Important: The stats package has been deprecated. Use the superseding command Statistics[OneWayANOVA] instead.
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$\mathrm{with}\left(\mathrm{stats}\[\mathrm{anova}\]\right)\:$

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$\mathrm{with}\left(\mathrm{stats}\[\mathrm{describe}\]\right)\:$

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$\mathrm{Treatment\_1}:=\left[10\,11\,8\right]$

${\mathrm{Treatment\_1}}{:=}\left[{10}{\,}{11}{\,}{8}\right]$
 (1) 
Three of the measures have the same value
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$\mathrm{Treatment\_2}:=\left[\mathrm{Weight}\left(9\,3\right)\,11\right]$

${\mathrm{Treatment\_2}}{:=}\left[{\mathrm{Weight}}{}\left({9}{\,}{3}\right){\,}{11}\right]$
 (2) 
One bad measure
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$\mathrm{Treatment\_3}:=\left[\mathrm{missing}\,10\,11\,7\,12\right]$

${\mathrm{Treatment\_3}}{:=}\left[{\mathrm{missing}}{\,}{10}{\,}{11}{\,}{7}{\,}{12}\right]$
 (3) 
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$\mathrm{data}:=\left[\mathrm{Treatment\_1}\,\mathrm{Treatment\_2}\,\mathrm{Treatment\_3}\right]$

${\mathrm{data}}{:=}\left[\left[{10}{\,}{11}{\,}{8}\right]{\,}\left[{\mathrm{Weight}}{}\left({9}{\,}{3}\right){\,}{11}\right]{\,}\left[{\mathrm{missing}}{\,}{10}{\,}{11}{\,}{7}{\,}{12}\right]\right]$
 (4) 
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$R:=\mathrm{oneway}\left(\mathrm{data}\right)$

${R}{:=}\left[\left[{2}{\,}\frac{{17}}{{33}}{\,}\frac{{17}}{{66}}\right]{\,}\left[{8}{\,}\frac{{65}}{{3}}{\,}\frac{{65}}{{24}}\right]{\,}\left[{10}{\,}\frac{{244}}{{11}}\right]\right]{\,}\left[{2}{\,}{8}{\,}\frac{{68}}{{715}}{\,}{0.089709850848}\right]$
 (5) 
The Fratio is 68/715 with 2 and 8 degrees of freedom.
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$\mathrm{Ratio}:={2}_{}$

${\mathrm{Ratio}}{:=}\left[{2}{\,}{8}{\,}\frac{{68}}{{715}}{\,}{0.089709850848}\right]$
 (6) 
the level of significance is measured with
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$\mathrm{sig}:=\mathrm{stats}\[\mathrm{statevalf}\,\mathrm{cdf}\,{\mathrm{fratio}}_{{\mathrm{Ratio}}_{1}\,{\mathrm{Ratio}}_{2}}\]\left({\mathrm{Ratio}}_{3}\right)$

${\mathrm{sig}}{:=}{0.08970985085}$
 (7) 
Since this is much smaller than 0.95, we conclude that there is no significance to the differences in means:
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$\mathrm{map}\left(\mathrm{mean}\,\left[\mathrm{Treatment\_1}\,\mathrm{Treatment\_2}\,\mathrm{Treatment\_3}\right]\right)$

$\left[\frac{{29}}{{3}}{\,}\frac{{19}}{{2}}{\,}{10}\right]$
 (8) 
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$\mathrm{evalf}\left(\right)$

$\left[{9.666666667}{\,}{9.500000000}{\,}{10.}\right]$
 (9) 
Now we change the treatment results to yield
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$\mathrm{data2}:=\left[\left[10\,11\,8\right]\,\left[\mathrm{Weight}\left(11\,3\right)\,13\right]\,\left[\mathrm{missing}\,14\,15\,11\,16\right]\right]\:$

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$\mathrm{Ratio2}:={\mathrm{oneway}\left(\mathrm{data2}\right)}_{2}$

${\mathrm{Ratio2}}{:=}\left[{2}{\,}{8}{\,}\frac{{4388}}{{715}}{\,}{0.97575671908}\right]$
 (10) 
The difference between
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$\mathrm{map}\left(\mathrm{mean}\,\mathrm{data2}\right)$

$\left[\frac{{29}}{{3}}{\,}\frac{{23}}{{2}}{\,}{14}\right]$
 (11) 
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$\mathrm{evalf}\left(\right)$

$\left[{9.666666667}{\,}{11.50000000}{\,}{14.}\right]$
 (12) 
is significant at the 0.05 level (since 0.976>0.95) but not at the 0.01 level (since 0.976<0.99).