In: Statistics and Probability

**For an ANOVA tell me whether the F-ratio and P value
will in-crease or decrease under the following
circumstances.**

**(a)The group sum of squares increases.**

**(b)The among group mean square increases.**

**(c)The within group sum or squares
decreases.**

**(d)The within group mean square decreases.**

**I'm having trouble understanding conceptually how this
works.**

For ANOVA test,

F = among group mean square / within group mean square = (group sum of squares / Numerator df) / (within group sum or squares / Denominator df)

Also, if F-ratio increases, P-values will decrease and approaches to zero.

P-value = P(F > F-ratio, Numerator df, Denominator df)

**(a)The group sum of squares increases.**

F = (group sum of squares / Numerator df) / (within group sum or squares / Denominator df)

Thus, F-ratio will increase as group sum of squares increases.

As, F-ratio increases, P-values will decrease.

**(b)The among group mean square increases.**

F = among group mean square / within group mean square

Thus, F-ratio will increase as among group mean squares increases.

As, F-ratio increases, P-values will decrease.

**(c)The within group sum or squares
decreases.**

F = (group sum of squares / Numerator df) / (within group sum or squares / Denominator df)

Thus, F-ratio will increase as within group sum or squares decreases.

As, F-ratio increases, P-values will decrease.

**(d)The within group mean square decreases.**

F = among group mean square / within group mean square

Thus, F-ratio will increase as within group mean squares increases.

As, F-ratio increases, P-values will decrease.

PLEASE EXPLAIN YOUR REASONING
ANOVA is based on an F-ratio that is calculated as the ratio of
two variance estimates, the variance between groups and the
variance within groups, but enables conclusions to be made about
the means of the samples involved. What is the logic of that? I.e.,
explain the rationale that supports the use of variance
estimates.

12.14â€‰Calculating the ANOVA F test
P-value. For each of the following situations,
find the degrees of freedom for the F statistic and then
use R to calculate the P-value.
(a) Six groups are being compared with five
observations per group. The value of the F statistic is
2.47.
(b) Four groups are being compared with 11
observations per group. The value of the F statistic is
5.03.
(c) Five groups are being compared using 65 total...

In ANOVA, the F value is statistically
significant when the __________- groups variance is significantly
bigger than the ___________-groups variance

The One-Way ANOVA applet lets you see how the
F statistic and the P-value depend on the
variability of the data within groups, the sample size, and the
differences among the means.
(a)
The black dots are at the means of the three groups. Move these
up and down until you get a configuration that gives a
P-value of about 0.01. What is the value of the F
statistic?
This answer has not been graded yet.
(b)
Now increase the...

The One-Way ANOVA applet lets you see how the F statistic and
the P-value depend on the variability of the data within groups,
the sample size, and the differences among the means. (a) The black
dots are at the means of the three groups. Move these up and down
until you get a configuration that gives a P-value of about 0.01.
What is the value of the F statistic? This answer has not been
graded yet. (b) Now increase the...

The One-Way ANOVA applet lets you see how the
F statistic and the P-value depend on the
variability of the data within groups, the sample size, and the
differences among the means.
(a)
The black dots are at the means of the three groups. Move these
up and down until you get a configuration that gives a
P-value of about 0.01. What is the value of the F
statistic?
(b)
Now increase the variation within the groups by sliding the...

The One-Way ANOVA applet lets you see how the
F statistic and the P-value depend on the
variability of the data within groups, the sample size, and the
differences among the means.
Corporate advertising tries to enhance the image of the
corporation. A study compared two ads from two sources, the
Wall Street Journal and the National Enquirer.
Subjects were asked to pretend that their company was considering a
major investment in Performax, the fictitious sportswear firm in
the ads....

ANOVA
Source of
Variation
SS
df
MS
F
p-value
Factor A
33,443.41
3
11,147.80
Factor B
24,232.44
2
12,116.22
Interaction
168,937.71
6
28,156.29
Error
135,865.32
36
3,774.04
Total
362,478.88
47
(a)
What kind of ANOVA is this?
One-factor ANOVA
Two-factor ANOVA with
replication
Two-factor ANOVA without
replication
(b)
Calculate each F test statistic and the
p-value for each F test using Excel's function
=F.DIST.RT(F,DF1,DF2). (Round your
Fcalc values to 3 decimal places and
p-values to...

Castle-in-Sand generates a rate of return of \(20 \%\) on its investments and maintains a plowback ratio of \(0.30 .\) Its earnings this year will be \(\$ 4\) per share. Investors expect a \(12 \%\) rate of return on the stock.
Required:
(a.) Find the price and \(\mathrm{P} / \mathrm{E}\) ratio of the firm.
(b.) What happens to the P/E ratio if the plowback ratio is reduced to 0.20? Why?
(c.) Show that if plowback equals zero, the earnings-price ratio,...

Castle-in-Sand generates a rate of return of on its investments and maintains a plowback ratio of Its earnings this year will be per share. Investors expect a rate of return on the stock.
Required:
(a.) Find the price and ratio of the firm.
(b.) What happens to the P/E ratio if the plowback ratio is reduced to 0.20? Why?
(c.) Show that if plowback equals zero, the earnings-price ratio, E/P, falls to the expected rate of return on the stock.

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