document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878246>Question 878246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following data represents the number of units produced by four operators during three different shifts :<BR>\n" );
document.write( "Shifts	Operator<BR>\n" );
document.write( "	A	B	C	D<BR>\n" );
document.write( "I	10	8	12	13<BR>\n" );
document.write( "II	10	12	14	15<BR>\n" );
document.write( "III	12	10	11	14\r<BR>\n" );
document.write( "\n" );
document.write( "         Perform a two-way analysis of variance and interpret the result.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #529803 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=529803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> M1 vs M2   nonsignificant<BR>\n" );
document.write( "M1 vs M3   nonsignificant<BR>\n" );
document.write( "M1 vs M4   nonsignificant<BR>\n" );
document.write( "M2 vs M3   nonsignificant<BR>\n" );
document.write( "M2 vs M4   P<.05<BR>\n" );
document.write( "M3 vs M4   nonsignificant         <BR>\n" );
document.write( "M2 vs M4: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=%2814-10%29%2Fsqrt%281%2F3%2B+2%2F3%29+=+4 ALIGN=MIDDLE  ALT=\"t+=%2814-10%29%2Fsqrt%281%2F3%2B+2%2F3%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "p-value = 2*P(t> 4 when df = 4) = 2*tcdf(4,100,4) = 0.02<BR>\n" );
document.write( ".02 < .05<BR>\n" );
document.write( "and for example<BR>\n" );
document.write( "M1 vs M2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=%2810.6667+-+10%29%2Fsqrt%281.1547%2F3%2B+2%2F3%29=+.65 ALIGN=MIDDLE  ALT=\"t+=%2810.6667+-+10%29%2Fsqrt%281.1547%2F3%2B+2%2F3%29=+.65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "p-value = 2*P(t> .65 when df = 4) = 2*tcdf(.65,100,4) = 2*.28 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );