Hi, Ivan.
I think your problem may not be so simple as you've described it.
But to begin with the simplest: In terms of area in mm^2, simply
multiplying length x width, all of the ultrasound (US) samples except one
have smaller areas than any of the high-speed drill (AR) samples; 6 of
the 10 AR samples have larger areas than the largest US sample, and if
that sample were ignored (3.5 x 2.2 = 7.70 mm^2) ALL of the AR samples
have larger areas than the remaining nine US samples. This pattern would
be significant (p < .001) by Tukey's "Compact" test (1959).
A similar pattern is true of the widths; the pattern for the
lengths is less compelling, but would still be significant (p < .01).
Similar results would be expected from the parametric methods you mention
in your message (quoted below).
But do you really desire to compare AR with US only on the raw dimensions
of the cavities? One could define some "degree of departure" from the
nominal dimensions (2.0 mm x 3.0 mm), and one might even specify
"acceptable" and "unacceptable" ranges of values for this measure.
I do not know what would be "unacceptable" for this exercise. But when
one is preparing a cavity in a person's tooth, the prepared cavity would
be unacceptably small if some of the decayed matter remained in the
tooth; and the cavity would be unacceptably large if so much of the
tooth had been removed that what remained was too weak to hold the dental
filling.
You might also ask how far each prepared cavity departed from the
intended rectangular shape. But this may not be a realistic question.
(I've had dentists working on my teeth since about 1945, and I think
that _none_ of the fillings they prepared were rectangular in shape!)
In quoting your original message below, I have taken the liberty of
supplying corrected English, in [square brackets].
On Fri, 20 Jul 2001, Ivan Balducci wrote:
> Dear members,
> I am an engineering brazilian. My job is to help researches in Dental
[ I am a Brazilian engineer. My job is to help researchers ... ]
> School about Statistics.
> My doubt is...
[ My concern is: ]
>
> How can I to comaparing two instruments:
> Ultra Som ...versus...Alta Rotação (High Sound & High Rotation)
[ How can I compare two instruments:
Ultra Som versus Alta Rotação (ultrasound vs. high-speed drill) ]
>
> Theses instruments are used in Operative Dentistry
> to perform preparos cavitarios (cavity prepair)
[(cavity preparation)]
> The shape of the prepair is rectangule
{ The shape of the cavity is rectangular. ]
>
> WellThe situation isThe specificated area = 6mm2 (= 2mm x 3mm)
[ ... The specified area = ... ]
> width = 2mm; length = 3mm
>
> Two samplessize sample is 10 (n = 10) for each instrument
>
> How can I aproach this problem?
> I can to do an Analysis Multivariate (T2 Hotteling) : instrument US x
> instrument AR ?
[ I can do a multivariate analysis (Hotelling's T^2) ... ]
Yes, this is possible.
> I can to do a IC (95%), or t-test, separately for each variable (width
> and length) and instrument ?
[ I can do a confidence interval (CI), or t-test ... ]
These are also possible.
> I can to compare the areas (width x length)...for instrument US against
> instrument AR ?
[ I can compare the areas ... ]
And so is this.
> Well...
> Which is the best, the correct way to approach a problem of this kind?
Any of the ways mentioned above are possible and correct. It is not
clear whether any of them is "best", because it is not clear how "best"
may usefully be defined. It is also not clear what the specific
questions are that you really desire to address. I have tried to
indicate some of the range of interesting questions that you might be
interested in.
> Data:[In the data below, I think you have interchanged the
> labels "width" and "length".]
> US:
> width: 2.8 2.9 2.9 3.03.0 3.12.7 2.5 3.5 3.2
> length: 1.9 2.0 1.9 1.92.0 2.02.0 1.9 2.2 2.0
>
> AR:
> width: 3.2 3.3 3.5 3.23.5 3.6 3.5 3.7 4.13.4
> length: 2.3 2.1 2.1 2.22.7 2.6 2.5 2.4 2.02.5
>
> very thanks for the attention and sorry my english
[ Thank you very much for your attention to my problem. ]
(Alternatively, you could simply write TIA, for "Thanks in advance".)
-- Don.
Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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