document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088675>Question 1088675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem.\r<BR>\n" );
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document.write( "A researcher conducts an experiment comparing three treatment conditions. The data consist of n =20 scores for each treatment condition.\r<BR>\n" );
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document.write( "a.  If the researcher used an independent-measures design, then how many individuals were needed for the study and what are the df-values for the F-ratio?  Explain in detail and show all formulas with symbols (and plug in numbers), steps, processes and calculations for all parts of the answers.\r<BR>\n" );
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document.write( "b.  If the researcher used a repeated measures-design, then how many individuals were needed for the study and what are the df-values for the F-ratio?  Explain in detail and show all formulas with symbols (and plug in numbers), steps, processes and calculations for all parts of the answers.<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 #702980 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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/cgi-bin/show-face.mpl?user=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)The independent-measures design F-ratio has df = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29 ALIGN=MIDDLE  ALT=\"highlight%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2857%29 ALIGN=MIDDLE  ALT=\"highlight%2857%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "df(between treatments) = k-1 = 3 – 1 = 2<BR>\n" );
document.write( "df(Total) = N-1 = 60 – 1 = 59<BR>\n" );
document.write( "df(error) = df(Total) - df(between treatments) = 59 - 2 = 57<BR>\n" );
document.write( "Hence, the independent-measures design F-ratio has df = 2, 57<BR>\n" );
document.write( "60 individuals were needed for the study\r<BR>\n" );
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document.write( "b) The repeated-measures F-ratio has df = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29 ALIGN=MIDDLE  ALT=\"highlight%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2838%29 ALIGN=MIDDLE  ALT=\"highlight%2838%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "df(between subjects) = n-1 = 20 – 1 = 19<BR>\n" );
document.write( "df(within treatments) = &#931; df inside each treatment = 19 + 19 + 19 = 57  \r<BR>\n" );
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document.write( "df(between treatments) = k-1 = 3 – 1 = 2<BR>\n" );
document.write( "df(error) = df(within treatments) - df(between subjects) = 57 - 19 = 38\r<BR>\n" );
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document.write( "Hence, the repeated-measures F-ratio has df = 2, 38<BR>\n" );
document.write( "20 individuals were needed for the study (same subjects for each treatment)<BR>\n" );
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