Chapter 13: Q.22 (page 766)

What is the $F$ statistic?

Short Answer

Expert verified

The value of $F - s t a t i s t i c = 10.404$ .

Step by step solution

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

Calculate the F statistics

To find the value of $F$ -statistic:

From our Table, we can calculate

s_{1} = 8, s_{2} = 15, s_{3} = 2, s_{4} = 16

We now can calculate:

{SS}_{between} = \sum [\frac{{(s_{j})}^{2}}{n_{j}}] - \frac{{(\sum s_{j})}^{2}}{n}

$S S_{between} = \frac{s_{1}^{2}}{5} + \frac{s_{2}^{2}}{5} + \frac{s_{3}^{2}}{5} + \frac{s_{4}^{2}}{5} - \frac{{(s_{1} + s_{2} + s_{3} + s_{4})}^{2}}{20}$

$where n_{1} = n_{2} = n_{3} = n_{4} = 5 and n = n_{1} + n_{2} + n_{3} + n_{4} = 20$

We calculate,

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

Calculate the sum of squares within the group

${SS}_{between} = 109, 8 - 84.05 = 25.75$

$S_{total} = \sum x^{2} - \frac{{(\sum x)}^{2}}{n}$

$S_{total} = 123 - 84.05$

$S_{total} = 38.95$

${SS}_{within} = {SS}_{total} - {SS}_{between}$

${SS}_{within} = 13.2$

Calculate the mean of square

We calculate $M S_{between}$ like:

$M S_{between} = \frac{S S_{between}}{k - 1}, where k = 4$

${MS}_{between} = \frac{25.75}{3} = 8.58333$

We calculate $M S_{within}$ like:

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

${MS}_{within} = \frac{13.2}{16} = 0.825$

Now, we can find $F -$ statistic:

F = \frac{M S_{between}}{M S_{within}} = \frac{8.58333}{0.825}

$F = 10.404$

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What is the $F$ statistic?

Short Answer

Step by step solution

Given Information

Calculate the F statistics

Calculate the sum of squares within the group

Calculate the mean of square

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What is the F statistic?

Short Answer

Step by step solution

Given Information

Calculate the F statistics

Calculate the sum of squares within the group

Calculate the mean of square

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Calculus

Decision Maths

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

What is the $F$ statistic?