Question

A published paper compares the lengths of three different bird species; A, B and C. An ANOVA rejects the null hypothesis (A=B=C) at p=0.0001. Your colleague shows that paper as proof that A and B are significantly different. Give at least one reason that he may be wrong.

Answer #1

The hypothesis for carrying out ANOVA is defined as:

Choose a level of significance, say .

If p-value < , then the null hypothesis is rejected, otherwise not.

In the given problem, there are 3 treatments, namely A, B and C. It is given that the null hypothesis has been rejected as the p-value = 0.0001 is too low.

This implies that the alternate hypothesis is accepted, that is atleast one of the treatment means is different from the remaining.

There could be a possibility that the difference between B and C is insignificant, however, the difference between A and B is significant.

It could also be possible that the all the three treatment means are different.

Thus, the colleagues interpretation may be wrong as the null hypothesis would be rejected even in case where the difference between the treatment means A and B may not be significant, however, they might be significantly different from C. There is possibility that the colleagues statement is correct, but, this can not be proved until Post-Hoc analysis have been carried out.

A consumer preference study compares the effects of three
different bottle designs (A, B, and C)
on sales of a popular fabric softener. A completely randomized
design is employed. Specifically, 15 supermarkets of equal sales
potential are selected, and 5 of these supermarkets are randomly
assigned to each bottle design. The number of bottles sold in 24
hours at each supermarket is recorded. The data obtained are
displayed in the following table.
Bottle Design Study Data
A
B
C
17...

An experiment was designed to compare the lengths of time that
four different drugs provided pain relief after surgery. The
results (in hours) follow. Is there enough evidence to reject the
null hypothesis that there is no significant difference in the
length of pain relief provided by the four drugs at α =
.05?
Drug
A
B
C
D
7
6
8
3
2
5
12
4
3
5
10
4
7
4
8
8
(a) Find the test statistic....

A consumer preference study compares the effects of three
different bottle designs (A, B, and C)
on sales of a popular fabric softener. A completely randomized
design is employed. Specifically, 15 supermarkets of equal sales
potential are selected, and 5 of these supermarkets are randomly
assigned to each bottle design. The number of bottles sold in 24
hours at each supermarket is recorded. The data obtained are
displayed in the following table.
Bottle Design Study Data
A
B
C
19...

An experiment was designed to compare the lengths of time that
four different drugs provided pain relief after surgery. The
results (in hours) follow. Is there enough evidence to reject the
null hypothesis that there is no significant difference in the
length of pain relief provided by the four drugs at α =
.05?
Drug
A
B
C
D
4
5
11
3
5
4
9
3
3
3
12
4
6
5
11
10
(a) Find the test statistic....

A consumer preference study compares the effects of three
different bottle designs (A, B, and C)
on sales of a popular fabric softener. A completely randomized
design is employed. Specifically, 15 supermarkets of equal sales
potential are selected, and 5 of these supermarkets are randomly
assigned to each bottle design. The number of bottles sold in 24
hours at each supermarket is recorded. The data obtained are
displayed in the following table.
Bottle Design Study Data
A
B
C
16...

1A) An experiment was designed to compare the lengths of time
that four different drugs provided pain relief after surgery. The
results (in hours) follow. Is there enough evidence to reject the
null hypothesis that there is no significant difference in the
length of pain relief provided by the four drugs at α =
.05?
Drug
A
B
C
D
2
4
9
4
8
6
8
2
7
6
11
2
3
5
10
9
(a) Find the test...

5. In one-way, repeated-measures ANOVA,
MSTreatment= 10,
MSResidual= 5,
dfTreatment= 2, and
dfResidual= 35. What is the value
of F?
a) 2
b) 50
c) 220
d) 5
6.Which of the following represents the alternative hypothesis
for a two-tailed, one-way, repeated-measures ANOVA?
a) All of the population means differ.
b) µ1 = µ2 = µ3
c) µ1 ? µ2 ? µ3
d) At least one population mean is different from at least one
of the others.
7.If the cutoff q...

An experiment was designed to compare the lengths of time that
four different drugs provided pain relief after surgery. The
results (in hours) follow. Is there enough evidence to reject the
null hypothesis that there is no significant difference in the
length of pain relief provided by the four drugs at α =
.05?
Drug
A
B
C
D
5
5
9
2
8
5
9
2
3
5
12
3
4
6
9
8
(a) Find the test statistic....

8) Arnold compares the means of three groups and calculates a
value of -2.01 for the F ratio. This necessarily implies that. .
Group of answer choices
a. the mean of the first group is the highest of the three
groups
b. the mean of the third group is the highest of the three
groups
c. the differences between the means are statistically
significant
d. he made an error is his calculation
9) The problem with conducting multiple t-tests instead...

Travel-Times: There are three different ways I
can go to work in the morning. I want to see if there is a
difference in mean travel-times between the three different ways.
The sample data is depicted below. The second table displays
results from an ANOVA test on this data with software. I claim
there is a difference in mean travel-times between the three
different routes.
Travel Times in Minutes
x
Interstate
23
24
22
22
21
20
22.0
Route 15...

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