Which of the following is TRUE?All the other options are correct.An increase in MSwithin will result in a decrease in the F-ratioAn increase in MSbetween will result in an increase in the F-ratioWhen MSbetween and MSwithin are equal, the null hypothesis is true The following table shows the results of an analysis of variance comparing 3 treatment conditions with a sample of n = 6participants in each treatment. Note that several values are missing in the table. What is the missing value for the F-ratio?SourceSSdfMSBetween30XX F= xxXXWithinXXXXXXTotal80XX12.5117.426.194.51

Name: Which of the following is TRUE?All the other options are correct.An i
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Description: Which of the following is TRUE?All the other options are correct.An increase in MSwithin will result in a decrease in the F-ratioAn increase in MSbetween will result in an increase in the F-ratioWhen MSbetween and MSwithin are equal, the null hypoth

Given: Sample size, n = 6 Number of treatments, k = 3 N=nk=3×6=18 SS df MS F Between 30 xx…

Answered: participants in each treatment. Note…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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Which of the following is TRUE?
All the other options are correct.
An increase in MSwithin will result in a decrease in the F-ratio
An increase in MSbetween will result in an increase in the F-ratio
When MSbetween and MSwithin are equal, the null hypothesis is true

The following table shows the results of an analysis of variance comparing 3 treatment conditions with a sample of n = 6
participants in each treatment. Note that several values are missing in the table. What is the missing value for the F-ratio?
Source
SS
df
MS
Between
30
XX F= xx
XX
Within
XX
XX
XX
Total
80
XX
12.51
17.42
6.19
4.51

Expert Solution

Step 1

Given:

Sample size, n = 6

Number of treatments, k = 3

N=nk= $3 \times 6 = 18$

	SS	df	MS	F
Between	30	xx	xx	xx
Within	xx	xx	xx
Total	80	xx

Step 2

Now for solving the above table:

For SS within treatments:

$S S_{B e t w e e n} + S S_{W i t h i n} = S S_{T o t a l} S S_{w i t h i n} = S S_{T o t a l} - S S_{B e t w e e n}$

Therefore,

$\begin{array}{rcl} S S_{W i t h i n} & = & 80 - 30 \\ = & 50 \end{array}$

For degrees of freedom:

For Between treatments:

$\begin{array}{rcl} d f & = & 3 - 1 \\ = & 3 - 1 \\ = & 2 \end{array}$

Step 3

For within treatments:

$\begin{array}{rcl} d f & = & N - k \\ = & 18 - 3 \\ = & 15 \end{array}$

For total:

$\begin{array}{rcl} d f & = & N - 1 \\ = & 18 - 1 \\ = & 17 \end{array}$

For MS:

$\begin{array}{rcl} M S_{B e t w e e n} & = & \frac{S S_{B e t w e e n}}{d f_{B e t w e e n}} \\ = & \frac{30}{2} \\ = & 15 \end{array}$

$\begin{array}{rcl} M S_{W i t h i n} & = & \frac{S S_{W i t h i n}}{d f} \\ = & \frac{50}{15} \\ = & 3.33 \end{array}$

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