Dear List/SPSS personnel
I've just been told that our School will have to pay the princely sum of $Au2,500 per individual user of SPSS in future! Given the cash-strapped status of most schools of medicine, I wonder how this can be justified? If what I have been told is true(??), then we (and doubtless many other schools in Australia) will simply not be able to afford to use SPSS and will be forced to use alternative packages. It appears to me that what is going on is not a little "cutting off SPSS's nose to spite its face". Patricia ______________________________ Patricia RĂ©go Evaluation Officer School of Medicine The University of Queensland (Ph: 61-7-33464683; [hidden email]) and Skills Development Centre Queensland Health (Ph: 61-7-3636-6449; [hidden email]) |
Can someone answer a very basic stats question for me?
When I was taught how to round I was told that when the last digit is 5 or greater you round up 4 or less, round down. Why is it that introductory stats texts, at least in the behavioral sciences, recommend rounding down if the last digit is 5. Then there some other strange recommendations about a number where 3.6AB (where A & B are digits) and if B is exactly 5 then you round A up if it is odd and down if it is even. What is the logic for this? Thanks Matt Matthew Pirritano, Ph.D. Assistant Professor of Psychology Smith Hall 116C Chapman University Department of Psychology One University Drive Orange, CA 92866 Telephone (714)744-7940 FAX (714)997-6780 |
The rule you learned introduces cumulative rounding errors. The 'round to even' rule reduces rounding errors. Here's an overly simplistic example:
data list free /x up even. begin data 1.25 1.3 1.2 1.35 1.4 1.4 1.45 1.5 1.4 1.55 1.6 1.6 1.65 1.7 1.6 1.75 1.8 1.8 1.85 1.9 1.8 1.95 2.0 2.0 end data. descriptive variables=x up even /statistics sum. -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Pirritano, Matthew Sent: Thursday, September 07, 2006 12:09 AM To: [hidden email] Subject: Very basic question Can someone answer a very basic stats question for me? When I was taught how to round I was told that when the last digit is 5 or greater you round up 4 or less, round down. Why is it that introductory stats texts, at least in the behavioral sciences, recommend rounding down if the last digit is 5. Then there some other strange recommendations about a number where 3.6AB (where A & B are digits) and if B is exactly 5 then you round A up if it is odd and down if it is even. What is the logic for this? Thanks Matt Matthew Pirritano, Ph.D. Assistant Professor of Psychology Smith Hall 116C Chapman University Department of Psychology One University Drive Orange, CA 92866 Telephone (714)744-7940 FAX (714)997-6780 |
In reply to this post by Pirritano, Matthew
Matthew Pirritano asks about the strange rounding rule that if the last digit is 5, then round up if the next to last digit is odd, and round down if the next to last digit is even. This is also called rounding to the even digit. Always rounding the 5 up or always rounding it down can cause biases, according to some sources. Other sources point out that if you always round 0,1,2,3,4 down and always round 6,7,8,9 up then rounding 5 up will keep a balance (5 digits go down and 5 digits go up). If you conceive of the number 3.85 as a discrete quantity, the latter rule makes more sense. If you conceive of 3.85 as representing anything from 3.845000.. to 3.854999.. then the former rule makes more sense.
As far as I can tell, there is no one who seriously advocates always rounding the 5 downward. Here are some websites that explain some of the logic behind some of the choices: http://mathforum.org/library/drmath/view/58928.html http://www.pacific.edu/college/psychology/Statistics/Rounding.html http://math.about.com/od/arithmetic/a/Rounding.htm Steve Simon, [hidden email], Standard Disclaimer. Look for my book "Statistical Evidence in Medical Trials" newly published by OUP. For more details, see http://www.childrens-mercy.org/stats/evidence.asp <https://webmail.cmh.edu/exchweb/bin/redir.asp?URL=http://www.childrens-mercy.org/stats/evidence.asp> ________________________________ From: SPSSX(r) Discussion on behalf of Pirritano, Matthew Sent: Thu 9/7/2006 12:09 AM To: [hidden email] Subject: Very basic question Can someone answer a very basic stats question for me? When I was taught how to round I was told that when the last digit is 5 or greater you round up 4 or less, round down. Why is it that introductory stats texts, at least in the behavioral sciences, recommend rounding down if the last digit is 5. Then there some other strange recommendations about a number where 3.6AB (where A & B are digits) and if B is exactly 5 then you round A up if it is odd and down if it is even. What is the logic for this? Thanks Matt Matthew Pirritano, Ph.D. Assistant Professor of Psychology Smith Hall 116C Chapman University Department of Psychology One University Drive Orange, CA 92866 Telephone (714)744-7940 FAX (714)997-6780 |
In reply to this post by Patricia Rego
There is SPSS-like alternative in the works called PSPP. It is an open-source initiative to implement the SPSS transformation language in a freely available tool. I've been evaluating it for effectiveness and have had success in using it on "production" code. Right now, it is useable in a command-line "batch" type environment. There is a GUI being built as well but it is in the alpha stage and I've never tried it.
Development is ongoing and anyone can contribute code or documentation. A thorough users manual is available. I think this tool would be appropriate in a research environment, but probably not for teaching introductory courses on statistical computing at the moment. I don't know what you are using it for. This software is available at: http://www.gnu.org/software/pspp/ The manual is at: http://www.gnu.org/software/pspp/manual/ Dan Williams Forecasting, Research and Analysis Office Finance and Policy Analysis Department of Human Services State of Oregon, USA (503) 947-5354 >>> Patricia Rego <[hidden email]> 9/6/2006 7:26:12 PM >>> Dear List/SPSS personnel I've just been told that our School will have to pay the princely sum of $Au2,500 per individual user of SPSS in future! Given the cash-strapped status of most schools of medicine, I wonder how this can be justified? If what I have been told is true(??), then we (and doubtless many other schools in Australia) will simply not be able to afford to use SPSS and will be forced to use alternative packages. It appears to me that what is going on is not a little "cutting off SPSS's nose to spite its face". Patricia ______________________________ Patricia RĂ©go Evaluation Officer School of Medicine The University of Queensland (Ph: 61-7-33464683; [hidden email]) and Skills Development Centre Queensland Health (Ph: 61-7-3636-6449; [hidden email]) |
In reply to this post by Pirritano, Matthew
However, 3.80 does not need rounding so it is 1, 2, 3, 4 down and
6,7,8,9 up leaving 5 to bias the result if you always round up or down. And if you think of 3.85 as a discrete quantity, why round it at all? Paul R. Swank, Ph.D. Professor, Developmental Pediatrics Director of Research, Children's Learning Institute Medical School University of Texas Health Science Center at Houston -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Simon, Steve, PhD Sent: Thursday, September 07, 2006 9:45 AM To: [hidden email] Subject: Re: Very basic question Matthew Pirritano asks about the strange rounding rule that if the last digit is 5, then round up if the next to last digit is odd, and round down if the next to last digit is even. This is also called rounding to the even digit. Always rounding the 5 up or always rounding it down can cause biases, according to some sources. Other sources point out that if you always round 0,1,2,3,4 down and always round 6,7,8,9 up then rounding 5 up will keep a balance (5 digits go down and 5 digits go up). If you conceive of the number 3.85 as a discrete quantity, the latter rule makes more sense. If you conceive of 3.85 as representing anything from 3.845000.. to 3.854999.. then the former rule makes more sense. As far as I can tell, there is no one who seriously advocates always rounding the 5 downward. Here are some websites that explain some of the logic behind some of the choices: http://mathforum.org/library/drmath/view/58928.html http://www.pacific.edu/college/psychology/Statistics/Rounding.html http://math.about.com/od/arithmetic/a/Rounding.htm Steve Simon, [hidden email], Standard Disclaimer. Look for my book "Statistical Evidence in Medical Trials" newly published by OUP. For more details, see http://www.childrens-mercy.org/stats/evidence.asp <https://webmail.cmh.edu/exchweb/bin/redir.asp?URL=http://www.childrens- mercy.org/stats/evidence.asp> ________________________________ From: SPSSX(r) Discussion on behalf of Pirritano, Matthew Sent: Thu 9/7/2006 12:09 AM To: [hidden email] Subject: Very basic question Can someone answer a very basic stats question for me? When I was taught how to round I was told that when the last digit is 5 or greater you round up 4 or less, round down. Why is it that introductory stats texts, at least in the behavioral sciences, recommend rounding down if the last digit is 5. Then there some other strange recommendations about a number where 3.6AB (where A & B are digits) and if B is exactly 5 then you round A up if it is odd and down if it is even. What is the logic for this? Thanks Matt Matthew Pirritano, Ph.D. Assistant Professor of Psychology Smith Hall 116C Chapman University Department of Psychology One University Drive Orange, CA 92866 Telephone (714)744-7940 FAX (714)997-6780 |
In reply to this post by Pirritano, Matthew
I was surprised and disappointed when I started using SPSS (14.0) that
it doesn't have a simple feature for setting alternative rounding rules, since much of my SPSS work requires using special rounding (e.g., round 0 down and anything else up, rounding to various decimal places, etc.). I found a workaround using several lines of TRUNC and RND syntax (if anyone needs it, let me know), but it is a pain, and it seems like there should be a simpler drop-down menu manipulation available. I asked the SPSS product manager about it at a recent SPSS event and he said he may have a new rounding control feature available in 16.0 or 17.0. Lise ********************* Lise Valentine, Ph.D. Vice President and Research Director The Civic Federation 177 N. State Street, Suite 400 Chicago, IL 60601 phone (312) 201-9028 fax (312) 201-9041 [hidden email] -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Simon, Steve, PhD Sent: Thursday, September 07, 2006 9:45 AM To: [hidden email] Subject: Re: Very basic question Matthew Pirritano asks about the strange rounding rule that if the last digit is 5, then round up if the next to last digit is odd, and round down if the next to last digit is even. This is also called rounding to the even digit. Always rounding the 5 up or always rounding it down can cause biases, according to some sources. Other sources point out that if you always round 0,1,2,3,4 down and always round 6,7,8,9 up then rounding 5 up will keep a balance (5 digits go down and 5 digits go up). If you conceive of the number 3.85 as a discrete quantity, the latter rule makes more sense. If you conceive of 3.85 as representing anything from 3.845000.. to 3.854999.. then the former rule makes more sense. As far as I can tell, there is no one who seriously advocates always rounding the 5 downward. Here are some websites that explain some of the logic behind some of the choices: http://mathforum.org/library/drmath/view/58928.html http://www.pacific.edu/college/psychology/Statistics/Rounding.html http://math.about.com/od/arithmetic/a/Rounding.htm Steve Simon, [hidden email], Standard Disclaimer. Look for my book "Statistical Evidence in Medical Trials" newly published by OUP. For more details, see http://www.childrens-mercy.org/stats/evidence.asp <https://webmail.cmh.edu/exchweb/bin/redir.asp?URL=http://www.childrens- mercy.org/stats/evidence.asp> ________________________________ From: SPSSX(r) Discussion on behalf of Pirritano, Matthew Sent: Thu 9/7/2006 12:09 AM To: [hidden email] Subject: Very basic question Can someone answer a very basic stats question for me? When I was taught how to round I was told that when the last digit is 5 or greater you round up 4 or less, round down. Why is it that introductory stats texts, at least in the behavioral sciences, recommend rounding down if the last digit is 5. Then there some other strange recommendations about a number where 3.6AB (where A & B are digits) and if B is exactly 5 then you round A up if it is odd and down if it is even. What is the logic for this? Thanks Matt Matthew Pirritano, Ph.D. Assistant Professor of Psychology Smith Hall 116C Chapman University Department of Psychology One University Drive Orange, CA 92866 Telephone (714)744-7940 FAX (714)997-6780 |
In reply to this post by Pirritano, Matthew
At 01:09 AM 9/7/2006, Pirritano, Matthew wrote:
>When I was taught how to round I was told that when the last digit is >5 or greater you round up 4 or less, round down. Why is it that >introductory stats texts, at least in the behavioral sciences, >recommend rounding down if the last digit is 5. Then there some other >strange recommendations about a number where 3.6AB (where A & B are >digits) and if B is exactly 5 then you round A up if it is odd and >down if it is even. What is the logic for this? You've had some answers about those rules. The answer I'd give is: it doesn't matter. It doesn't matter, because numbers that you want to round are usually from a fairly complex measurement or calculation, and are effectively a very long string of decimals. You'll get 3.85 exactly, too rarely to mention. (Exactly 3.85 is likely not possible, in the binary number representation that SPSS uses.) About the only case where these rules matter is when you're rounding exactly one digit. And in that case, where you believe '3.85' is your exact value, as Swank, Paul R wrote: >If you think of 3.85 as a discrete quantity, why round it at all? For calculations, and accumulation of rounding errors, the answer is simple: don't round before calculating. Rounding can only lose you precision. If you're dealing with quantities that have already been rounded to two decimals, you still don't want to round them any further before calculating. (Financial accounting may use different conventions. If so, follow those.) Rounding matters in presentation of numbers: you don't want to give all those decimals, especially as most are meaningless, within the actual precision of the values. But, as I wrote, the rules for when the value to be removed by rounding is exactly 5 don't matter, because that essentially never happens. Now, At 12:08 PM 9/7/2006, Lise Valentine wrote: >I was surprised and disappointed that [SPSS] doesn't have a simple >feature for setting alternative rounding rules, since much of my SPSS >work requires using special rounding (e.g., round 0 down and anything >else up, rounding to various decimal places, etc.). I'm guessing, but I imagine it wasn't thought of because in numerical analysis (of which statistical computation is a special case) it's almost never advisable to round except for presenting results; and for that, 'rounding to the nearest' is almost always unambiguous. >I found a workaround using several lines of TRUNC and RND syntax. At the moment, that's probably the best you can do, though if it took several lines, there may be simplifications. And it may not matter to you, but while you can round to integers exactly, you usually can't round exactly to decimal fractions. That is, a number calculated as 3.85 probably differs from it by a tiny amount. For that reason in accounting systems using binary arithmetic, it's usual to keep amounts in cents, not dollars, so they can be represented exactly. I'm interested in why you need these, but you can put that down to excessive curiosity, if you like. Good luck to all, Richard |
In reply to this post by Pirritano, Matthew
This is/was a fairly relevant issue many years ago with one of the
versions of SPSS. One could AGGREGATE some data, read it into SPSS, then export it to a Dbase type format. Sometimes if you had a number that fell exactly on the fence, like 42.5, it would round up and sometimes it would round down, when you exported it to have no decimal places. I could never figure out the pattern. My fix for it was to multiply the number by 100 then divide in the back-end. Simple, but it worked. It has been many years since I have done such a procedure. I do not know if it was ever fixed. But, for the purposes of reporting results to clients, it makes a huge difference. Zachary -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Swank, Paul R Sent: Thursday, September 07, 2006 11:05 AM To: [hidden email] Subject: Re: Very basic question However, 3.80 does not need rounding so it is 1, 2, 3, 4 down and 6,7,8,9 up leaving 5 to bias the result if you always round up or down. And if you think of 3.85 as a discrete quantity, why round it at all? Paul R. Swank, Ph.D. Professor, Developmental Pediatrics Director of Research, Children's Learning Institute Medical School University of Texas Health Science Center at Houston -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Simon, Steve, PhD Sent: Thursday, September 07, 2006 9:45 AM To: [hidden email] Subject: Re: Very basic question Matthew Pirritano asks about the strange rounding rule that if the last digit is 5, then round up if the next to last digit is odd, and round down if the next to last digit is even. This is also called rounding to the even digit. Always rounding the 5 up or always rounding it down can cause biases, according to some sources. Other sources point out that if you always round 0,1,2,3,4 down and always round 6,7,8,9 up then rounding 5 up will keep a balance (5 digits go down and 5 digits go up). If you conceive of the number 3.85 as a discrete quantity, the latter rule makes more sense. If you conceive of 3.85 as representing anything from 3.845000.. to 3.854999.. then the former rule makes more sense. As far as I can tell, there is no one who seriously advocates always rounding the 5 downward. Here are some websites that explain some of the logic behind some of the choices: http://mathforum.org/library/drmath/view/58928.html http://www.pacific.edu/college/psychology/Statistics/Rounding.html http://math.about.com/od/arithmetic/a/Rounding.htm Steve Simon, [hidden email], Standard Disclaimer. Look for my book "Statistical Evidence in Medical Trials" newly published by OUP. For more details, see http://www.childrens-mercy.org/stats/evidence.asp <https://webmail.cmh.edu/exchweb/bin/redir.asp?URL=http://www.childrens- mercy.org/stats/evidence.asp> ________________________________ From: SPSSX(r) Discussion on behalf of Pirritano, Matthew Sent: Thu 9/7/2006 12:09 AM To: [hidden email] Subject: Very basic question Can someone answer a very basic stats question for me? When I was taught how to round I was told that when the last digit is 5 or greater you round up 4 or less, round down. Why is it that introductory stats texts, at least in the behavioral sciences, recommend rounding down if the last digit is 5. Then there some other strange recommendations about a number where 3.6AB (where A & B are digits) and if B is exactly 5 then you round A up if it is odd and down if it is even. What is the logic for this? Thanks Matt Matthew Pirritano, Ph.D. Assistant Professor of Psychology Smith Hall 116C Chapman University Department of Psychology One University Drive Orange, CA 92866 Telephone (714)744-7940 FAX (714)997-6780 |
In reply to this post by Pirritano, Matthew
For excessive curiosity:
It may not be advisable to round, but that is what the Cook County (Chicago) clerk does in calculating property tax rates. I use SSPS purely because it has the capacity to handle data on 1.7 million properties and 1500 local taxing agencies, not because of its statistical features (also it is what the county's research staff uses, so they can transfer me the files easily). At different stages of the labyrinthine computations used to determine property tax rates in this county, the clerk uses special rounding rules, and different governments have different numbers of decimal places in their rates, all of which are the sums of individual fund rates which have been multiplied and divided by various things before being summed. I didn't make it up, I just have to replicate his system (done on an archaic mainframe, not in SPSS) so I can then test hypothetical changes to it when people come up with property tax reform proposals. I'd expected among all the bells and whistles that SPSS would allow me to easily control rounding rules and truncation at various decimal places, but alas. Lise -----Original Message----- From: Richard Ristow [mailto:[hidden email]] Sent: Thursday, September 07, 2006 2:50 PM To: Pirritano, Matthew; [hidden email] Cc: Lise Valentine Subject: Re: Very basic question Now, At 12:08 PM 9/7/2006, Lise Valentine wrote: >I was surprised and disappointed that [SPSS] doesn't have a simple >feature for setting alternative rounding rules, since much of my SPSS >work requires using special rounding (e.g., round 0 down and anything >else up, rounding to various decimal places, etc.). I'm guessing, but I imagine it wasn't thought of because in numerical analysis (of which statistical computation is a special case) it's almost never advisable to round except for presenting results; and for that, 'rounding to the nearest' is almost always unambiguous. >I found a workaround using several lines of TRUNC and RND syntax. At the moment, that's probably the best you can do, though if it took several lines, there may be simplifications. And it may not matter to you, but while you can round to integers exactly, you usually can't round exactly to decimal fractions. That is, a number calculated as 3.85 probably differs from it by a tiny amount. For that reason in accounting systems using binary arithmetic, it's usual to keep amounts in cents, not dollars, so they can be represented exactly. I'm interested in why you need these, but you can put that down to excessive curiosity, if you like. Good luck to all, Richard |
Thank you! The curious are feeling better.
At 06:21 PM 9/7/2006, Lise Valentine wrote: >It may not be advisable to round, but that is what the Cook County >(Chicago) clerk does in calculating property tax rates. OK: it's a financial application. I hinted, I hope loudly enough, that those do have different rules. And, of course, whatever the rules are, you're stuck with them. >At different stages of the labyrinthine computations used to determine >property tax rates in this county, the clerk uses special rounding >rules, and different governments have different numbers of decimal >places in their rates, all of which are the sums of individual fund >rates which have been multiplied and divided by various things before >being summed. Like, you multiply rate a (which is such-and-such percent, to one decimal past the percent) by temporary tax-relief amount b (which is 0.91 this year, and goes to 0.92 next year until it expires in 2016), and get a current effective rate which has to be rounded to one decimal past the percent, ... ? I'm making that up, of course, but is that the right flavor? I feel your pain. And I've got no magic to solve it. A lot of times calculations like that will themselves generate fairly long decimal strings and the rounding rules won't matter much. But of course they insist that you get EXACTLY the results the rounding rules would give, not just very close. >I didn't make it up, I just have to replicate his system (done on an >archaic mainframe, not in SPSS) so I can then test hypothetical >changes to it when people come up with property tax reform proposals. It's not the system it was written on; it's the quality and cleanliness of the design, which sounds like it's awful. >I'd expected among all the bells and whistles that SPSS would allow me >to easily control rounding rules and truncation at various decimal >places, but alas. Good luck. And be careful with 'equality' comparisons, whether a digit is exactly 5. In a fraction, allow a little 'fuzz', like testing whether it's 5 within one part in 10,000, to avoid problems with the fraction you want, not being exactly representable. (And your predecessor may have some small bugs in his code through not taking the same precautions.) By the way, if it helps, if I wanted to round QUANTITY to three decimal places in SPSS, I'd do something like this, which is very careful: NUMERIC #FRACTION(F8.5). * Multiply QUANTITY by 1000, so you'll be rounding . * to an integer. Split the result into integer and . * fraction, very carefully: . COMPUTE QUANTITY = 1E3*QUANTITY. COMPUTE #FRACTION = QUANTITY. COMPUTE QUANTITY = TRUNC(QUANTITY). NUMERIC #ROUNDUP(F2). * Here "0.5" is within 1/10,000 of 0.5 . DO IF #FRACTION GT 0.5+1E-4. . COMPUTE #ROUNDUP = 1. ELSE IF #FRACTION LT 0.5-1E-4. . COMPUTE #ROUNDUP = 0. ELSE. * Here's the hard part: splitting the 5's: . * Here are alternatives: . * -- Round up: . . COMPUTE #ROUNDUP = 1. * -- Round to even: . . DO IF MOD(QUANTITY,2) EQ 0 /* Even */. . COMPUTE #ROUNDUP = 0. . ELSE. /* Odd */. . COMPUTE #ROUNDUP = 1. . END IF. * -- Or, implement other rounding rule. . END IF. COMPUTE QUANTITY = QUANTITY + #ROUNDUP. COMPUTE QUANTITY = QUANTITY/1E3. That last step loses the exactness of the rounding, though it introduces only a tiny possible error. END IF. |
In reply to this post by Patricia Rego
The University of Queensland (UQ) is a federally funded public
University. The university has a license for SPSS and many of its options. Patricia, the terms and costs for SPSS software are listed here: http://www.its.uq.edu.au/index.html?page=28041&pid=0 Queensland Health Skills Development Cenre is a state funded unit. I would expect that the needs and license costs might be differ to that of a public university?! Regards, Jason "Queensland Health Skills Development Centre is one of most technologically advanced and comprehensive skills development centres in the world. Opened jointly on 23 September 2004 by the Premier of Queensland, the Hon. Peter Beattie and the then Queensland Minister for Health, Hon. Gordon Nuttall, it is the only one of seven in Oceania to have a complete suite of virtual reality and simulation training equipment. It covers over 3500sqm, with 26 session rooms, laboratories, and even a fully-functional operating theatre and hospital ward. Based on the Herston Campus, the Skills Development Centre (SDC)provides healthcare professionals - doctors, nurses and allied health professionals - in Australia and Asia Pacific, tools and training to improve their skills and enhance the quality of patient care." |
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