andrew@orca.UUCP (Andrew Klossner) (07/31/85)
>> I am positive that more than .007% of the >> people I know are affected by Nutrasweet-sweetened soft drinks, >> so I am much more inclined to believe the 10% figure. > > 3-digit precision based solely on anecdotal evidence? > This sugar/aspartame/honey/etc stuff > is getting more & more ridiculous every day! Both the quoted numbers (.007% and 10%) have only one significant digit. Leading and trailing zeroes are not significant. If we're going to argue that science is on our side, we must avoid abusing mathematics, the language of science. -=- Andrew Klossner (decvax!tektronix!orca!andrew) [UUCP] (orca!andrew.tektronix@csnet-relay) [ARPA]
hollombe@ttidcc.UUCP (The Polymath) (08/03/85)
In article <1634@orca.UUCP> andrew@orca.UUCP (Andrew Klossner) writes: >>> I am positive that more than .007% of the >>> people I know are affected by Nutrasweet-sweetened soft drinks, >>> so I am much more inclined to believe the 10% figure. >> >> 3-digit precision based solely on anecdotal evidence? >> This sugar/aspartame/honey/etc stuff >> is getting more & more ridiculous every day! > >Both the quoted numbers (.007% and 10%) have only one significant >digit. Leading and trailing zeroes are not significant. > >If we're going to argue that science is on our side, we must avoid >abusing mathematics, the language of science. I agree. 10% has only one significant digit, but .007% has three. The decimal point makes the two leading zeros significant (i.e.: the original article claims accuracy to three decimal places). -_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_ The Polymath (aka: Jerry Hollombe) Citicorp TTI Common Sense is what tells you that a ten 3100 Ocean Park Blvd. pound weight falls ten times as fast as a Santa Monica, CA 90405 one pound weight. (213) 450-9111, ext. 2483 {philabs,randvax,trwrb,vortex}!ttidca!ttidcc!hollombe
oliver@unc.UUCP (Bill Oliver) (08/04/85)
In article <1634@orca.UUCP> andrew@orca.UUCP (Andrew Klossner) writes: >>> I am positive that more than .007% of the >>> people I know are affected by Nutrasweet-sweetened soft drinks, >>> so I am much more inclined to believe the 10% figure. >> >> 3-digit precision based solely on anecdotal evidence? >> This sugar/aspartame/honey/etc stuff >> is getting more & more ridiculous every day! > >Both the quoted numbers (.007% and 10%) have only one significant >digit. Leading and trailing zeroes are not significant. > >If we're going to argue that science is on our side, we must avoid >abusing mathematics, the language of science. > > -=- Andrew Klossner (decvax!tektronix!orca!andrew) [UUCP] > (orca!andrew.tektronix@csnet-relay) [ARPA] Perhaps the misunderstanding is due to problems of measurement as opposed to numerical representation. While, indeed, as far as representation goes, 7E-3 and 1E1 are of the same significance, a measurement of 0.007 has a much different significance than 10. For instance, a measurement of 0.007 grams implies an accuracy of 0.0005 grams, while a measurement of 10 grams implies an accuracy of 0.5 grams. Indeed, in this case, 10 is by no means the same as 10.000, and the trailing zeroes are of great importance. Bill Oliver
thomas@utah-gr.UUCP (Spencer W. Thomas) (08/05/85)
In article <622@ttidcc.UUCP> hollombe@ttidcc.UUCP (The Polymath) writes: >I agree. 10% has only one significant digit, but .007% has three. The >decimal point makes the two leading zeros significant (i.e.: the original >article claims accuracy to three decimal places). > The original article may claim accurace to 3 decimal places, but the way I learned significant digits, you should write 0.00700% to specify 3 digits of accuracy. 10% is a toughie - you really can't tell whether the meaning is 10%+/-5% (1 digit) or 10%+/-.5% (2 digits). For 3 digits, you should write 10.0%. The best way to write numbers to clearly specify the number of siginificant digits is to use scientific notation. Thus: 1 digit 3 digits 7e-3 7.00e-3 1e+1 1.00e+1 -- =Spencer ({ihnp4,decvax}!utah-cs!thomas, thomas@utah-cs.ARPA) "You don't get to choose how you're going to die. Or when. You can only decide how you're going to live." Joan Baez
hollombe@ttidcc.UUCP (The Polymath) (08/06/85)
In article <82@unc.unc.UUCP> oliver@unc.UUCP (Bill Oliver) writes: >In article <1634@orca.UUCP> andrew@orca.UUCP (Andrew Klossner) writes: >>>> I am positive that more than .007% of the >>>> people I know are affected by Nutrasweet-sweetened soft drinks, >>>> so I am much more inclined to believe the 10% figure. >>> >>> 3-digit precision based solely on anecdotal evidence? >>> This sugar/aspartame/honey/etc stuff >>> is getting more & more ridiculous every day! >> >>Both the quoted numbers (.007% and 10%) have only one significant >>digit. Leading and trailing zeroes are not significant. >> >>If we're going to argue that science is on our side, we must avoid >>abusing mathematics, the language of science. >> >> -=- Andrew Klossner (decvax!tektronix!orca!andrew) [UUCP] > >Perhaps the misunderstanding is due to problems of measurement as >opposed to numerical representation. While, indeed, as far as >representation goes, 7E-3 and 1E1 are of the same significance, >a measurement of 0.007 has a much different significance than >10. For instance, a measurement of 0.007 grams implies an accuracy >of 0.0005 grams, while a measurement of 10 grams implies an accuracy >of 0.5 grams. Indeed, in this case, 10 is by no means the same as >10.000, and the trailing zeroes are of great importance. This is what I was trying to say in an earlier posting. My apologies for my misuse of terminology. (... I will not shoot from the hip. I will not shoot from the hip. I will not shoot from the hip. I will not shoot from the hip. ...) -_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_ The Polymath (aka: Jerry Hollombe) Citicorp TTI Common Sense is what tells you that a ten 3100 Ocean Park Blvd. pound weight falls ten times as fast as a Santa Monica, CA 90405 one pound weight. (213) 450-9111, ext. 2483 {philabs,randvax,trwrb,vortex}!ttidca!ttidcc!hollombe
seifert@hammer.UUCP (Snoopy) (08/07/85)
In article <622@ttidcc.UUCP> hollombe@ttidcc.UUCP (The Polymath) writes: >>Both the quoted numbers (.007% and 10%) have only one significant >>digit. Leading and trailing zeroes are not significant. >> Wrongo. .007 has ONE significant digit, .00700 has THREE. 007 (no leading decimal point) naturally has ten significant digits, since all of James Bond's fingers are significant! :-) Snoopy tektronix!hammer!seifert
jeff@rtech.UUCP (Jeff Lichtman) (08/08/85)
> In article <1634@orca.UUCP> andrew@orca.UUCP (Andrew Klossner) writes: > >>> I am positive that more than .007% ... > >> > >> 3-digit precision based solely on anecdotal evidence? > > > >Both the quoted numbers (.007% and 10%) have only one significant > >digit. Leading and trailing zeroes are not significant. > > I agree. 10% has only one significant digit, but .007% has three. The > decimal point makes the two leading zeros significant (i.e.: the original > article claims accuracy to three decimal places). > > The Polymath (aka: Jerry Hollombe) The usual method of writing numbers (e.g. 10, .007) carries no information about accuracy. .007 could be accurate to one, two or three decimal places. The only way to express accuracy is to put the number in scientific notation, or to explicitly specify the accuracy of the number. In scientific notation, 7 * 10 ** -3 has one digit of accuracy, 7.0 * 10 ** -3 has two digits of accuracy, and 7.00 * 10 ** -3 has three digits of accuracy. This method of notation makes incidental zeros impossible. If you saw 1000000, how would you tell which of the zeros were part of the measurement, and which were padding? 1.00 * 10 ** 6 leaves no question that there are three significant digits. This and the fact that scientific notation allows huge numbers to be written compactly are the two main advantages of this method of expressing numbers. However, one should remember that the accuracy of real measurements doesn't often conform to the decimal system of expressing numbers. That is, real measurements are not usually accurate within some integral number of digits. The number of significant digits in a measurement usually only gives a rough idea of the accuracy of the measurement; a better method is to give some measure of accuracy along with the measurement, such as standard deviation or range of 95% confidence (e.g. 7.00 * 10 ** -3 +/- 2.5 * 10 ** -4 with 95% confidence). Figuring this out can take a bit of calculus if the number in question is calculated from several variables, each with its own accuracy: one must factor in not only the accuracy of each of the variables, but also the sensitivity of the derived measurement to changes in each of the raw measurements. -- Jeff Lichtman at rtech (Relational Technology, Inc.) aka Swazoo Koolak {amdahl, sun}!rtech!jeff {ucbvax, decvax}!mtxinu!rtech!jeff
halle@hou2b.UUCP (J.HALLE) (08/13/85)
Before this debate gets too out of hand, it might be prudent to remind people what the terms mean. Accuracy and precision are NOT synonymous. Precision refers to the number of significant figures, but is not necessarily a good indicator of accuracy. Accuracy refers to the reliability of the stated value. E.g., you could measure something to be 13.246792 inches long, but if your ruler was only so-so and/or your measurements had a lot of scatter, you could be accurate only to perhaps two decimal places. (13.246792 +/- 0.05, e.g.) It is not necessarily incorrect to state it this way (although it is bad form). 0.007% has three decimal points worth of precision, but that merely tells you the size of the scale. Its accuracy is unknown, though implied. Depending on the measurement method, three decimal places of precision could be "significant," or it could be a crude estimate. More information is required.
roy@phri.UUCP (Roy Smith) (08/14/85)
> The usual method of writing numbers (e.g. 10, .007) carries no information > about accuracy. .007 could be accurate to one, two or three decimal places. This is getting rather off the point, but some of you might like this. During one of my interviews for college, I was asked a typical stupid interview question: "What's the area of a table 3 meters wide by 4 meters long?" I poked around with various counter-probes like, "Do you mean the area of just the top surface, or the top and bottom combined?" and then came up with the obvious answer; 12 meters^2. Anyway, it turns out the "correct" answer is 1 * 10^1 meters^2; since the initial data only had 1 digit of accuracy, that's all the final answer can have. -- Roy Smith <allegra!phri!roy> System Administrator, Public Health Research Institute 455 First Avenue, New York, NY 10016
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (08/18/85)
> > The usual method of writing numbers (e.g. 10, .007) carries no information > > about accuracy. .007 could be accurate to one, two or three decimal places. The usual convention is to show accuracy past the last significant digit by postpending zeroes. 0.007 is presumed to be accurate to + or - 0.0005 otherwise. 10 is presumed to have 1 significant digit but 10. indicates two significant digits. Real measurement accuracy should not be expressed in such terms but should have the standard error given also. > This is getting rather off the point, but some of you might like > this. During one of my interviews for college, I was asked a typical > stupid interview question: "What's the area of a table 3 meters wide by 4 > meters long?" I poked around with various counter-probes like, "Do you > mean the area of just the top surface, or the top and bottom combined?" and > then came up with the obvious answer; 12 meters^2. > Anyway, it turns out the "correct" answer is 1 * 10^1 meters^2; > since the initial data only had 1 digit of accuracy, that's all the final > answer can have. This is a typical, but incorrect analysis. The number of significant digits in a computed quantity cannot be accurately estimated by any such simple rule. Assuming that the dimensions of the table were given only to the nearest meter (which is improbable), range arithmetic should be used, which means multiplying two rectangular distributions. If the input quantities had been assumed to follow a more Gaussian distribution, the best estimate of the area would be near 12 (with a very considerable standard deviation).
meister@linus.UUCP (Phillip W. Servita) (08/20/85)
In article <402@phri.UUCP> roy@phri.UUCP (Roy Smith) writes: > This is getting rather off the point, but some of you might like >this. During one of my interviews for college, I was asked a typical >stupid interview question: "What's the area of a table 3 meters wide by 4 >meters long?" I poked around with various counter-probes like, "Do you >mean the area of just the top surface, or the top and bottom combined?" and >then came up with the obvious answer; 12 meters^2. > > Anyway, it turns out the "correct" answer is 1 * 10^1 meters^2; >since the initial data only had 1 digit of accuracy, that's all the final >answer can have. When my high school physics teacher asked this (actually, the figures were different, but the question the same) question, and then told us the "correct" answer, i said: "BULL PATTIES!!!" this was 4 years ago, as a high school junior. If i was asked the same question now, however, I WOULD STILL SAY 12 METERS SQUARE. And when i would get the "correct answer" in return, I WOULD STILL SAY "BULL PATTIES!!!". Sorry, significant figures freaks, but the question "Whats the area of a table 3 meters wide by 4 meters long" is totally theoretical in nature. You have GIVEN me a table 3 by 4. i dont know how or care how you measured it, you have GIVEN me a table 3 by 4. and GIVEN: a table 3 x 4 meters THEN: that table has an area of 12 meters square. PERIOD. To illustrate this further, let me ask two other questions: 1) (the math majors question) What is the area of a two dimensional rectangular pink elephant 3 meters wide by 4 meters long? 2) (what the physics and sig figs people SHOULD ask) Using a stick ruled only in meters, i measured a table to be about 3 meters wide by 4 meters long. What is its area? (correct answer about 10 meters square) you were right with your 12 meters square answer. -phil
jim@cadomin.UUCP (Jim Easton) (08/22/85)
In reply to Phillip W. Servita I quote out of your posting; > .............. If i was asked the same question now, however, I WOULD STILL > SAY 12 METERS SQUARE. ... and you would be wrong. The correct answer is 12 square meters - the unit is square meters. 12 meters square implies a square which is 12 meters on a side, having an area of 144 square meters. Jim Easton (...!alberta!jim)
thomas@utah-gr.UUCP (Spencer W. Thomas) (08/24/85)
In article <509@linus.UUCP> meister@linus.UUCP (Philip W. Servita) writes: (various expletives deleted) > GIVEN: a table 3 x 4 meters > > THEN: that table has an area of 12 meters square. PERIOD. the number "3" used in a measurement context (rather than 3.0 or 3.000) means "3 +/- 0.5" Multiplying out the limit cases, we get that the area of the table is between 2.5x3.5 = 8.75 and 3.5x4.5 = 15.75 or approximately 1e1. Saying "3" instead of "3 +/- 0.5" is a convenient shorthand. While mathematically 3x4 is 12, when dealing with measurements you must ALWAYS consider the precision. > >2) (what the physics and sig figs people SHOULD ask) > > Using a stick ruled only in meters, i measured a table to be about > 3 meters wide by 4 meters long. What is its area? (correct answer > about 10 meters square) This is exactly what a measurement type means when he (or she) says the table is "3 meters by 4 meters". Again, it's a shorthand (or jargon) that you learn to understand when you enter the field (just like Kb and the like in CS). -- =Spencer ({ihnp4,decvax}!utah-cs!thomas, thomas@utah-cs.ARPA) "To feel at home, stay at home. A foreign country is not designed to make [one] comfortable. It's designed to make its own people comfortable." Clifton Fadiman