document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205060>Question 1205060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Fill in the missing values for this ANOVA summary table:<BR>\n" );
document.write( " 	S.S.	 d.f.	M.S.	F<BR>\n" );
document.write( "Between	1723.267	7	<BR>\n" );
document.write( "Within	<BR>\n" );
document.write( "TOTAL	2999.267	51\r<BR>\n" );
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document.write( "I am so stuck and have gotten this one wrong several times, please help! <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841684 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Refer to this page<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Inferential_Statistics_and_Probability_-_A_Holistic_Approach_(Geraghty)/13%3A_One_Factor_Analysis_of_Variance_(ANOVA)/13.05%3A_Understanding_the_ANOVA_Table\">https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Inferential_Statistics_and_Probability_-_A_Holistic_Approach_(Geraghty)/13%3A_One_Factor_Analysis_of_Variance_(ANOVA)/13.05%3A_Understanding_the_ANOVA_Table</a>\r<BR>\n" );
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document.write( "At the top of that page is the ANOVA template.<BR>\n" );
document.write( "Instead of \"factor\" we'll use \"between\".<BR>\n" );
document.write( "Instead of \"error\" we'll use \"within\".\r<BR>\n" );
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document.write( "Here's the table your teacher has given you<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >SS</TD><TD >df</TD><TD >MS</TD><TD >F</TD></tr><tr><TD >Between</TD><TD >1723.267</TD><TD >7</TD><TD ></TD><TD ></TD></tr><tr><TD >Within</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >Total</TD><TD >2999.267</TD><TD >51</TD><TD ></TD><TD ></TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "We know the SS (sum of squares) values for rows 1 and 3. <BR>\n" );
document.write( "The missing SS value is the difference of the two given SS values.\r<BR>\n" );
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document.write( "SS within = (SS total) - (SS between)<BR>\n" );
document.write( "SS within = 2999.267 - 1723.267<BR>\n" );
document.write( "SS within = 1276\r<BR>\n" );
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document.write( "\n" );
document.write( "Let's update the table<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >SS</TD><TD >df</TD><TD >MS</TD><TD >F</TD></tr><tr><TD >Between</TD><TD >1723.267</TD><TD >7</TD><TD ></TD><TD ></TD></tr><tr><TD >Within</TD><TD >1276</TD><TD ></TD><TD ></TD><TD ></TD></tr><tr><TD >Total</TD><TD >2999.267</TD><TD >51</TD><TD ></TD><TD ></TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "Refer back to the link I mentioned.<BR>\n" );
document.write( "Focus on the \"degrees of freedom (df)\" column.<BR>\n" );
document.write( "The df expressions are:<BR>\n" );
document.write( "between = k-1<BR>\n" );
document.write( "within = n-k<BR>\n" );
document.write( "total = n-1\r<BR>\n" );
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document.write( "Notice that <BR>\n" );
document.write( "df total = (df between) + (df within) = (k-1)+(n-k) = n-1 \r<BR>\n" );
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document.write( "The df value for \"between\" is 7<BR>\n" );
document.write( "k-1 = 7<BR>\n" );
document.write( "k = 7+1<BR>\n" );
document.write( "k = 8<BR>\n" );
document.write( "The df value for \"total\" is 51<BR>\n" );
document.write( "n-1 = 51<BR>\n" );
document.write( "n = 51+1<BR>\n" );
document.write( "n = 52<BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "df within = n-k = 52-8 = 44\r<BR>\n" );
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document.write( "Or we could say<BR>\n" );
document.write( "df within = (df total) - (df between)<BR>\n" );
document.write( "df within = 51 - 7<BR>\n" );
document.write( "df within = 44<BR>\n" );
document.write( "which is a faster shortcut.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Let's update the table<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >SS</TD><TD >df</TD><TD >MS</TD><TD >F</TD></tr><tr><TD >Between</TD><TD >1723.267</TD><TD >7</TD><TD ></TD><TD ></TD></tr><tr><TD >Within</TD><TD >1276</TD><TD >44</TD><TD ></TD><TD ></TD></tr><tr><TD >Total</TD><TD >2999.267</TD><TD >51</TD><TD ></TD><TD ></TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "According to that link I posted, <BR>\n" );
document.write( "MS between = (SS between)/(df between)<BR>\n" );
document.write( "MS between = (1723.267)/(7)<BR>\n" );
document.write( "MS between = 246.181<BR>\n" );
document.write( "and,<BR>\n" );
document.write( "MS within = (SS within)/(df within)<BR>\n" );
document.write( "MS within = (1276)/(44)<BR>\n" );
document.write( "MS within = 29<BR>\n" );
document.write( "There doesn't exist \"MS total\". <BR>\n" );
document.write( "We'll leave that cell blank.<BR>\n" );
document.write( "\"MS\" stands for \"Mean Square\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's update the table<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >SS</TD><TD >df</TD><TD >MS</TD><TD >F</TD></tr><tr><TD >Between</TD><TD >1723.267</TD><TD >7</TD><TD >246.181</TD><TD ></TD></tr><tr><TD >Within</TD><TD >1276</TD><TD >44</TD><TD >29</TD><TD ></TD></tr><tr><TD >Total</TD><TD >2999.267</TD><TD >51</TD><TD ></TD><TD ></TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "We have one last gap to fill in.<BR>\n" );
document.write( "To get the F statistic, we divide the MS between over the MS within\r<BR>\n" );
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document.write( "F = (MS between)/(MS within)<BR>\n" );
document.write( "F = (246.181)/(29)<BR>\n" );
document.write( "F = 8.489\r<BR>\n" );
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document.write( "Here is the fully completed ANOVA table.<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >SS</TD><TD >df</TD><TD >MS</TD><TD >F</TD></tr><tr><TD >Between</TD><TD >1723.267</TD><TD >7</TD><TD >246.181</TD><TD >8.489</TD></tr><tr><TD >Within</TD><TD >1276</TD><TD >44</TD><TD >29</TD><TD ></TD></tr><tr><TD >Total</TD><TD >2999.267</TD><TD >51</TD><TD ></TD><TD ></TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "The two cells under the F statistic are left blank.\r<BR>\n" );
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document.write( "Some ANOVA tables will include the F critical value and/or the p-value. However, I'll stop here since it appears your teacher wants just up to the F statistic.\r<BR>\n" );
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document.write( "Side note: This applies to single factor ANOVA only.<BR>\n" );
document.write( "</font> </SPAN>\n" );
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