Answer 1:
1) I believe that the appropriate number of
significant figures to use when calculating
averages would be the same number of significant
figures as used in the original measurements. In
other words, if your student teachers were
estimating radicle lengths to the nearest 0.1mm,
then the averages should be expressed in the same
units, to the nearest 0.1mm. Conservatively, the
average must be reported with no more significant
figures than the least precise measurement taken.
The precision or significant figures, of a
measurement are the smallest decimal place to
which the measurement is made, or estimated. In
the case of combining measurement through
addition, subtraction, or averaging, you are not
concerned with a number of significant figures per
se. Instead, you are looking for the smallest
decimal place of the least precise measurement.
An example is provided below.
Typically,
the number of significant figures in a measurement
is equal to the number of digits known with a high
degree of confidence, plus an additional digit
that is an estimate or approximation. The number
of digits known with a high degree of confidence
is usually limited by the measurement device or by
limits to human perception and judgment. For
instance, when using calipers that have tick marks
for every 0.1mm, a scientist can only measure to
the nearest 0.1mm with a high degree of
confidence, but can then usually estimate sizes by
eye to the nearest 0.01mm. The rationale behind
the conventions for significant figures is to
ensure that the results of any calculations
reflect the same degree of precision as the
measurements upon which the calculations were
based. For a good review on significant figures
and measurement precision, see the following
website:
click
here
Example: Five radicle length
measurements = 13.0, 12.54, 9.4, 12,
7.5 Average = (13.0 + 12.54 + 9.4 + 12 + 7.5) /
5 = 10.888 Least precise measurement is 12 a
rounding to the nearest ones digit, Answer =
11
When combining measurements using
addition or subtraction, the final result must
have no more significant digits (i.e., decimal
places) than the original measurements. In other
words, the final result should have the same
degree of precision as the least precise
measurement. In this example, the least precise
measurement is 12 because it is only measured to
the nearest ones digit, so the ones is the least
precise decimal place. Therefore the rounded
answer, in significant figures, is 11.
2)
The answer to your second question depends upon
how you intend to interpret the average radicle
lengths, which will in turn depend upon what
questions you are asking. There are three
options: 1) you can include zeros for seeds that
did not produce radicles but exclude seeds that
did not germinate; 2) you can exclude all seeds
that did not germinate or did not produce
radicles; and 3) you can include zeros for seeds
that both did not germinate and did not produce
radicles.
Given that you are measuring both
the number of seeds that are germinating andthe
length of the radicles that are growing, it seems
to me that you are askingtwo independent
questions. The first question is probably: Does
the proportionof seeds that germinate differ among
toxins? The second question may be one oftwo
choices #1) Does the growth of the seeds that
germinate differ amongtoxins? Or #2) Does the
growth of radicles produced by seeds differ
amongtoxins? To answer #1, you need to know the
average growth only of the seedsthat germinate and
can leave out any seeds that did not germinate.
In other words, if you want the average radicle
length to indicate the mean length to which
radicles grow in plants that have germinated, then
you should include a0 for any seed that has
germinated but has not produced a radicle, but you
should omit/exclude any seeds that did not
germinate (i.e., option 1 in the paragraph
above).
If, however, your second question
is choice #2, then you need to know the average
growth only of seeds that produce radicles.
Therefore, you should omit all seeds that did not
produce radicles as well all seeds that did not
germinate. This is the same as option 2 in the
first paragraph above. I think that both of these
approaches would be equally valid, but have
distinct interpretations.
The third option,
to include a 0 both for seeds that did not
germinate and for seeds that did not produce
radicles, does not seem a viable option because
itwould confound your second question, comparing
growth, with your first question, comparing
germination. The answers of the two questions
would no longer be independent since the average
growth calculations would depend in part upon the
proportion of seeds that germinate. In other
words, if one question deals with comparing the
proportion of germinating seeds among treatments,
and another question deals with comparing the
growth of the seeds (but not th
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