <TD align="right" bgcolor='#e0e0e0'>14</TD>
 <TD align="right" bgcolor='#e0e0e0'>15</TD>
 <TD align="right" bgcolor='#e0e0e0'>16</TD>
 <TD align="right" bgcolor='#e0e0e0'>17</TD>
 <TD align="right" bgcolor='#e0e0e0'>18</TD>
 <TD align="right" bgcolor='#e0e0e0'>19</TD>
 <TD align="right" bgcolor='#e0e0e0'>20</TD>
 </TR>
 <TR>
 <TD align="left" bgcolor=#e0e0e0>N1</TD>
 <TD colspan="12">&nbsp;</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>1</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">&nbsp;</TD>
 <TD align="right">0</TD>
 <TD align="right">0</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>2</TD>
 <TD align="right">1</TD>
 <TD align="right">1</TD>
 <TD align="right">1</TD>
 <TD align="right">2</TD>
 <TD align="right">2</TD>
 <TD align="right">2</TD>
 <TD align="right">3</TD>
 <TD align="right">3</TD>
 <TD align="right">3</TD>
 <TD align="right">4</TD>
 <TD align="right">4</TD>
 <TD align="right">4</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>3</TD>
 <TD align="right">3</TD>
 <TD align="right">4</TD>
 <TD align="right">5</TD>
 <TD align="right">5</TD>
 <TD align="right">6</TD>
 <TD align="right">7</TD>
 <TD align="right">7</TD>
 <TD align="right">8</TD>
 <TD align="right">9</TD>
 <TD align="right">9</TD>
 <TD align="right">10</TD>
 <TD align="right">11</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>4</TD>
 <TD align="right">6</TD>
 <TD align="right">7</TD>
 <TD align="right">8</TD>
 <TD align="right">9</TD>
 <TD align="right">10</TD>
 <TD align="right">11</TD>
 <TD align="right">12</TD>
 <TD align="right">14</TD>
 <TD align="right">15</TD>
 <TD align="right">16</TD>
 <TD align="right">17</TD>
 <TD align="right">18</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>5</TD>
 <TD align="right">9</TD>
 <TD align="right">11</TD>
 <TD align="right">12</TD>
 <TD align="right">13</TD>
 <TD align="right">15</TD>
 <TD align="right">16</TD>
 <TD align="right">18</TD>
 <TD align="right">19</TD>
 <TD align="right">20</TD>
 <TD align="right">22</TD>
 <TD align="right">23</TD>
 <TD align="right">25</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>6</TD>
 <TD align="right">12</TD>
 <TD align="right">14</TD>
 <TD align="right">16</TD>
 <TD align="right">17</TD>
 <TD align="right">19</TD>
 <TD align="right">21</TD>
 <TD align="right">23</TD>
 <TD align="right">25</TD>
 <TD align="right">26</TD>
 <TD align="right">28</TD>
 <TD align="right">30</TD>
 <TD align="right">32</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>7</TD>
 <TD align="right">15</TD>
 <TD align="right">17</TD>
 <TD align="right">19</TD>
 <TD align="right">21</TD>
 <TD align="right">24</TD>
 <TD align="right">26</TD>
 <TD align="right">28</TD>
 <TD align="right">30</TD>
 <TD align="right">33</TD>
 <TD align="right">35</TD>
 <TD align="right">37</TD>
 <TD align="right">39</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>8</TD>
 <TD align="right">18</TD>
 <TD align="right">20</TD>
 <TD align="right">23</TD>
 <TD align="right">26</TD>
 <TD align="right">28</TD>
 <TD align="right">31</TD>
 <TD align="right">33</TD>
 <TD align="right">36</TD>
 <TD align="right">39</TD>
 <TD align="right">41</TD>
 <TD align="right">44</TD>
 <TD align="right">47</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>9</TD>
 <TD align="right" bgcolor=#f0f0f0>21</TD>
 <TD align="right">24</TD>
 <TD align="right">27</TD>
 <TD align="right">30</TD>
 <TD align="right">33</TD>
 <TD align="right">36</TD>
 <TD align="right">39</TD>
 <TD align="right">42</TD>
 <TD align="right">45</TD>
 <TD align="right">48</TD>
 <TD align="right">51</TD>
 <TD align="right">54</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>10</TD>
 <TD align="right">24</TD>
 <TD align="right" bgcolor=#f0f0f0>27</TD>
 <TD align="right">31</TD>
 <TD align="right">34</TD>
 <TD align="right">37</TD>
 <TD align="right">41</TD>
 <TD align="right">44</TD>
 <TD align="right">48</TD>
 <TD align="right">51</TD>
 <TD align="right">55</TD>
 <TD align="right">58</TD>
 <TD align="right">62</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>11</TD>
 <TD align="right">27</TD>
 <TD align="right">31</TD>
 <TD align="right" bgcolor=#f0f0f0>34</TD>
 <TD align="right">38</TD>
 <TD align="right">42</TD>
 <TD align="right">46</TD>
 <TD align="right">50</TD>
 <TD align="right">54</TD>
 <TD align="right">57</TD>
 <TD align="right">61</TD>
 <TD align="right">65</TD>
 <TD align="right">69</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>12</TD>
 <TD align="right">30</TD>
 <TD align="right">34</TD>
 <TD align="right">38</TD>
 <TD align="right" bgcolor=#f0f0f0>42</TD>
 <TD align="right">47</TD>
 <TD align="right">51</TD>
 <TD align="right">55</TD>
 <TD align="right">60</TD>
 <TD align="right">64</TD>
 <TD align="right">68</TD>
 <TD align="right">72</TD>
 <TD align="right">77</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>13</TD>
 <TD align="right">33</TD>
 <TD align="right">37</TD>
 <TD align="right">42</TD>
 <TD align="right">47</TD>
 <TD align="right" bgcolor=#f0f0f0>51</TD>
 <TD align="right">56</TD>
 <TD align="right">61</TD>
 <TD align="right">65</TD>
 <TD align="right">70</TD>
 <TD align="right">75</TD>
 <TD align="right">80</TD>
 <TD align="right">84</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>14</TD>
 <TD align="right">36</TD>
 <TD align="right">41</TD>
 <TD align="right">46</TD>
 <TD align="right">51</TD>
 <TD align="right">56</TD>
 <TD align="right" bgcolor=#f0f0f0>61</TD>
 <TD align="right">66</TD>
 <TD align="right">71</TD>
 <TD align="right">77</TD>
 <TD align="right">82</TD>
 <TD align="right">87</TD>
 <TD align="right">92</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>15</TD>
 <TD align="right">39</TD>
 <TD align="right">44</TD>
 <TD align="right">50</TD>
 <TD align="right">55</TD>
 <TD align="right">61</TD>
 <TD align="right">66</TD>
 <TD align="right" bgcolor=#f0f0f0>72</TD>
 <TD align="right">77</TD>
 <TD align="right">83</TD>
 <TD align="right">88</TD>
 <TD align="right">94</TD>
 <TD align="right">100</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>16</TD>
 <TD align="right">42</TD>
 <TD align="right">48</TD>
 <TD align="right">54</TD>
 <TD align="right">60</TD>
 <TD align="right">65</TD>
 <TD align="right">71</TD>
 <TD align="right">77</TD>
 <TD align="right" bgcolor=#f0f0f0>83</TD>
 <TD align="right">89</TD>
 <TD align="right">95</TD>
 <TD align="right">101</TD>
 <TD align="right">107</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>17</TD>
 <TD align="right">45</TD>
 <TD align="right">51</TD>
 <TD align="right">57</TD>
 <TD align="right">64</TD>
 <TD align="right">70</TD>
 <TD align="right">77</TD>
 <TD align="right">83</TD>
 <TD align="right">89</TD>
 <TD align="right" bgcolor=#f0f0f0>96</TD>
 <TD align="right">102</TD>
 <TD align="right">109</TD>
 <TD align="right">115</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>18</TD>
 <TD align="right">48</TD>
 <TD align="right">55</TD>
 <TD align="right">61</TD>
 <TD align="right">68</TD>
 <TD align="right">75</TD>
 <TD align="right">82</TD>
 <TD align="right">88</TD>
 <TD align="right">95</TD>
 <TD align="right">102</TD>
 <TD align="right" bgcolor=#f0f0f0>109</TD>
 <TD align="right">116</TD>
 <TD align="right">123</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>19</TD>
 <TD align="right">51</TD>
 <TD align="right">58</TD>
 <TD align="right">65</TD>
 <TD align="right">72</TD>
 <TD align="right">80</TD>
 <TD align="right">87</TD>
 <TD align="right">94</TD>
 <TD align="right">101</TD>
 <TD align="right">109</TD>
 <TD align="right">116</TD>
 <TD align="right" bgcolor=#f0f0f0>123</TD>
 <TD align="right">130</TD>
 </TR>
 <TR>
 <TD align="right" bgcolor=#e0e0e0>20</TD>
 <TD align="right">54</TD>
 <TD align="right">62</TD>
 <TD align="right">69</TD>
 <TD align="right">77</TD>
 <TD align="right">84</TD>
 <TD align="right">92</TD>
 <TD align="right">100</TD>
 <TD align="right">107</TD>
 <TD align="right">115</TD>
 <TD align="right">123</TD>
 <TD align="right">130</TD>
 <TD align="right" bgcolor=#f0f0f0>138</TD>
 </TR>
</TABLE>

<H2>Was ist zu tun bei N1 oder N2 &gt; 20?</H2>
Bei N1 oder N2 &gt; 20 wird die
Testgr&ouml;&szlig;e U mit folgender Formel umgerechnet in eine
Testgr&ouml;&szlig;e Z:
 
<IMG src="./wilcform.gif"
 style='border:solid 1px red;'
 alt= "Formel" border='0'
 title='Formel'
 width="179" height="82">
 
Wenn die nun berechnete Testgr&ouml;&szlig;e Z &ge; 1.645, dann
wird die Nullhypothese &#132;beide Verteilungen sind gleich&#147;
abgelehnt. Die Zahl 1.645 ist das Quantil der
Standardnormalverteilung (&mu;=0 und &sigma;=1) f&uuml;r &alpha; = 5&#037;.
 
 
Mit der Testgr&ouml;&szlig;e Z kann aber auch in eine Tafel f&uuml;r die
Standardnormalverteilung (&mu;=0 und &sigma;=1) gegangen werden. Ihr Tafelwert
ist die Fl&auml;che unter Dichte von 0 bis Z. F&uuml;r den
einseitigen Test muss noch die Fl&auml;che 0.5
addiert werden.
 
Beispiel:
 
F&uuml;r das Ende der obigen Tabelle ist N1 = N2 = 20
und der Tafelwert ist 138.
Eine Testgr&ouml;&szlig;e U, die geringf&uuml;gig gr&ouml;&szlig;er ist als der Tafelwert,
muss eine Fl&auml;che nahe 95&#037; liefern. Dort ist gerade der Punkt
zwischen Annehmen und Ablehnen der Nullhypothese. Mit U=139
erh&auml;lt man Z=1.65 und eine Fl&auml;che von
0.5 + 0.4505 = 0.9505.
 
 
<IMG src="./wilc67.gif"
 alt="NV" border='1'
 width="340" height="224">

<TABLE border='1' bordercolor='gray' cellspacing='0' cellpadding='4'>
 <TR>
 <TH>Fl&auml;che unter der Dichtefunktion einer
 Normalverteilung von 0 bis Z
 </TH>
 </TR>
 <TR>
 <TD align="middle">Beispiel: wenn Z=1.65
 ist die Fl&auml;che 0.4505
 </TD>
 </TR>
 <TR>
 <TD>
<PRE>
 Z | 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900
---------------------------------------------------------------------------
0.00| 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359
0.10| 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753
0.20| 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.30| 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.40| 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879
0.50| 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224
0.60| 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549
0.70| 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852
0.80| 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133
0.90| 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389
1.00| 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.10| 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.20| 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.30| 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.40| 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.50| 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.60| 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545
1.70| 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633
1.80| 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706
1.90| 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767
2.00| 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.10| 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.20| 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890
2.30| 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916
2.40| 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936
2.50| 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952
2.60| 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964
2.70| 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974
2.80| 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981
2.90| 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986
3.00| 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990
3.10| 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993
3.20| 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995
3.30| 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997
3.40| 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998
3.50| 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998
3.60| 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
3.70| 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
3.80| 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
3.90| 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
</PRE>
 </TD>
 </TR>
</TABLE>

<H2>Literatur</H2>
Blalock, H.M.: 
Social Statistics. 
ISBN: 0070661758 
New York: McGraw-Hill 1979
 
 
<HR>
<ADDRESS>
&copy; Dr. O. Hochmuth 


</ADDRESS>
</BODY>
</HTML>