document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62823>Question 62823</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072868244/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How could nonparametric data be transformed into parametric data that could be used in an ANOVA? How do the fe and fo in a nonparametric test correspond to the SSE and the SSA in an ANOVA? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43724 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=43724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't know the answer to your question.  This is what Wikipedia<BR>\n" );
document.write( "says relating a nonparametric test to ANOVA.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "Kruskal-Wallis one-way analysis of variance<BR>\n" );
document.write( "From Wikipedia, the free encyclopedia<BR>\n" );
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document.write( "In statistics, the Kruskal-Wallis one-way analysis of variance by ranks (named after William Kruskal and Allen Wallis) is a non-parametric method for testing equality of population medians among groups. Intuitively, it is identical to a one-way analysis of variance with the data replaced by their ranks. It is an extension of the Mann-Whitney U test to 3 or more groups.\r<BR>\n" );
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document.write( "Since it is a non-parametric method, the Kruskal-Wallis test does not assume a normal population, unlike the analogous one-way analysis of variance. However, it still assumes that population variabilities among groups are equal. To get around this limitation of the Kruskal-Wallis test, some statisticians suggest using a robust test for equal locations among groups instead.<BR>\n" );
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document.write( "[edit] Method<BR>\n" );
document.write( "Rank all data from all groups together; i.e., rank the data from 1 to N ignoring group membership. Assign any tied values the average of the ranks they would have received had they not been tied. <BR>\n" );
document.write( "The test statistic is given by: , where: <BR>\n" );
document.write( "ng is the number of observations in group g <BR>\n" );
document.write( "rij is the rank (among all observations) of observation j from group i <BR>\n" );
document.write( "N is the total number of observations across all groups <BR>\n" );
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document.write( " is the average of all the rij, equal to (N + 1) / 2. <BR>\n" );
document.write( "Notice that the denominator of the expression for K is exactly (N &#8722; 1)N(N + 1) / 12. Thus . <BR>\n" );
document.write( "A correction for ties can be made by dividing K by , where G is the number of groupings of different tied ranks, and ti is the number of tied values within group i that are tied at a particular value. This correction usually makes little difference in the value of K unless there are a large number of ties. <BR>\n" );
document.write( "Finally, the p-value is approximated by . If some ni's are small (i.e., less than 5) the probability distribution of K can be quite different from this chi-square distribution. If a table of the chi-square probability distribution is available, the critical value of chi-square, , can be found by entering the table at g &#8722; 1 degrees of freedom and looking under the desired significance or alpha level. The null hypothesis of equal population medians would then be rejected if . Appropriate multiple comparisons would then be performed on the group medians. <BR>\n" );
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