# Stats Question

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## Stats Question

 Dear List: I have a data set which provides me with the time it took an individual to evacuate from the WTCs on 9 /  11. (Time they reached street level minus time they started to evacuate). Currently the research team is debating how to calculate the rate of evacuation. One school of thought is to divide the time of evacuation (End time minus begin time) by the floor the individual started on. The other school of thought is to use the time itself as the outcome (End Time minus begin time)  and use the floor they started on as control variable (in regression). I would be interested in how other folks would view this situation. As always I very much appreciate the time and thoughts of other individuals.  thank you. martin sherman Martin F. Sherman, Ph.D. Professor of Psychology Director of Masters Education: Thesis Track Loyola College 222 B Beatty Hall 4501 North Charles Street Baltimore, MD 21210 410 617-2417 (Office) 410 617-5341 (FAX) [hidden email]
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 Hi Martin, I am rather with the Second School - I see no reason why the evacuation time should be directly proportional to the floor number, as the First School seems to take for granted. I would rather expect a relation in form expected evacuation time = mean time for reaching the staircase + possibly non-linear function of the floor number ...which can be better fitted using a regression in the form suggested by the Second School of Thought :-) Greetings Jan -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Martin Sherman Sent: Thursday, June 22, 2006 3:07 PM To: [hidden email] Subject: Stats Question Dear List: I have a data set which provides me with the time it took an individual to evacuate from the WTCs on 9 /  11. (Time they reached street level minus time they started to evacuate). Currently the research team is debating how to calculate the rate of evacuation. One school of thought is to divide the time of evacuation (End time minus begin time) by the floor the individual started on. The other school of thought is to use the time itself as the outcome (End Time minus begin time)  and use the floor they started on as control variable (in regression). I would be interested in how other folks would view this situation. As always I very much appreciate the time and thoughts of other individuals.  thank you. martin sherman Martin F. Sherman, Ph.D. Professor of Psychology Director of Masters Education: Thesis Track Loyola College 222 B Beatty Hall 4501 North Charles Street Baltimore, MD 21210 410 617-2417 (Office) 410 617-5341 (FAX) [hidden email]
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## Re: Stats Question

 In reply to this post by msherman Martin: I see this as a case of censored data. You are underestimating evacuation time if those who did not survive are not counted. It the towers had resisted the attack, the mean evacuation time would have been higher than that computed only with the data from the surviving people. May be Cox's regression can help you. About the use of the floor number as a covariate, I think it's a good idea. Any action you take would be speculative. Why not take a common start time for all the people on tower 1 and another for tower 2 (the time when the planes crashed), and all data from the people who did not survive are censored at the time when each tower fell down? Greetings Frederic %%%%%%%%%%%%%%%%%%%%%%% Frederic Villamayor Unitat de Bioestadística Àrea de Desenvolupament Preclínic CIDF Ferrer Grupo Juan de Sada, 32 08028 - Barcelona Espanya E-mail: [hidden email] Tel: +34 935093236 Fax: +34 934112764 WWW: www.ferrergrupo.com %%%%%%%%%%%%%%%%%%%%%%% "Sanity is not statistical" 1984 (George Orwell) Martin Sherman <[hidden email]> Enviado por: "SPSSX(r) Discussion" <[hidden email]> 22/06/2006 15:07 Por favor, responda a Martin Sherman <[hidden email]> Para [hidden email] cc Asunto [SPSSX-L] Stats Question Dear List: I have a data set which provides me with the time it took an individual to evacuate from the WTCs on 9 /  11. (Time they reached street level minus time they started to evacuate). Currently the research team is debating how to calculate the rate of evacuation. One school of thought is to divide the time of evacuation (End time minus begin time) by the floor the individual started on. The other school of thought is to use the time itself as the outcome (End Time minus begin time)  and use the floor they started on as control variable (in regression). I would be interested in how other folks would view this situation. As always I very much appreciate the time and thoughts of other individuals.  thank you. martin sherman Martin F. Sherman, Ph.D. Professor of Psychology Director of Masters Education: Thesis Track Loyola College 222 B Beatty Hall 4501 North Charles Street Baltimore, MD 21210 410 617-2417 (Office) 410 617-5341 (FAX) [hidden email]
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## Re: Stats Question

 In reply to this post by msherman A "rate of evacuation" may be defined in different ways, depending on purpose of the exercise. One reasonable way would be to define it as "velocity of descent", equivalent to time per floor. The rate would be simply total time (start to exit) divided number of floors. If this average is called b, you will have b=total time/number of floors and therefore total time = b(number of floors), irrespective of the starting floor. The other approach you suggest is computing a regression equation in the form Total time = b0 + b1(number of floors). This differs from the previous one in the presence of b0, i.e. a certain constant time that is independent of the starting floor. There might be some substantive reason to think that b0 is not zero. For instance, people may have to negotiate one (or a number of) "difficult" floors requiring more time than the regular cruising speed of descent for the remaining floors. The relative importance of b0 on total time (b0/total time) would be inversely proportional to the number of floors to descend. The first approach, instead, assumes that the number of "difficult" floors is proportional to total number of floors, and therefore its relative importance is zero or constant irrespective of the starting floor. Trying the two approaches may put these contrasting "schools of thought" to the test. If b0 is significantly different from zero, the second school is right, otherwise it is the first one. What if b0 is negative? It would mean that there were some "easy" floors that were descended at more than regular speed, such as for instance the last few floors before reaching ground zero. With a few refinements, the model may test also this possibility along with the "difficult floors" hypothesis, because both or any of them may have been present. All in all, this line of inquiry would require the second approach. To test the easy and difficult floor hypotheses separately one may need to use a more complicated functional form, instead of the simple regression mentioned before. Otherwise what one gets is the net effect of the two (a zero value for b0 may mean that the delay caused by difficult floors was offset by the presence of especially easy floors, and thus b0=0 may not mean absence of difficult floors unequivocally). Hope this helps. Hector -----Mensaje original----- De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Martin Sherman Enviado el: Thursday, June 22, 2006 10:07 AM Para: [hidden email] Asunto: Stats Question Dear List: I have a data set which provides me with the time it took an individual to evacuate from the WTCs on 9 /  11. (Time they reached street level minus time they started to evacuate). Currently the research team is debating how to calculate the rate of evacuation. One school of thought is to divide the time of evacuation (End time minus begin time) by the floor the individual started on. The other school of thought is to use the time itself as the outcome (End Time minus begin time)  and use the floor they started on as control variable (in regression). I would be interested in how other folks would view this situation. As always I very much appreciate the time and thoughts of other individuals.  thank you. martin sherman Martin F. Sherman, Ph.D. Professor of Psychology Director of Masters Education: Thesis Track Loyola College 222 B Beatty Hall 4501 North Charles Street Baltimore, MD 21210 410 617-2417 (Office) 410 617-5341 (FAX) [hidden email]
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## Re: Stats Question

 In reply to this post by Frederic Villamayor Forcada Frederic, Great idea about using Cox. However, your reasoning applies only to people that could possibly start descent. All people in or above the floors where the planes crashed into were not able to do so, and possibly also many or all the people in the floor/s immediately below, because of the destruction around that may have killed some of the people instantly, destroyed access to stairs, or left people otherwise unable to start descending. The situation is similar to a medical study on survival time after successful heart surgery. People who died on the operating table without having their surgery successfully completed should not actually be counted, I suppose. Hector Maletta -----Mensaje original----- De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Frederic Villamayor Forcada Enviado el: Thursday, June 22, 2006 11:08 AM Para: [hidden email] Asunto: Re: Stats Question Martin: I see this as a case of censored data. You are underestimating evacuation time if those who did not survive are not counted. It the towers had resisted the attack, the mean evacuation time would have been higher than that computed only with the data from the surviving people. May be Cox's regression can help you. About the use of the floor number as a covariate, I think it's a good idea. Any action you take would be speculative. Why not take a common start time for all the people on tower 1 and another for tower 2 (the time when the planes crashed), and all data from the people who did not survive are censored at the time when each tower fell down? Greetings Frederic %%%%%%%%%%%%%%%%%%%%%%% Frederic Villamayor Unitat de Bioestadística Àrea de Desenvolupament Preclínic CIDF Ferrer Grupo Juan de Sada, 32 08028 - Barcelona Espanya E-mail: [hidden email] Tel: +34 935093236 Fax: +34 934112764 WWW: www.ferrergrupo.com %%%%%%%%%%%%%%%%%%%%%%% "Sanity is not statistical" 1984 (George Orwell) Martin Sherman <[hidden email]> Enviado por: "SPSSX(r) Discussion" <[hidden email]> 22/06/2006 15:07 Por favor, responda a Martin Sherman <[hidden email]> Para [hidden email] cc Asunto [SPSSX-L] Stats Question Dear List: I have a data set which provides me with the time it took an individual to evacuate from the WTCs on 9 /  11. (Time they reached street level minus time they started to evacuate). Currently the research team is debating how to calculate the rate of evacuation. One school of thought is to divide the time of evacuation (End time minus begin time) by the floor the individual started on. The other school of thought is to use the time itself as the outcome (End Time minus begin time)  and use the floor they started on as control variable (in regression). I would be interested in how other folks would view this situation. As always I very much appreciate the time and thoughts of other individuals.  thank you. martin sherman Martin F. Sherman, Ph.D. Professor of Psychology Director of Masters Education: Thesis Track Loyola College 222 B Beatty Hall 4501 North Charles Street Baltimore, MD 21210 410 617-2417 (Office) 410 617-5341 (FAX) [hidden email]
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## Re: Stats Question

 In reply to this post by Hector Maletta Hector, I'd just want to remark that what you are defining of "velocity of descent" is not a velocity, but a period (time elapsing between the beginning and the end of a cycle). Velocity is inversely proportional to period, and period is defined in time units. I'd like to think in a rate of evacuation as something that increases as evacuation is quicker. Otherwise it is confusing. Greetings Frederic %%%%%%%%%%%%%%%%%%%%%%% Frederic Villamayor Unitat de Bioestadística Àrea de Desenvolupament Preclínic CIDF Ferrer Grupo Juan de Sada, 32 08028 - Barcelona Espanya E-mail: [hidden email] Tel: +34 935093236 Fax: +34 934112764 WWW: www.ferrergrupo.com %%%%%%%%%%%%%%%%%%%%%%% "Sanity is not statistical" 1984 (George Orwell) Hector Maletta <[hidden email]> Enviado por: "SPSSX(r) Discussion" <[hidden email]> 22/06/2006 16:10 Por favor, responda a Hector Maletta <[hidden email]> Para [hidden email] cc Asunto Re: [SPSSX-L] Stats Question A "rate of evacuation" may be defined in different ways, depending on purpose of the exercise. One reasonable way would be to define it as "velocity of descent", equivalent to time per floor. The rate would be simply total time (start to exit) divided number of floors. If this average is called b, you will have b=total time/number of floors and therefore total time = b(number of floors), irrespective of the starting floor. The other approach you suggest is computing a regression equation in the form Total time = b0 + b1(number of floors). This differs from the previous one in the presence of b0, i.e. a certain constant time that is independent of the starting floor. There might be some substantive reason to think that b0 is not zero. For instance, people may have to negotiate one (or a number of) "difficult" floors requiring more time than the regular cruising speed of descent for the remaining floors. The relative importance of b0 on total time (b0/total time) would be inversely proportional to the number of floors to descend. The first approach, instead, assumes that the number of "difficult" floors is proportional to total number of floors, and therefore its relative importance is zero or constant irrespective of the starting floor. Trying the two approaches may put these contrasting "schools of thought" to the test. If b0 is significantly different from zero, the second school is right, otherwise it is the first one. What if b0 is negative? It would mean that there were some "easy" floors that were descended at more than regular speed, such as for instance the last few floors before reaching ground zero. With a few refinements, the model may test also this possibility along with the "difficult floors" hypothesis, because both or any of them may have been present. All in all, this line of inquiry would require the second approach. To test the easy and difficult floor hypotheses separately one may need to use a more complicated functional form, instead of the simple regression mentioned before. Otherwise what one gets is the net effect of the two (a zero value for b0 may mean that the delay caused by difficult floors was offset by the presence of especially easy floors, and thus b0=0 may not mean absence of difficult floors unequivocally). Hope this helps. Hector -----Mensaje original----- De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Martin Sherman Enviado el: Thursday, June 22, 2006 10:07 AM Para: [hidden email] Asunto: Stats Question Dear List: I have a data set which provides me with the time it took an individual to evacuate from the WTCs on 9 /  11. (Time they reached street level minus time they started to evacuate). Currently the research team is debating how to calculate the rate of evacuation. One school of thought is to divide the time of evacuation (End time minus begin time) by the floor the individual started on. The other school of thought is to use the time itself as the outcome (End Time minus begin time)  and use the floor they started on as control variable (in regression). I would be interested in how other folks would view this situation. As always I very much appreciate the time and thoughts of other individuals.  thank you. martin sherman Martin F. Sherman, Ph.D. Professor of Psychology Director of Masters Education: Thesis Track Loyola College 222 B Beatty Hall 4501 North Charles Street Baltimore, MD 21210 410 617-2417 (Office) 410 617-5341 (FAX) [hidden email]
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 In reply to this post by Spousta Jan Hi SJ> Perhaps I understand it wrong, but as far as I know, for Cox SJ> regression you would need data even about the dead persons - from SJ> which floor they started to evacuate, how much time they spent SJ> during  the evacuation before the structure collapsed, and all SJ> other predictors known about the survivors. I fear that this will SJ> be a big problem here - you cannot interview these people. :-( I didn't follow the thread until now. Jan is absolutely right, you are missing the information about "uncensored" cases. Regards, Marta
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 Hi all. As Hector noted yesterday, people in the crash floors and higher floors could not escape to its fate. They did not evacuate, so they are not included in the study. But people from the lower flors had the possibility to evacuate. I do not know if there are data available, but I'd for each of these persons it should be known:         Which was the floor where they were at the moment of the crash?         Did they reach the ground floor?         When? As I suggested yesterday, evacuation time could be approximated by the time from the crash to the arrival at the ground floor. Censoring time would be the time until the final building falling down. As deads cannot be interviewed nothing more than approximations can be done. With this data, Cox's regression can be applied, and the different covariates can be assessed. I've never used Cox's regression. Please, you wiser co-listers let us know if my reasoning is wrong. HTH Frederic %%%%%%%%%%%%%%%%%%%%%%% Frederic Villamayor Unitat de Bioestadística Àrea de Desenvolupament Preclínic CIDF Ferrer Grupo Juan de Sada, 32 08028 - Barcelona Espanya E-mail: [hidden email] Tel: +34 935093236 Fax: +34 934112764 WWW: www.ferrergrupo.com %%%%%%%%%%%%%%%%%%%%%%% "Sanity is not statistical" 1984 (George Orwell) Marta García-Granero <[hidden email]> Enviado por: "SPSSX(r) Discussion" <[hidden email]> 23/06/2006 09:53 Por favor, responda a Marta García-Granero              <[hidden email]> Para [hidden email] cc Asunto Re: [SPSSX-L] Stats Question Hi SJ> Perhaps I understand it wrong, but as far as I know, for Cox SJ> regression you would need data even about the dead persons - from SJ> which floor they started to evacuate, how much time they spent SJ> during  the evacuation before the structure collapsed, and all SJ> other predictors known about the survivors. I fear that this will SJ> be a big problem here - you cannot interview these people. :-( I didn't follow the thread until now. Jan is absolutely right, you are missing the information about "uncensored" cases. Regards, Marta
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## Re: Stats Question

 In reply to this post by Frederic Villamayor Forcada I do not remember whether I expressed it right. My idea was about time elapsed divided number of floors, i.e. time per floor, which is the reciprocal of velocity (floors per unit of time). Hector -----Mensaje original----- De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Frederic Villamayor Forcada Enviado el: Friday, June 23, 2006 4:31 AM Para: [hidden email] Asunto: Re: Stats Question Hector, I'd just want to remark that what you are defining of "velocity of descent" is not a velocity, but a period (time elapsing between the beginning and the end of a cycle). Velocity is inversely proportional to period, and period is defined in time units. I'd like to think in a rate of evacuation as something that increases as evacuation is quicker. Otherwise it is confusing. Greetings Frederic %%%%%%%%%%%%%%%%%%%%%%% Frederic Villamayor Unitat de Bioestadística Àrea de Desenvolupament Preclínic CIDF Ferrer Grupo Juan de Sada, 32 08028 - Barcelona Espanya E-mail: [hidden email] Tel: +34 935093236 Fax: +34 934112764 WWW: www.ferrergrupo.com %%%%%%%%%%%%%%%%%%%%%%% "Sanity is not statistical" 1984 (George Orwell) Hector Maletta <[hidden email]> Enviado por: "SPSSX(r) Discussion" <[hidden email]> 22/06/2006 16:10 Por favor, responda a Hector Maletta <[hidden email]> Para [hidden email] cc Asunto Re: [SPSSX-L] Stats Question A "rate of evacuation" may be defined in different ways, depending on purpose of the exercise. One reasonable way would be to define it as "velocity of descent", equivalent to time per floor. The rate would be simply total time (start to exit) divided number of floors. If this average is called b, you will have b=total time/number of floors and therefore total time = b(number of floors), irrespective of the starting floor. The other approach you suggest is computing a regression equation in the form Total time = b0 + b1(number of floors). This differs from the previous one in the presence of b0, i.e. a certain constant time that is independent of the starting floor. There might be some substantive reason to think that b0 is not zero. For instance, people may have to negotiate one (or a number of) "difficult" floors requiring more time than the regular cruising speed of descent for the remaining floors. The relative importance of b0 on total time (b0/total time) would be inversely proportional to the number of floors to descend. The first approach, instead, assumes that the number of "difficult" floors is proportional to total number of floors, and therefore its relative importance is zero or constant irrespective of the starting floor. Trying the two approaches may put these contrasting "schools of thought" to the test. If b0 is significantly different from zero, the second school is right, otherwise it is the first one. What if b0 is negative? It would mean that there were some "easy" floors that were descended at more than regular speed, such as for instance the last few floors before reaching ground zero. With a few refinements, the model may test also this possibility along with the "difficult floors" hypothesis, because both or any of them may have been present. All in all, this line of inquiry would require the second approach. To test the easy and difficult floor hypotheses separately one may need to use a more complicated functional form, instead of the simple regression mentioned before. Otherwise what one gets is the net effect of the two (a zero value for b0 may mean that the delay caused by difficult floors was offset by the presence of especially easy floors, and thus b0=0 may not mean absence of difficult floors unequivocally). Hope this helps. Hector -----Mensaje original----- De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Martin Sherman Enviado el: Thursday, June 22, 2006 10:07 AM Para: [hidden email] Asunto: Stats Question Dear List: I have a data set which provides me with the time it took an individual to evacuate from the WTCs on 9 /  11. (Time they reached street level minus time they started to evacuate). Currently the research team is debating how to calculate the rate of evacuation. One school of thought is to divide the time of evacuation (End time minus begin time) by the floor the individual started on. The other school of thought is to use the time itself as the outcome (End Time minus begin time)  and use the floor they started on as control variable (in regression). I would be interested in how other folks would view this situation. As always I very much appreciate the time and thoughts of other individuals.  thank you. martin sherman Martin F. Sherman, Ph.D. Professor of Psychology Director of Masters Education: Thesis Track Loyola College 222 B Beatty Hall 4501 North Charles Street Baltimore, MD 21210 410 617-2417 (Office) 410 617-5341 (FAX) [hidden email]
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 In reply to this post by Frederic Villamayor Forcada I saw the original posting and then watched the exchanges about how to work this problem. I'd like to ask a really basic question, more out of curiosity than anything else. The question is where did these data come from? I read the popularly published account of the attack (the name of which I forget) and find it kind of hard to believe that people could recall very accurately when they started down and when they hit the 'ground floor' however you define that. I doubt also that there were 'official' records of people coming down. To the extent that the accounts in the book are accurate, I'd also think that one's velocity down the stairs depended on when one started down. Velocity would have slowed as volume increased and as rescue people started up. But, mainly, I'm curious of the circumstances of the data's collection. Gene Maguin