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a) Why should the stated values of A0, A1, A2, A3 ad A4 be taken for granted? b) How can I be sure (after taking stated facts for granted) that helium was produced in nuclear reactions taking place in cathodes? The purpose of statistical protocols, as far as I know, is not to answer that kind of questions. Such protocols are designed to deal with random experimental errors. For example, is a relation inferred from experimental data real or apparent (caused by randomness)? Robert’s protocol, in step 9, mentions the confidence level of 95%. What does the concept “level of confidence” mean? Statisticians deal with samples but their pronouncements refer to populations from which samples are taken. Levels of confidence tell us how reliable such pronouncements are. Samples of larger sizes usually correspond to more reliable inferences than samples of smaller sizes. The important point is that statistical protocols are used to validate statements about populations, not about samples. In the situation described by Robert samples (experimental values of A0, A1, A2, A3 and A4) are taken for granted. His protocol can then be used to validate the claim of proportionality. Is the amount of helium really proportional to the duration of electrolysis (under specified conditions) or is the inferred proportionality apparent? After all, other kinds of relations, such as quadratic, cubic or exponential, are also possible. In that context a statistical protocol could be useful. But questions (a) and (b) above are not statistical. I do not think that a statistical protocol would help me to answer them. To decide about (a) I would ask about work of other scientists; do they also observe similar facts? To decide about (b) I would ask about other indicators of nuclear processes, for example, about excess heat, or about tritium. Experimental data are usually easier to accept when they are consistent with confirmed theories. But, according to scientific methodology, theories should be justified by experimental data, not the other way around. 4) Appended on 7/23/05:A newspaper may refer to a confidence level while describing a gallup poll. Suppose that a random sample consists of 15,300 questioners collected from a very large population of potential voters. After using a protocol a statistician makes a prediction (an inference based on the sample) that the election will be won by X. The level of confidence, such as 95%, refers to a particular prediction about the entire population; it does not refer to the sample. Suppose that 8307 of questioned voters said that they will vote for X. The statistician would probably assume that only a negligible error, if any, was made in extracting this number from the pile of returned 15,300 questioners. Numbers, like 15,300 and 8,307, are assumed to be exact. But the inference made from the sample might not be very reliable. In that respect the situation described by Robert is different. Each of the five numbers (five laboratory measurements: A0, A1, A2, A3 and A4) is always associated with random errors, such as 5% or 25%. The bar of error associated with a single laboratory measurement depends on the instrument used; it can be determined by a technician after performing measurements on many samples containing the same amount of helium. Systematic errors can be minimized, if not totally eliminated, through frequent calibrations of laboratory instruments. But random errors are always associated with results of single measurements. That seems to an important difference between samples of physicists and samples of sociologists. Suppose the goal is to decide whether or not the true relation between the amounts of helium ( A _{k}) and durations of electrolysis
(t_{k}) is linear. That is an inference and the concept of level of confidence is applicable. Results of five laboratory measurements of
A_{k}, when plotted against durations, usually do not fall on a straight line. That is why bars of errors, associated with numbers, become
important. The initial hypothesis is that the relation is linear. But then it is either accepted or rejected, acccording to known error bars.
It is impossible to be 100% certain that the true relation is linear (or quadratic, cubic, etc.) when error bars are very large. Yes, I know that
most readers are familiar with all this. Before finishing these observations let me focus on another well known fact. Physicists make inferences about laws of nature. Such laws are either deterministic or probabilistic. The field of cold fusion has no laws; only working hypothesis, based on irreproducible data. Are these hypotheses deterministic or probabilistic? How can an error bar be associated with the result of a single irreproducible measurement? I do not know how to answer that question. But I can think about a similar situation in sociology. Suppose a survey is conducted to predict the result of an election. A social scientist uses a protocol and makes a statement that 57% (plus or minus 5%) people support X. The level of confidence of that inference, is said to be 95%. Then a scandalous revelation about X appears in the news and less than 1% of people actually vote for X on the election day. Does this mean that the protocol was faulty? Not at all. The protocol is based on the assumption that the conditions influencing people to vote, one way or another, do not change significantly. Behavior of social groups becomes unpredictable when such conditions change frequently. Essential conditions on which successful observations of cold fusion phenomena, such as generation of helium, depend have not yet been recognized. Presumably these conditions change frequently without our ability to control them. That is how irreproducibility is usually interpreted by cold fusion researchers. In my opinion inferences (based on logically derived protocols, or on Mont Carlo codes, are useless when one is dealing with irreproducible data. Identifying essential conditions, and finding ways of controlling them, should be the number one priority of cold fusion researchers. Everything else, including attempts to commercialize “magic devices,” should wait till experimental data become reproducible. Yes, I know that everybody knows this. 5) Appended on 7/24: I have no doubt that both RobertÕs protocols were written under the assumption that experimental data are reproducible. That would certainly apply to generation of oxygen (rather than helium) during ordinary electrolysis of water. In one of my messages about the first protocol I wrote that the Òmuch larger thanÓ seems to be too vague to be associated with the single level of confidence. The reply is worth quoting. Ludwik, Thanks for pointing out that there is some vagueness in the original 2002 Bockris-Bass-McKubre (BBM) Protocol <http://www.lenr-canr.org/acrobat/BassRWfivefrozen.pdf> as published in JNE by me alone, before Mike McKubre suggested the improvements in generality leading to our ICCF10 version [attached], which would benefit from clarification. I was tacitly assuming that any randomness in the errors is a Gaussian stochastic process. Also I should not have assumed that dA > 0 so I should have written |dA| instead of dA in the first test. In that case, if one accepts the approximate sample value of sigma as an "estimator" for the Standard Deviation sigma, then One Sigma gives a 68% Confidence Limit and Two Sigma gives a 95% Confidence Limit, and Three Sigma gives a 99.7% Confidence Limit, etc.So, my first test |dA| << delta-Ashould be understood as a preliminary test to ensure that sigma has a good chance of being a fair estimator, i.e. the "bias" dA should be negligible in comparison to the real quantity of interest, namely delta-A. Therefore by " << " I mean "an order of magnitude", i.e. I would HOPE that ÊÊÊÊÊÊÊ 2*sigmaÊ < Êdelta-A Ê and in order to claim that the confidence is much "greater" than 95% [as I said] one would HOPE that Ê ÊÊÊÊÊÊÊ 2*sigma Ê<<Ê delta-AÊ in the sense that 3.sigma/(delta-A)Ê <Ê 1,ÊÊor Ê ÊÊÊÊÊÊÊ sigma/delta-AÊÊ <Ê 1/3Ê =Ê 0.33Ê In retrospect, my 2002 paper would be more clear [since sigmaÊ& dAÊ& delta-A all have the same dimension {inÊthe originalÊcase, energy}] if I had formulated the conclusions as: Ê Test 1: Ê ÊÊÊÊÊÊÊ (|dA|/delta-A) < 0.10ÊÊÊ==> Ê estimator of sigma is OK Ê Test 2: Ê ÊÊÊÊÊÊÊ (sigma/delta-A)Ê <Ê 1.00ÊÊ [68.3% Confidence] Ê ÊÊÊÊÊÊÊ (sigma/delta-A) Ê<Ê 0.50ÊÊ [95.4% Confidence] Ê ÊÊÊÊÊÊÊ (sigma/delta-A)Ê <Ê 0.33ÊÊ [99.7% Confidence]If anybody ever performs the BBM Protocol, then I would take that as an opportunity to similarly clarify the test at the bottom of the Bass-McKubre Abstract for ICCF10 [attached]; the reason for its lamentable brevity is that I ran out of space and didn't wan't to go onto a second page. . . . but my REAL intent is that any layman (like a Senator who had studied humanities & law) who can merely count on his or her fingers will need only to see a ROUGHLY linear fit to the data and instantly conclude that "this is not an accidental correlation; this is a physical Cause & Effect which should be further researched because of its self-evident immense potential benefit to humanity!" Thanks again for your interest, Bob
a) So much about the first protocol; I would be happy to check the validity of the BBM protocol (with another Monte Carlo code) after
learning more about how to turn the inequality shown in the last line of the appendix into confidence levels of specific inferences. APPENDIX:
SIG
or dE, depending which is larger. That what the max is for. The RIGHT, in the same inequality, is the product of DELE by the smallest value
in the {Ck} set. That what the min is for. ================================================ This is a generalization of the protocol proposed by Bass [1], which is more realistically flexible in several respects. An arbitrary number N <= 3 of similarly prepared samples is allowed, and neither the voltage nor the current is required to be constant. However, the previous protocol may be recovered as a special case when N = 5. Let N >= 3 denote the number of similarly prepared samples. Let the suffix k denote any particular sample, k = 0, 1, 2, ... , (N -1), where the suffix k = 0 is reserved for the case of a control blank. Let { Ck }, k = 0, 1, 2, . . . , (N -1), denote the hypothesized causal inputs, where, as in Bass & Gleeson [2], each Ck may be e.g. the result of continuous monitoring of the input electrical power [product of instantaneous voltage & current] and its numerical integration over the complete duration of the preparation of the kth sample to give the total amount Ck ( 0 of electrical work done on the sample, or the total energy input. By definition, C0 = 0. Similarly, let {Ek }, k = 0, 1, 2,. . ., (N -1), denote the measured effect outputs. Three possibilities for the output effects { Ek }are: (1) Ek = amount of excess enthalpy; (2) Ek = amount of Helium-4; (3) Ek = amount of Helium-3. Now define the estimator of variance SIG^{2} by the sum over all k ofSIG^{2} = [1/(N-2)] * ( { (Ek - dE - Ck *(E)2 } )where dE denotes mean effect-bias error, and where (E denotes mean effect-increment factor. Next, again summing over all k, define ALP = SUM { Ek }, BET = SUM { (Ek *Ck.) },GAM = SUM { Ck },DEL = SUM { ( Ck )^{2} },and verify by setting to zero the gradient of SIG with respect to the vector [ dE, DELE ]^{T }that
a necessary & sufficient condition for sample standard deviation SIG to be minimized is thatdE = (
max(
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