Transcript Q2.pptx

Loggerhead Turtles
Question #2
Scoring
4 Complete
3 Substantial
2 Developing
1 Minimal
0
Intent of Question
The primary goals of this question were to
assess a student's ability to
(1) describe a Type I error and its consequence
in a particular study;
(2) draw an appropriate conclusion from a
p-value; and
(3) describe a flaw in a study and its effect on
the conclusions that can be drawn from the
study.
Question #2
The National Park Service is interested in determining whether placing predator cages
over the loggerhead turtle nests on Cape Lookout National Seashore will keep
raccoons from stealing eggs from the nests. Due to budget constraints, funding for the
predator cages will only be approved if the Park Service can provide convincing
evidence that the predator cages increase the number of turtles that successfully
fledge from the nests.
The Park Service plans to collect data from a random sample of the loggerhead turtle
nests which are laid at Cape Lookout one season. A test of significance will be
conducted at a significance level of 𝛼 = 0.05 for the following hypotheses:
H0 : 𝜇C = 𝜇NC
Ha : 𝜇C > 𝜇NC ,
where 𝜇C is the mean number of eggs that successfully hatch per nest for all
loggerhead turtle nests on Cape Lookout with a cage and 𝜇NC is the mean number of
eggs that successfully hatch per nest for all nests on Cape Lookout with no cage.
Part a
Part a solution
a) Describe what a Type I error
In the context of the study, a Type I
error means concluding that the
mean number of eggs that
successfully hatch per nest is higher
for nests with predator cages than
for nests without predator cages
when, in reality, there is no
difference in the fledgling rates for
nests with and without cages. The
consequence of this error is that the
National Park Service will receive
funding for the predator cages when
they are not actually keeping
predators away from the turtle nests,
thus wasting money that could be
more effectively spent.
would be in the context of the study,
and also describe a consequence of
making this type of error.
Scoring
Parts (a), (b), and (c) are scored as
essentially correct (E), partially correct (P), or incorrect (I).
Part (a) is scored as follows:
Essentially correct (E) if the response correctly includes the following two
components:
1) Describes the error in context by referring to the difference in mean
number of eggs hatched for nests with and without cages.
2) Describes a consequence of the study as spending funds on a method
that is not effective and/or the continued stealing of eggs by predators.
Partially correct (P) if the response correctly includes only one of the two
components listed above.
Incorrect (I) if the response correctly includes neither of the two
components listed above.
Part a scoring notes
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If a response provides more than one description of a Type I error, score the
weakest attempt.
Referring to the symbolic hypotheses is not sufficient for context.
If a response describes a Type I error incorrectly, the response can get the
consequence component correct if it is consistent with the incorrectly described
error.
If a response gives an incomplete description of a Type I error (for example, "we
reject the null hypothesis of no difference between the mean number of eggs
hatched for nests with and without cages"), the response can get the consequence
component correct if the consequence is consistent with the partial description of
the error.
If a response provides no description of a Type I error, the response cannot get the
consequence component correct.
Describing the Type I error only in terms of the consequence (for example, "They
approve funding for the cages when they should not") should get credit for the
consequence but should not get credit for the error, because there is no reference
to the mean number of eggs hatched for nests with and without cages.
Question #2 - continued
• Each season, the Park Service moves approximately
half of the turtle nests at Cape Lookout very soon after
they are laid because they are laid in locations that are
vulnerable to extreme high tides. The Park Service
decides to collect data for their study by randomly
selecting 35 of the nests that were moved and placing
a cage over them and comparing the fledgling rate to
the rate for 35 randomly selected nests that were
neither moved nor caged. This resulted in a p-value of
0.0003 for the hypotheses stated above. If it was
reasonable to conduct a test of significance for the
hypotheses stated above using the data collected, what
would the p-value of 0.0003 lead you to conclude?
Part b solution
Because the p-value of 0.0003 is less than
a= 0.05, we reject the null hypothesis. There is
convincing statistical evidence the mean number
of eggs that successfully hatch per nest is
greater for nests with a predator cage than for
nests without a predator cage for the population
of loggerhead turtle nests on Cape Lookout.
Scoring
Parts (a), (b), and (c) are scored as
essentially correct (E), partially correct (P), or incorrect (I).
Part (b) is scored as follows:
Essentially correct (E) if the response provides a correct conclusion in
context, with justification based on linkage between the p-value and
the given 𝛼 = 0.05.
Partially correct (P) if
the response provides a correct conclusion, with linkage to the pvalue, but not in context;
OR
if the response provides a correct conclusion in context, but without
justification based on linkage to the p-value.
Incorrect (I) if the response does not meet the criteria for E or P.
Part b scoring notes
Notes:
• The conclusion must be related to the alternative
hypothesis.
• A response that fails to reject H0 is scored as incorrect (I).
• Wording that states or implies the alternative hypothesis
is proven lowers the score one level (that is, from E to P
or P to I).
• Since 𝛼 = 0.05 is given, explicit linkage between the size
of the p-value and 𝛼 = 0.05 is required (for example,
stating that the p-value is small is not sufficient).
Question #2 - continued
Part c
Describe the primary flaw
in the study described in
part (b), and explain why it
is a concern.
Part c - solution
This study did not incorporate
randomization into the assignment
of experimental units to treatments,
in this case in the assignment of
nests to being caged or not caged.
Because only nests that were moved
received cages, it becomes
impossible to distinguish whether
the observed differences in fledgling
rates were due to the treatment (the
predator cages) or due to factors
related to the movement of the
nests.
Scoring
Parts (a), (b), and (c) are scored as
essentially correct (E), partially correct (P), or incorrect (I)
Part (c) is scored as follows:
Essentially correct (E) if the response correctly includes the following
two components:
1) States that the experiment did not incorporate random assignment.
2) Describes how confounding is present in this experiment due to the
lack of randomization.
Partially correct (P) if the response correctly includes only one of the
two components listed above.
Incorrect (I) if the response correctly includes none of the components
listed above.
Part c scoring notes
Notes:
• If for the first component a response provides additional
proposed flaws (for example, "the sample size is too
small"), score the weakest attempt.
• Simply referring to "confounding" is not sufficient for the
second component unless the concept of confounding is
clearly explained.
• Saying "the results cannot be generalized" or "the results
will be inaccurate" does not describe how confounding is
present and is not sufficient for the second component.
• Incorrect application of statistical concepts (for example,
saying that the results will be "skewed") results in a loss of
credit for the second component.
Scoring
4
Complete Response
All three parts essentially correct
3
Substantial Response
Two parts essentially correct and one part partially correct
2
Developing Response
Two parts essentially correct and one part incorrect
OR
One part essentially correct and one or two parts partially correct
OR
Three parts partially correct
1
Minimal Response
One part essentially correct and two parts incorrect
OR
Two parts partially correct and one part incorrect