Dear Colleagues,
I have what I believe to be a rather simple-minded
statistics problem, but there's no one around here with
whom I can consult, hence my writing to you. I was
assigned to come up with an answer to this little problem
by my Direktor and (as usual) he wants a definitive
answer _yesterday_.
I have a set of six numbers, as follows:
6.77597
7.04532
7.17026
7.13235
7.56820
6.97272
which represent results from six different measurements of
the same thing in six different trials, one measurement
per trial. (As a consequence of measurement the samples
are destroyed, so it is not possible to measure the same
sample six different times. Therefore, I had to set up
six separate, independent experiments and measure my
parameter of interest once in each experiment.)
The question I seek to answer is: are the 6 values
obtained in the measuring process reproducible within
statistically meaningful boundaries? I suppose another
way of asking the same question is: is the null hypothesis
Ho satisfied with respect to this series of measured
values?
Using MINITAB 11.21 (the only statistics programme
available to me) I saw that the population distribution
for these six values is _sort of_ symmetric though not
quite normal. This observation, plus the fact that the
sample size is so small (n = 6) suggested that I might
obtain the answer I seek using Wilcoxon's Signed Rank
Test.
Using the default confidence interval (CI) of 95.0, I
obtained the following:
Estimated Achieved
N Median Confidence Confidence Interval
C1 6 7.089 94.1 ( 6.874, 7.369)
Four of the six measured values fall within the confidence
interval, though two measured values (6.77597 and 7.56820)
each lie slightly outside the confidence boundaries (which
I presume is defined by a confidence interval of 94.1).
Next I raised the confidence interval from the default
(95.0) to 97.5, in which case I obtained
Estimated Achieved
N Median Confidence Confidence Interval
C1 6 7.089 96.4 ( 6.776, 7.568)
As you see, now _all_ six measurements fall within the
confidence interval, which I take to be defined as 96.4.
With these results in hand, the question then becomes
one of interpretation. I am given to understand that (in
the absence of complicating factors) the confidence
interval contains all values of Ho that would be retained
had they been tested using alpha = (100 - CI) x (0.01).
In that case, would I be correct to say that the six
measured values are reproducible (i.e. the null
hypothesis is satisfied) at the significance level
alpha = (100 - 96.4) x (0.01) = 0.036?
If I am doing everything wrong, could someone please
explain to me what the correct procedure should be for me
to use to check on the reproducibility of the six measured
values in question? Please keep in mind that the question
I seek to answer is (I believe) a relatively simple one,
so I hope that forthcoming explanations will likewise be
relatively simple. (No Einstein-Bose stats, please.)
As I do not regularly consult this usegroup,
responders are kindly requested to contact me _directly_
at
[EMAIL PROTECTED]
Thanks in advance to all responders for your help in
the above matter; I look forward to hearing from you at
your earliest convienience, since the Direktor is already
harassing me about this.
Regards,
S. Shapiro
[EMAIL PROTECTED]
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