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  • Originally posted by Herlock Sholmes View Post

    Yup as I expected. No proper answer. Strip away your arrogant bluster and we’re left with a bag of fresh air. Rather sad.
    It's been a pleasure, Sherlock.

    But, all good things must come to an end and I think we should knock it on the head in the interests of not demolishing Casebook.Org's bandwidth.

    Comment


    • Originally posted by Fleetwood Mac View Post

      Except that hasn't happened, Sherlock.

      Another example of your inability to comprehend what is put before you.
      It’s what you’ve attempted to do though (a failed emphatically of course)

      We can’t prove that Phillips minimum TOD was accurate; we can’t prove that Phillips minimum TOD was inaccurate. As I’ve been saying all along. Phillips doesn’t help us one single jot when assessing the witnesses. Therefore he is of no use to us.

      Point proven. (Well, it was actually proven days ago)

      Regards

      Sir Herlock Sholmes

      “It is useless to attempt to reason a man out of a thing he was never reasoned into.”

      Comment


      • Sorry George, I missed this.

        Originally posted by GBinOz View Post

        Hi Jon,

        I am also struggling with the concept that doctors in 1888 would shun the use of so valuable an instrument as the thermometer. Admittedly there is no mention of its use in any of the testimony, but there is also no mention of using a scalpel for the autopsy, so was it just too "nuts and bolts" to specify the methods and tools of trade.
        Exactly, the doctor is not required to justify how he reached his decision. Even the coroner will know that thermometers could/would/should be used, because they are available. If the time of death is critical a coroner might even ask if the thermometer was used, or perhaps he just expected it was used?

        harry kindly pointed to an article in Ripperologist #71 that seems to reinforce Jeff's opinion, but my mind's still a whorl at the very idea.
        Yes, 50% of us may expect it was used, the other 50% may not, but the evidence lacks direct reference to a thermometer, or to the doctor saying "it felt", or "I felt".

        I thought it is as well to just mention the obvious.
        A thermometer is designed for use in specific parts of the body, you can't just place it on the hand to take the temperature of a hand.
        Doctors did grasp the hand or touch the face, to feel if it was cold, but that is not because they didn't use thermometers in places where it was expected to be used, like in the brain, in the abdomen, under the arm and in the anal passage.
        Last edited by Wickerman; 08-08-2022, 09:35 PM.
        Regards, Jon S.

        Comment


        • Ok,

          I've just found an MSc thesis (in biology; red words are a link to it), that examines the accuracy of estimating ToD using the two most common methods. There's the Glaister Equation (98.7-InternalTemp)/1.5 = PMI (and the thesis notes that the 1.5 constant is often debated in the literature and people argue for all sorts of modifications, so if Dr. P used 1.5, and as we are still not settled on what the right value should be, more variation is introduced, and the margin of error increases; I've also seen it presented with other initial constants, like 98.6, 98.4, or 97.7, etc, again, introducing variation, and variation = error). The other is Henssge's Nomogram, which was not invented until around 1981 (a Nomogram is a graphical way to provide the solution to a complicated equation; basically draw some lines connecting things like body temp and ambient temperature, etc, and where they intersect gives your solution; the Nomogram gives a range i.e. X +-y hours), not a single value, while the Glaister Equation of course gives a single value, and it requires research to determine the range of error.

          I can't find a reference to when the Glaister Equation was first introduced, but I believe it was in the 1800s. It's certainly a simple equation, being linear, which means it has to be a pretty crude method since cooling is exponential, but that doesn't mean it isn't useful as it is intended to produce an estimation, not a "solution".

          Although Dr. Phillips would not have had access to the Henssge Nomogram, since it wasn't invented until nearly 100 years later, in the literature (such as the above thesis, and peer reviewed articles like this one, see the last line of the abstract), the HN is still considered the most accurate.

          Now, we've been wondering about the accuracy of these methods to estimate the ToD for intervals under 5 hours. The Glaister Equation is the only one that I think Dr. Phillips might have had access to (I know he didn't have the HN, which is considered more accurate, but we'll look at that anyway).

          The studies I've presented so far have only looked at post-mortem intervals (PMI) starting at 5 hours, and the margin of error for those is in the +-3 hour range. It has been suggested that those margins of error will not apply to shorter PMI, which I've agreed with, we don't know. The claim, however, is that the margin of error will get smaller, making the estimate more reliable, and I have suggested that may not be the case, it could be that the margin of error is smaller (approaching a limit of roughly +-1 hour), or it may be the margin of error gets larger (I mentioned that sometimes the body temperature increases post-mortem, sometimes it doesn't, and so that adds variation, which equals more error), or it may be that the +-3 we see is the margin of error for short intervals and it tends to increase over time, out to something like +-7 hours.

          Unfortunately, without actual evidence, I have no way of knowing which of those is true. From his posts I believe FM is quite sure that it gets smaller, but he has not provided any evidence to justify that surity.

          Anyway, I stumbled across this thesis (link at the start of this post), and the study involves taking temperature readings when the PMI was known in order to evaluate the accuracy of both the Glaister Equation and the Henssge's Nomogram. And fortunately, they cover the PMI of interest to us, they include PMI from 1 hour out to 12 hours. Note, they tested the Glaister Equation using /1.5 and /2.0, and found the latter to perform better overall. They considered the GE a "match" if the calculated time was within +-1 hour (note, that already covers our case, but hey, let's continue).

          On page 13 they show the following data.

          Click image for larger version  Name:	ToD_ShortInterval.jpg Views:	0 Size:	97.1 KB ID:	792022

          Now note something. Neither method is accurate for PMI less than 4 hours (so 0-3 hours, they are rubbish). The error in the ToD estimation does not get smaller for very short intervals, it gets worse! They look to be reasonable starting around 4 hours out to 10, hours, but even then the Glaisser Equation tends to always overestimate the PMI (although the by around 2.5 hours PMI, the tendency is to overestimate, but the actual ToD looks to fall in the error range at the low end of the HN, and in the low end of the +-1 hour margin of error for the Glaisser equation with /1.5, the one Dr. P. might have used, but overall the error was within 1 hour 4 times, and more than 1 hour 8 times).

          Also, on page 16, they found that the margin of error when the environment was cooler than 13C, results in even larger errors.

          In short, research shows that Dr. Phillips' estimate has to be viewed as having a wide margin of error, one that easily encompasses the ToD one would come to based upon the witness statements.

          Once again, I put to the group, there is no conflict between Dr. Phillips' estimate of the PMI and the ToD one derives from the witness statements. In short, there is no conflict between the witnesses and the expert medical testimony.

          - Jeff
          Last edited by JeffHamm; 08-08-2022, 10:18 PM.

          Comment


          • Originally posted by Abby Normal View Post

            no you know what is certain though Trevor?, is that posters like Doctored Whatsit can find the clues and you cant.
            But what the good Dr Watsit posted is nothing more than conjecture its not a clue. If i were you i would stick to playing cluedo that way you cant make yourself look foolish.

            www.trevormarriott.co.uk
            Last edited by Trevor Marriott; 08-08-2022, 10:07 PM.

            Comment


            • Originally posted by JeffHamm View Post
              Ok,

              I've just found an MSc thesis (in biology; red words are a link to it), that examines the accuracy of estimating ToD using the two most common methods. There's the Glaister Equation (98.7-InternalTemp)/1.5 = PMI (and the thesis notes that the 1.5 constant is often debated in the literature and people argue for all sorts of modifications, so if Dr. P used 1.5, and as we are still not settled on what the right value should be, more variation is introduced, and the margin of error increases; I've also seen it presented with other initial constants, like 98.6, 98.4, or 97.7, etc, again, introducing variation, and variation = error). The other is Henssge's Nomogram, which was not invented until around 1981 (a Nomogram is a graphical way to provide the solution to a complicated equation; basically draw some lines connecting things like body temp and ambient temperature, etc, and where they intersect gives your solution; the Nomogram gives a range i.e. X +-y hours), not a single value, while the Glaister Equation of course gives a single value, and it requires research to determine the range of error.

              I can't find a reference to when the Glaister Equation was first introduced, but I believe it was in the 1800s. It's certainly a simple equation, being linear, which means it has to be a pretty crude method since cooling is exponential, but that doesn't mean it isn't useful as it is intended to produce an estimation, not a "solution".

              Although Dr. Phillips would not have had access to the Henssge Nomogram, since it wasn't invented until nearly 100 years later, in the literature (such as the above thesis, and peer reviewed articles like this one, see the last line of the abstract), the HN is still considered the most accurate.

              Now, we've been wondering about the accuracy of these methods to estimate the ToD for intervals under 5 hours. The Glaister Equation is the only one that I think Dr. Phillips might have had access to (I know he didn't have the HN, which is considered more accurate, but we'll look at that anyway).

              The studies I've presented so far have only looked at post-mortem intervals (PMI) starting at 5 hours, and the margin of error for those is in the +-3 hour range. It has been suggested that those margins of error will not apply to shorter PMI, which I've agreed with, we don't know. The claim, however, is that the margin of error will get smaller, making the estimate more reliable, and I have suggested that may not be the case, it could be that the margin of error is smaller (approaching a limit of roughly +-1 hour), or it may be the margin of error gets larger (I mentioned that sometimes the body temperature increases post-mortem, sometimes it doesn't, and so that adds variation, which equals more error), or it may be that the +-3 we see is the margin of error for short intervals and it tends to increase over time, out to something like +-7 hours.

              Unfortunately, without actual evidence, I have no way of knowing which of those is true. From his posts I believe FM is quite sure that it gets smaller, but he has not provided any evidence to justify that surity.

              Anyway, I stumbled across this thesis (link at the start of this post), and the study involves taking temperature readings when the PMI was known in order to evaluate the accuracy of both the Glaister Equation and the Henssge's Nomogram. And fortunately, they cover the PMI of interest to us, they include PMI from 1 hour out to 12 hours. Note, they tested the Glaister Equation using /1.5 and /2.0, and found the latter to perform better overall. They considered the GE a "match" if the calculated time was within +-1 hour (note, that already covers our case, but hey, let's continue).

              On page 13 they show the following data.

              Click image for larger version Name:	ToD_ShortInterval.jpg Views:	0 Size:	97.1 KB ID:	792022

              Now note something. Neither method is accurate for PMI less than 4 hours (so 0-3 hours, they are rubbish). The error in the ToD estimation does not get smaller for intervals less than 5 hours, it gets worse! They look to be reasonable starting around 4 hours out to 10 or 12 hours, but under 4 hours they grossly overestimate the PMI.

              In short, research shows that Dr. Phillips' estimate has to be viewed as having a wide margin of error, one that easily encompasses the ToD one would come to based upon the witness statements.

              Once again, I put to the group, there is no conflict between Dr. Phillips' estimate of the PMI and the ToD one derives from the witness statements. In short, there is no conflict between the witnesses and the expert medical testimony.

              - Jeff
              Except for the fact that the witness testimony has not been tested, and on the face of it discrepancies are shown in that witness testimony

              www.trevormarriott.co.uk

              Comment


              • Now, if Dr. Phillips did take actual body temperature readings, which we have no indication that he did, but going with that assumption then is 2 hour estimate for the PMI means he must have measured a 3 degree drop in temperature (3/1.5 = 2; and that would be the version of the Glaisser Equation he would have access to).

                The thesis found that TempDrop/2 produced a more accurate estimate, so that means we can calculate that more accurate estimate ourselves, producing an estimated PMI of 1.5 hours (3/2 = 1.5 hours).

                And the witness based PMI is around 50 minutes to 1 hour, so the difference now between Dr. P and the witnesses is only 30-40 minutes, and even the very best modern equipment, based upon knowing the actual starting body temperature at the time of death, and knowing all the other factors that a murder case would not know, still had a margin of error of +-38 minutes (the previous article I've mentioned).

                Harry has mentioned that he cannot believe that Dr. P. could be off by 1 hour when estimating the PMI of 2 hours, but as the above data shows, at the shortest actual PMI (case 1), where the actual PMI was 1 hour, the estimate of the GE was roughly 7.5 hours! That's an overestimation of 6.5 hours! Overestimating by 1 hour is considered a match in this thesis (although only just).

                Seriously, we have to set our "common sense" aside. Common sense is what we use when we don't know how things work. Things are far more complicated than common sense leads us to believe. This is why we have to look at actual data, at actual measurements, and actual research, and not base our opinions on what we imagine. Human imagination creates fiction, and while that is wonderful entertainment, it is not useful for evaluating reality. Estimation of the PMI is a very complicated problem, and the methods we have even today are not precise, they have quite large margins of error. Dr. Phillips did not have the benefit of the 130+ years of research into this question, so there is no blame or negative criticism being placed upon him by simply pointing out his estimate is likely to have been an overestimate by an hour. In fact, I've said a few times now, I'm very impressed at how well his estimate corresponds to the other information we have, and from the information we have there is no conflict between any of them.

                And yes, that last statement is based upon also considering the witnesses to have some margin of error in their recollections of the time. I've suggested that a +-15 minute error in their stated time, which is probably being overly generous, but making it larger just makes it less possible to say there is a conflict. What I don't see is any indication that any of the witnesses "lied". Sure, Long's identification could be an error, but there's still Richardson and Cadosch. We would have to reject all 3 of them, at which point, we're still left with Dr. P's estimate that still allows for a ToD around 5:25 - we can't rule that out based upon Dr. P's statement. And given the witnesses provide information that we have no objective reason to dismiss, the most likely ToD based upon the information we have available to us is somewhere in the vicinity of 5:25.

                - Jeff

                Comment


                • Originally posted by Trevor Marriott View Post

                  Except for the fact that the witness testimony has not been tested, and on the face of it discrepancies are shown in that witness testimony

                  www.trevormarriott.co.uk
                  Hi Trevor,

                  I have acknowledged that a few times, and I agree with you. The problem is we cannot test their testimony. We do, however, have Richardson's legging spring found at the scene, which appears to corroborate his statement (yes, I know, it's not definitive, but nothing is in this case). We also have the fact he testifies he closed the door, but later the door was found open (Dr. W. I believe brought that to our attention), which again could be questioned but which on the face of it fits with someone leaving the property after Richarson. We don't, and never will, have proof, but what we have are a number of bits of information that show no obvious flaws in the major flow of the statements. We do have some conflict in the exact stated times of some events (most notably between Long's siting and Cadoch's trips to the loo), but those could easily be the result of the unreliable nature of such exact details obtained from eye witnesses, so we have to consider the possibility the witnesses are mistaken in detail only so that we don't throw the baby out with the bathwater.

                  In short, I'm not claiming this definitively proves the murder can only have happened at 5:25ish; nothing can do that anymore, and yes, it is entirely possible all the witnesses were wrong, and that Richardson lied, etc. But we have no evidence of that, only speculation based upon such things do sometimes happen. What we do have are a number of statements about how things were found (legging's spring; open door), that are consistent with Richardson's statement, and if we presume he's lying, those now have to be viewed as lucky coincidences. We turn what looks like corroboration into coincidence just so we can dismiss Richardson, and in my view that is unsafe and unwise.

                  Dr. Phillips estimation does not contradict the witnesses, removing the only real point of contention between the information we have to work with. I do not think it is a bad thing to keep an open mind, but I do think that the information we actually have to work with has to lead to the best working hypothesis is for a murder around 5:25ish, and that alternatives must be viewed as distant seconds (but not impossible). To argue for the less probable hypothesis is to bet on the long odds, and without something evidential (not simply could have lied, might have lied, could be wrong, might have misheard, etc) then one should acknowledge they're going against the information we have and working on a less supported possibility.

                  - Jeff

                  Comment


                  • Originally posted by Abby Normal View Post

                    umm no. what George "perfectly Illustrates" in his post is that, par for the course with him, he takes minor in consequential discrepencies and tries to blow them up into something nefarious, and that you and your ilk invariably follow along, and miss the important point that three witnesses independently corroberate a later tod.
                    Its the exact point that im making, and no surprise that you missed it.

                    your reply is actually Exhibit A in the case that you dont really understand posts, the subject matter at hand or how to correctly analyze the facts. even when they are served up to you on a platter.
                    Abby thats just nonsense, you clearly haven't been paying attention to this thread , start at the beginning an try follow whats actually been discussed on both sides . Try being constructive for a change instead of an ass.
                    'It doesn't matter how beautiful your theory is. It doesn't matter how smart you are . If it doesn't agree with experiment, its wrong'' . Richard Feynman

                    Comment


                    • Originally posted by JeffHamm View Post
                      Now, if Dr. Phillips did take actual body temperature readings, which we have no indication that he did, but going with that assumption then is 2 hour estimate for the PMI means he must have measured a 3 degree drop in temperature (3/1.5 = 2; and that would be the version of the Glaisser Equation he would have access to).

                      The thesis found that TempDrop/2 produced a more accurate estimate, so that means we can calculate that more accurate estimate ourselves, producing an estimated PMI of 1.5 hours (3/2 = 1.5 hours).

                      And the witness based PMI is around 50 minutes to 1 hour, so the difference now between Dr. P and the witnesses is only 30-40 minutes, and even the very best modern equipment, based upon knowing the actual starting body temperature at the time of death, and knowing all the other factors that a murder case would not know, still had a margin of error of +-38 minutes (the previous article I've mentioned).

                      Harry has mentioned that he cannot believe that Dr. P. could be off by 1 hour when estimating the PMI of 2 hours, but as the above data shows, at the shortest actual PMI (case 1), where the actual PMI was 1 hour, the estimate of the GE was roughly 7.5 hours! That's an overestimation of 6.5 hours! Overestimating by 1 hour is considered a match in this thesis (although only just).

                      Seriously, we have to set our "common sense" aside. Common sense is what we use when we don't know how things work. Things are far more complicated than common sense leads us to believe. This is why we have to look at actual data, at actual measurements, and actual research, and not base our opinions on what we imagine. Human imagination creates fiction, and while that is wonderful entertainment, it is not useful for evaluating reality. Estimation of the PMI is a very complicated problem, and the methods we have even today are not precise, they have quite large margins of error. Dr. Phillips did not have the benefit of the 130+ years of research into this question, so there is no blame or negative criticism being placed upon him by simply pointing out his estimate is likely to have been an overestimate by an hour. In fact, I've said a few times now, I'm very impressed at how well his estimate corresponds to the other information we have, and from the information we have there is no conflict between any of them.

                      And yes, that last statement is based upon also considering the witnesses to have some margin of error in their recollections of the time. I've suggested that a +-15 minute error in their stated time, which is probably being overly generous, but making it larger just makes it less possible to say there is a conflict. What I don't see is any indication that any of the witnesses "lied". Sure, Long's identification could be an error, but there's still Richardson and Cadosch. We would have to reject all 3 of them, at which point, we're still left with Dr. P's estimate that still allows for a ToD around 5:25 - we can't rule that out based upon Dr. P's statement. And given the witnesses provide information that we have no objective reason to dismiss, the most likely ToD based upon the information we have available to us is somewhere in the vicinity of 5:25.

                      - Jeff
                      Sterling work Mr. Hamm. If I was wearing a hat I’d take it off to you. Without wishing to sound like I’m gloating (much) this really is the final nail-in-the-coffin for the suggestion that we can dismiss the witnesses on the basis of Phillips estimate. Your research and post had proved this beyond any doubt at all. I’m not easily amazed but if anyone now stands up and tries to dispute this I’ll be gobsmacked. So from some one poster we’ve had the “well Phillips was a competent Doctor” argument, we’ve even had it suggested that we should accept Phillips estimate via some kind of courtesy. We seen and heard all manner of desperation now surely the only honest response to your information should be an unconditional concession….

                      We cannot dismiss the witnesses in the basis of Phillips estimate. On this particular point it’s game over.
                      Regards

                      Sir Herlock Sholmes

                      “It is useless to attempt to reason a man out of a thing he was never reasoned into.”

                      Comment


                      • Originally posted by Herlock Sholmes View Post

                        Sterling work Mr. Hamm. If I was wearing a hat I’d take it off to you. Without wishing to sound like I’m gloating (much) this really is the final nail-in-the-coffin for the suggestion that we can dismiss the witnesses on the basis of Phillips estimate. Your research and post had proved this beyond any doubt at all. I’m not easily amazed but if anyone now stands up and tries to dispute this I’ll be gobsmacked. So from some one poster we’ve had the “well Phillips was a competent Doctor” argument, we’ve even had it suggested that we should accept Phillips estimate via some kind of courtesy. We seen and heard all manner of desperation now surely the only honest response to your information should be an unconditional concession….

                        We cannot dismiss the witnesses in the basis of Phillips estimate. On this particular point it’s game over.
                        But we cannot readily accept them either, so in effect the whole Chapman case is inconclusive as to the time of death, and in the grand scheme of things it is readily accepted that her killer was JTR so lests bring all of these pointless arguments to a close.

                        www.trevormarriott.co.uk

                        Comment


                        • Originally posted by Herlock Sholmes View Post

                          That’s fine. You accept that Phillips could have been wrong.
                          Yes just as he could have been right ,as you yourself have mentioned, . And the same goes for the witnesses. Bingo we agree .

                          Did you get that Abby, the whole point of the topic from my first post.

                          Its not a contest whos wrong or right its only peoples opinions . The truth of the matter can never be determined one way or the other.based on the uncertainty evidence at hand .
                          'It doesn't matter how beautiful your theory is. It doesn't matter how smart you are . If it doesn't agree with experiment, its wrong'' . Richard Feynman

                          Comment


                          • Ok, one last bit. I've extracted the values from their figure (shown above in my post 1369). I've calculated the error between the actual PMI and the estimated value from the Glaisser Equation (/1.5 version) for the 12 cases they present.

                            I've calculated the average error between the estimated PMI and the actual PMI for all cases where the actual PMI is less than 3, between 3 and 6 hours, and greater than 6 hours (which, as there are only 2 of those, are at 10h).

                            Here's the error (positive values mean the estimate overestimates by this much, a negative value means an underestimation of the real PMI).
                            Actual.....AverageError.........................Nu mber of cases:
                            <3..........5.6 hours.......................................4
                            3-6.........0.9 hours (54 minutes) ...................6
                            >6..........3.1 hours.......................................2

                            The average error for the entire data set was 2.86 hours. Note, at all PMI, the tendency is to overestimate the true PMI, and that overestimation is by a lot for very short PMI, improves for 3-6 hours (but still overestimates by just short of an hour), and may get worse beyond that.

                            This is a pretty small data set, but so far it is the only data set I've come across that looks at actual PMI intervals that correspond to what we appear to be dealing with, and there is no indication the precision gets better for very short PMI, rather it points to the opposite conclusion, that the estimations tend to be large overestimations early on, settle towards a smaller overestimation, and may then start to get worse again.

                            Anyway, unless I happen across another, and larger, data set covering this period I don't think there's much more I can add. I think I've been transparent in both my interpretations, the basis upon which I derive them, and why I often suggest that things probably don't work the way we feel they should. Having done research for some time now I've come to realize that common sense is really just another way to say we're confident in our ignorance. I still fall for that myself as, despite all evidence to the contrary, I am actually human.

                            - Jeff

                            Comment


                            • Originally posted by Herlock Sholmes View Post

                              Sterling work Mr. Hamm. If I was wearing a hat I’d take it off to you. Without wishing to sound like I’m gloating (much) this really is the final nail-in-the-coffin for the suggestion that we can dismiss the witnesses on the basis of Phillips estimate. Your research and post had proved this beyond any doubt at all. I’m not easily amazed but if anyone now stands up and tries to dispute this I’ll be gobsmacked. So from some one poster we’ve had the “well Phillips was a competent Doctor” argument, we’ve even had it suggested that we should accept Phillips estimate via some kind of courtesy. We seen and heard all manner of desperation now surely the only honest response to your information should be an unconditional concession….

                              We cannot dismiss the witnesses in the basis of Phillips estimate. On this particular point it’s game over.
                              agree on all points. good job Jeff and thanks for posting all this excellent research. and yes herlock it really is game over!
                              "Is all that we see or seem
                              but a dream within a dream?"

                              -Edgar Allan Poe


                              "...the man and the peaked cap he is said to have worn
                              quite tallies with the descriptions I got of him."

                              -Frederick G. Abberline

                              Comment


                              • Originally posted by JeffHamm View Post
                                Ok, one last bit. I've extracted the values from their figure (shown above in my post 1369). I've calculated the error between the actual PMI and the estimated value from the Glaisser Equation (/1.5 version) for the 12 cases they present.

                                I've calculated the average error between the estimated PMI and the actual PMI for all cases where the actual PMI is less than 3, between 3 and 6 hours, and greater than 6 hours (which, as there are only 2 of those, are at 10h).

                                Here's the error (positive values mean the estimate overestimates by this much, a negative value means an underestimation of the real PMI).
                                Actual.....AverageError.........................Nu mber of cases:
                                <3..........5.6 hours.......................................4
                                3-6.........0.9 hours (54 minutes) ...................6
                                >6..........3.1 hours.......................................2

                                The average error for the entire data set was 2.86 hours. Note, at all PMI, the tendency is to overestimate the true PMI, and that overestimation is by a lot for very short PMI, improves for 3-6 hours (but still overestimates by just short of an hour), and may get worse beyond that.

                                This is a pretty small data set, but so far it is the only data set I've come across that looks at actual PMI intervals that correspond to what we appear to be dealing with, and there is no indication the precision gets better for very short PMI, rather it points to the opposite conclusion, that the estimations tend to be large overestimations early on, settle towards a smaller overestimation, and may then start to get worse again.

                                Anyway, unless I happen across another, and larger, data set covering this period I don't think there's much more I can add. I think I've been transparent in both my interpretations, the basis upon which I derive them, and why I often suggest that things probably don't work the way we feel they should. Having done research for some time now I've come to realize that common sense is really just another way to say we're confident in our ignorance. I still fall for that myself as, despite all evidence to the contrary, I am actually human.

                                - Jeff
                                thanks for all the info and insight Jeff. much appreciated!
                                "Is all that we see or seem
                                but a dream within a dream?"

                                -Edgar Allan Poe


                                "...the man and the peaked cap he is said to have worn
                                quite tallies with the descriptions I got of him."

                                -Frederick G. Abberline

                                Comment

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