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Dear Glenn,
That's a great example - wish I'd had it to hand when I used to nag my
students about this.
The key point to understand is of course the accuracy of the measurement -
just because there is a readout with 3 significant figures doesn't mean that
the measurement is accurate to 1 part in a thousand.
The t-test also illustrates the difference between statistical signifance
and practical significance. Clearly the measured difference is practically
insignificant even if it is statistically significant (even assuming that
the t-test was appropriate, which it may not be). It would be interesting to
recalculate with the input data rounded off to integers, though even then it
really is the practical significance of the difference that's most
important.
BTW, there's nothing special about decimal places. We should also round off
integers according to the measurement accuracy. For example, it makes no
sense to record blood pressure to a precision of +/- 1 mmHg (e.g. 122/84) -
it should be rounded to the nearest 5 mmHg at least (120/85). Indeed +/-10
(120/80) is probably more appropriate.
Chris
On 5/21/07, Glenn Fleisig wrote:
>
> Hi everyone,
>
>
>
> This is general question relevant to a lot of our research. It should
> be simple, but I don't recall the answer.
>
>
>
> How many digits should be used in reporting data?
>
>
>
> Here is an example. A biomechanist is trying to show a difference
> between Technique A and Technique B. He/she recruits 36 subjects and
> records each one of them performing both techniques, using equipment
> that measures each person to the nearest 0.1 unit. How many decimal
> places should be used in reporting the data? I can make a "common
> sense" determination, but is there some accepted procedure or guideline?
>
>
>
> Example data:
>
>
>
> TECHNIQUE A
>
> Subject 1: 13.3 units
>
> Subject 2: 35.0 units
>
> Subject 3: 22.2 units
>
> .
>
> .
>
> .
>
> Subject 36: 18.4 units
>
>
>
>
>
> TECHNIQUE B
>
> Subject 1: 12.9 units
>
> Subject 2: 35.0 units
>
> Subject 3: 21.9 units
>
> .
>
> .
>
> .
>
> Subject 36: 18.5 units
>
>
>
>
>
> Even though the mean within-subject difference is less than 0.1 units, a
> paired t-test reveals a statistically significant difference.
>
> Technique A mean: 25.33333 units
>
> Technique B mean: 25.36170 units
>
> Average difference : 0.02837 units
>
> Paired t-test p-value: 0.035
>
>
>
> How many decimal places would you use in reporting these mean values and
> difference in your paper? Why?
>
>
>
> Thanks in advance,
>
> - Glenn S. Fleisig, Ph.D.
>
> Glenn S. Fleisig, Ph.D., Smith & Nephew Chair of Research
> American Sports Medicine Institute
> 833 St. Vincent's Drive, Suite 100
> Birmingham, AL 35205
> (email) glennf@asmi.org
> (tel) 205-918-2139
> www.asmi.org
>
>
>
>
> ---------------------------------------------------------------
> Information about BIOMCH-L: http://www.Biomch-L.org
> Archives: http://listserv.surfnet.nl/archives/Biomch-L.html
> ---------------------------------------------------------------
>
--
Dr. Chris Kirtley MB ChB, PhD
from 1 May to 31 July 2007 I am at:
Stiftung Orthopädische Universitätsklinik Heidelberg
Leiter Ganganalyselabor
Anschrift: Schlierbacher Landstr. 200a
69118 Heidelberg
Tel: 49+06221-96 6724
Fax: 49+06221-96 6725
Clinical Gait Analysis: http://www.univie.ac.at/cga
Book:
http://www.amazon.co.uk/exec/obidos/ASIN/0443100098/203-6674734-4427132
That's a great example - wish I'd had it to hand when I used to nag my
students about this.
The key point to understand is of course the accuracy of the measurement -
just because there is a readout with 3 significant figures doesn't mean that
the measurement is accurate to 1 part in a thousand.
The t-test also illustrates the difference between statistical signifance
and practical significance. Clearly the measured difference is practically
insignificant even if it is statistically significant (even assuming that
the t-test was appropriate, which it may not be). It would be interesting to
recalculate with the input data rounded off to integers, though even then it
really is the practical significance of the difference that's most
important.
BTW, there's nothing special about decimal places. We should also round off
integers according to the measurement accuracy. For example, it makes no
sense to record blood pressure to a precision of +/- 1 mmHg (e.g. 122/84) -
it should be rounded to the nearest 5 mmHg at least (120/85). Indeed +/-10
(120/80) is probably more appropriate.
Chris
On 5/21/07, Glenn Fleisig wrote:
>
> Hi everyone,
>
>
>
> This is general question relevant to a lot of our research. It should
> be simple, but I don't recall the answer.
>
>
>
> How many digits should be used in reporting data?
>
>
>
> Here is an example. A biomechanist is trying to show a difference
> between Technique A and Technique B. He/she recruits 36 subjects and
> records each one of them performing both techniques, using equipment
> that measures each person to the nearest 0.1 unit. How many decimal
> places should be used in reporting the data? I can make a "common
> sense" determination, but is there some accepted procedure or guideline?
>
>
>
> Example data:
>
>
>
> TECHNIQUE A
>
> Subject 1: 13.3 units
>
> Subject 2: 35.0 units
>
> Subject 3: 22.2 units
>
> .
>
> .
>
> .
>
> Subject 36: 18.4 units
>
>
>
>
>
> TECHNIQUE B
>
> Subject 1: 12.9 units
>
> Subject 2: 35.0 units
>
> Subject 3: 21.9 units
>
> .
>
> .
>
> .
>
> Subject 36: 18.5 units
>
>
>
>
>
> Even though the mean within-subject difference is less than 0.1 units, a
> paired t-test reveals a statistically significant difference.
>
> Technique A mean: 25.33333 units
>
> Technique B mean: 25.36170 units
>
> Average difference : 0.02837 units
>
> Paired t-test p-value: 0.035
>
>
>
> How many decimal places would you use in reporting these mean values and
> difference in your paper? Why?
>
>
>
> Thanks in advance,
>
> - Glenn S. Fleisig, Ph.D.
>
> Glenn S. Fleisig, Ph.D., Smith & Nephew Chair of Research
> American Sports Medicine Institute
> 833 St. Vincent's Drive, Suite 100
> Birmingham, AL 35205
> (email) glennf@asmi.org
> (tel) 205-918-2139
> www.asmi.org
>
>
>
>
> ---------------------------------------------------------------
> Information about BIOMCH-L: http://www.Biomch-L.org
> Archives: http://listserv.surfnet.nl/archives/Biomch-L.html
> ---------------------------------------------------------------
>
--
Dr. Chris Kirtley MB ChB, PhD
from 1 May to 31 July 2007 I am at:
Stiftung Orthopädische Universitätsklinik Heidelberg
Leiter Ganganalyselabor
Anschrift: Schlierbacher Landstr. 200a
69118 Heidelberg
Tel: 49+06221-96 6724
Fax: 49+06221-96 6725
Clinical Gait Analysis: http://www.univie.ac.at/cga
Book:
http://www.amazon.co.uk/exec/obidos/ASIN/0443100098/203-6674734-4427132