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Answers without the blur. Sign up and see all textbooks for free! Q.22

Expert-verified Found in: Page 766 ### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208 # What is the $F$ statistic?

The value of $F-statistic=10.404$.

See the step by step solution

## Step 1: Given Information

 Team 1 Team 2 Team 3 Team 4 1 2 0 3 2 3 0 4 0 2 1 4 3 4 1 3 2 4 0 2

## Step 2: Calculate the F statistics

To find the value of $\text{F}$-statistic:

From our Table, we can calculate

${s}_{1}=8,{s}_{2}=15,{s}_{3}=2,{s}_{4}=16$

We now can calculate:

${\mathbf{SS}}_{\text{between}}=\sum \left[\frac{{\left({s}_{j}\right)}^{2}}{{n}_{j}}\right]-\frac{{\left(\sum {s}_{j}\right)}^{2}}{n}$

$S{S}_{\text{between}}=\frac{{s}_{1}^{2}}{5}+\frac{{s}_{2}^{2}}{5}+\frac{{s}_{3}^{2}}{5}+\frac{{s}_{4}^{2}}{5}-\frac{{\left({s}_{1}+{s}_{2}+{s}_{3}+{s}_{4}\right)}^{2}}{20}$

$\text{where}{n}_{1}={n}_{2}={n}_{3}={n}_{4}=5\text{and}n={n}_{1}+{n}_{2}+{n}_{3}+{n}_{4}=20$

We calculate,

$\frac{\left(8{\right)}^{2}}{5}+\frac{\left(15{\right)}^{2}}{5}+\frac{\left(2{\right)}^{2}}{5}+\frac{\left(16{\right)}^{2}}{5}-\frac{\left(8+15+2+16{\right)}^{2}}{20}$

## Step 3: Calculate the sum of squares within the group

${\mathbf{SS}}_{\text{between}}=109,8-84.05=\mathbf{25}\mathbf{.}\mathbf{75}$

${\mathbf{S}}_{\text{total}}=\sum {x}^{2}-\frac{{\left(\sum x\right)}^{2}}{n}$

${S}_{\text{total}}=123-84.05$

${\mathbf{S}}_{\text{total}}=\mathbf{38}\mathbf{.}\mathbf{95}$

${\mathbf{SS}}_{\text{within}}={\mathbf{SS}}_{\text{total}}-{\mathbf{SS}}_{\text{between}}$

${\mathrm{SS}}_{\text{within}}=13.2$

## Step 4: Calculate the mean of square

We calculate $M{S}_{\text{between}}$ like:

$M{S}_{\text{between}}=\frac{S{S}_{\text{between}}}{k-1},\text{where}\mathrm{k}=4$

${\mathbf{MS}}_{\text{between}}=\frac{25.75}{3}=\mathbf{8}\mathbf{.}\mathbf{58333}$

We calculate $M{S}_{\text{within}}$ like:

$M{S}_{\text{within}}=\frac{S{S}_{\text{within}}}{n-k}$

${\mathbf{MS}}_{\text{within}}=\frac{13.2}{16}=\mathbf{0}\mathbf{.}\mathbf{825}$

Now, we can find $F-$statistic:

$\mathrm{F}=\frac{M{S}_{\text{between}}}{M{S}_{\text{within}}}=\frac{8.58333}{0.825}$

$F=10.404$ ### Want to see more solutions like these? 