91影视

Two are more numbers of mathematical average called mean.

The T Method for Identifying Significantly Different 渭i 鈥檚

Find value \({Q_{\alpha ,}}{I_{\left( {j - 1} \right)}}\)at the Table A.10. in the appendix of the book for given \(\alpha \).

Compute and list the sample means in increasing order. Calculate

\(w = {Q_{\alpha ,}}{I_{\left( {j - 1} \right)}}.\sqrt {\frac{{MSE}}{J}} \)

and underline pairs of the sample means that differ by less than W . The pair of sample which are not underscored by the same line corresponding of population or treatment means that they are significantly different. From the mentioned table, and\(\alpha = 0.05\)

\({Q_{\alpha ,}}{I_{\left( {j - 1} \right)}} = {Q_{0.5,5,15,}}\)\( = 4.37\)

The value of

\(MSE = 278.8\)

Compute the w value as

\(w = {Q_{\alpha ,}}{I_{\left( {j - 1} \right)}}.\sqrt {\frac{{MSE}}{J}} = 4.37..\sqrt {\frac{{272.8}}{4}} = 36.09\)

First order the sample means

\({\overline x _{3.}} < {\overline x _{1.}}\,\,\, < {\overline x _{4.}}\,\, < {\overline x _{2.}} < {\overline x _{5.}}\)

The following table

The bold values are smaller than w

Start with mean third sample

\({\overline x _{1.}} - {\overline x _{3.}} = 462 - 437.5 = 24.5 < w = 36.09,\)

Indicated that pair \(\left( {3,1} \right)\)underline as pair:

\(\begin{aligned}{l}\,\,\,\,{\overline x _{3.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{1.}}\\\underline {\,\,\,437.5\,\,\,\,\,\,\,462\,\,\,\,\,\,\,\,} \,\end{aligned}\)

Do the same for all pairs

\({\overline x _{4.}} - {\overline x _{3.}} = \,469 - 437.5 = 31.8 < w = 36.09\)

So the pair \(\left( {4,3} \right)\) underline as a pair:

\(\begin{aligned}{l}\,\,{\overline x _{3.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{4.}}\\\underline {\,\,\,437.5\,\,\,\,\,\,\,469.3\,\,\,\,\,\,\,\,} \end{aligned}\)

Next pair

\({\overline x _{2.}} - {\overline x _{3.}} = 515.8 - 469.3 = 78.3 > w = 36.09\)

So the pair (3,2)should not underline together.

Look at the first difference

\({\overline x _{1.}} - {\overline x _{3.}} = 469.3 - 462 = 7.3 < w = 36.09\)

So the pair \(\left( {1,4} \right)\) underline together:

\(\begin{aligned}{l}\,\,{\overline x _{1.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{4.}}\\\underline {\,\,\,462\,\,\,\,\,\,\,469.3\,\,\,\,\,\,\,\,} \end{aligned}\)

Three pair where each pair is underline with another The group is:

\(\begin{aligned}{l}\,\,{\overline x _{3.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{1.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{4.}}\,\,\,\,\,\,\,\,\,\,\\\underline {\,\,\,437.5\,\,\,\,\,\,\,462\,\,\,\,\,\,\,\,\,\,\,\,469.3\,\,\,\,\,\,\,\,} \end{aligned}\)

The next pair is\(\left( {1,2} \right)\)

\({\overline x _{2.}} - {\overline x _{1.}} = 515.8 - 462 = 53.8 > w = 36.09\)

So the pair \(\left( {1,2} \right)\)should not underlined together.

\({\overline x _{2.}} - {\overline x _{4.}} = 515.8 - 469.3 = 46.5 > w = 36.09\)

So the pair \(\left( {4,2} \right)\)should not underlined together.

\({\overline x _{5.}} - {\overline x _{2.}} = 532.1 - 515.8 = 16.3 > w = 36.09\)

So the pair \(\left( {2,5} \right)\)should underlined together.

\(\begin{aligned}{l}\,{\overline x _{2.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{5.}}\\\underline {\,515.8\,\,\,\,\,\,\,532.1\,\,\,\,\,\,\,\,} \end{aligned}\)

Basically two group have formed one group 1,3,4 and the other group 5:

The conclusion is that there are no significant differences within groups, between the group there is a significant difference in the brand.

\(\begin{aligned}{l}\,\,{\overline x _{3.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{1.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{4.}}\,\,\,\,\,\,\,\,\,\,\\\underline {\,\,\,437.5\,\,\,\,\,\,\,462\,\,\,\,\,\,\,\,\,\,\,\,469.3\,\,\,\,\,\,\,\,} \end{aligned}\)\(\begin{aligned}{l}\,{\overline x _{2.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{5.}}\\\underline {515.8\,\,\,\,\,\,\,\,532.1\,\,\,\,\,\,} \end{aligned}\)

Hence,

\(\begin{aligned}{l}\,\,{\overline x _{3.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{1.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{4.}}\,\,\,\,\,\,\,\,\,\,\\\underline {\,\,\,437.5\,\,\,\,\,\,\,462\,\,\,\,\,\,\,\,\,\,\,\,469.3\,\,\,\,\,\,\,\,} \end{aligned}\) \(\begin{aligned}{l}\,{\overline x _{2.}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\overline x _{5.}}\\\underline {515.8\,\,\,\,\,\,\,\,532.1\,\,\,\,\,\,} \end{aligned}\)