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Recently there was a discussion about experimental null results.
I noticed a discrepancy between the meaning of "null result" in one old paper, and the suggested meaning in the FAQ: http://hermes.physics.adelaide.edu.a.../experiments.h tml The FAQ states about The Kennedy-Thorndike Experiment: "Their null result is consistent with SR." With SR is specifically meant Einstein's version of the Special Relativity Theory. Some time ago that statement fooled me into thinking that the K-T results supported the null hypothesis. I am aware of no good reason to add "null" to "result", as that adds no useful information but may instead mislead the reader, and the following claim that the result is "consistent with SR" may increase the misunderstanding as the results do not clearly favour SR. (My suggestion now for the FAQ: just replace by "Their results are not inconsistent with SR".) I am sure that I'm not the only one who has been misled by that kind of statements, see the Google groups thread starting from Message-ID: et It turns out that I (and some others) did not correctly understand the meaning of "null result". A definition is given in http://en.wikipedia.org/wiki/Null_result: " Generally, a null result is the consequence of an analysis or experiment that does not detect a proposition or principle original to the analysis or experiment. In science, it can be a result that shows none of the data which would have been expected. It is a value of testable information. It is literally a product of an investigation that is a quantity of no importance. In statistics, specifically, a null result occurs when there are non-significant differences between experimental and control conditions. While some differences may in fact be observed, they are below the threshold set prior to testing. The cutoff for these significance values varies, but is often .05. This is considered evidence for the null hypothesis. In physics, the results of the Michelson-Morley experiment, which did not detect the aether, was of this type. This experiment's famous failed detection, commonly referred to as the null result, caused the aether theory to be abandoned. Shortly after was formed the basis of Albert Einstein's theory of relativity, in which the aether was not included. " Thus, "null result" can simply mean that the expected effect could not be confirmed. That a certain effect was not found does *not* necessarily mean that no effect was found! A "null hypothesis" expresses the expectation that no difference will be found between two values. - In the SR context, the "null hypothesis" for MMX is that no significant signal difference should be found for different orientations. - In M-M's context of stationary ether theory, failure to detect an "ether wind" of =30 km/s could be a "null result". - A "null result" does therefore *not* imply that the result is in agreement with a "null hypothesis". Recently I gave some K-T citations, and I will repeat the main results and end conclusion he Daily effect: "the amplitude of the resulting sine curve is 0.06 +/- 0.05. [... ] this is found to correspond to a velocity V_b = 24 +/- 19 kilometers per second." Overall effect: "their resultant is 10 +/- 10 km per sec. In view of relative velocities amounting to thousands of kilometers per second known to exist among the nebulae, this can scarcely be regarded as other than a clear null result" The correct interpretation of these words is now obvious: 10 +/- 10 km/s was a "clear null result" for their expectation to find 10 km/s. In conclusion, their "clear null result" should not be interpreted as supporting the "null hypothesis". Harald |
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#2
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On 11/20/2003 10:23 AM, Harry wrote:
[...] In conclusion, [K&T's] "clear null result" should not be interpreted as supporting the "null hypothesis". But, as I stated in the FAQ, their null result is consistent with SR. They called it a "null result", not me. Precisely what that means is, as you say, not crystal clear; their consistency with the prediction of SR is indeed crystal clear. Tom Roberts |
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#3
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- repeat of my earlier posting follows below -
Tom Roberts wrote in message ... On 11/20/2003 10:23 AM, Harry wrote: [...] In conclusion, [K&T's] "clear null result" should not be interpreted as supporting the "null hypothesis". But, as I stated in the FAQ, their null result is consistent with SR. They called it a "null result", not me. Precisely what that means is, as you say, not crystal clear; their consistency with the prediction of SR is indeed crystal clear. Tom Roberts Wrong. [Suppressed insults], I just *made it* crystal clear. But I used tact... evidently too much! And my suggested change was already a compromise in your direction in which I allowed for the same bias as in the overall presentation. Better would be: "Their results are not necessarily inconsistent with SR". The rest that I have to say about this I will write to you in a personal mail in order not to embarrass you in public without necessity. I do appreciate your efforts very much and hold you in high esteem... but it is dropping. By the way, you may have forgotten, the FAQ also contains a factual error in the precision estimation of Esclangon. Your erroneous factor 100 is also there. One zero of the "factor 100" needs to be removed to make your claim not obviously wrong. Regards, Harald PS I don't see the original in Google... and you snipped all away. To make sure, I copy it here below (with the abovementioned small correction, and suppressing the above supplementary conclusion). __________________________________________________ __________________________ Recently there was a discussion about experimental null results. I noticed a discrepancy between the meaning of "null result" in one old paper, and the suggested meaning in the FAQ: http://hermes.physics.adelaide.edu.a.../experiments.h tml The FAQ states about The Kennedy-Thorndike Experiment: "Their null result is consistent with SR." With SR is specifically meant Einstein's version of the Special Relativity Theory. Some time ago that statement fooled me into thinking that the K-T results supported the null hypothesis. I am aware of no good reason to add "null" to "result", as that adds no useful information but may instead mislead the reader, and the following claim that the result is "consistent with SR" may increase the misunderstanding as the results do not clearly favour SR. (My suggestion now for the FAQ: just replace by "Their results are not inconsistent with SR".) [or, better: Their results are not necessarily inconsistent with SR"] I am sure that I'm not the only one who has been misled by that kind of statements, see the Google groups thread starting from Message-ID: et It turns out that I (and some others) did not correctly understand the meaning of "null result". A definition is given in http://en.wikipedia.org/wiki/Null_result: " Generally, a null result is the consequence of an analysis or experiment that does not detect a proposition or principle original to the analysis or experiment. In science, it can be a result that shows none of the data which would have been expected. It is a value of testable information. It is literally a product of an investigation that is a quantity of no importance. In statistics, specifically, a null result occurs when there are non-significant differences between experimental and control conditions. While some differences may in fact be observed, they are below the threshold set prior to testing. The cutoff for these significance values varies, but is often .05. This is considered evidence for the null hypothesis. In physics, the results of the Michelson-Morley experiment, which did not detect the aether, was of this type. This experiment's famous failed detection, commonly referred to as the null result, caused the aether theory to be abandoned. Shortly after was formed the basis of Albert Einstein's theory of relativity, in which the aether was not included. " Thus, "null result" can simply mean that the expected effect could not be confirmed. That a certain effect was not found does *not* necessarily mean that no effect was found! A "null hypothesis" expresses the expectation that no difference will be found between two values. - In the SR context, the "null hypothesis" for MMX is that no significant signal difference should be found for different orientations. - In M-M's context of stationary ether theory, failure to detect an "ether wind" of =30 km/s could be a "null result". - A "null result" does therefore *not* imply that the result is in agreement with a "null hypothesis". Recently I gave some K-T citations, and I will repeat the main results and end conclusion he Daily effect: "the amplitude of the resulting sine curve is 0.06 +/- 0.05. [... ] this is found to correspond to a velocity V_b = 24 +/- 19 kilometers per second." Overall effect: "their resultant is 10 +/- 10 km per sec. In view of relative velocities amounting to thousands of kilometers per second known to exist among the nebulae, this can scarcely be regarded as other than a clear null result" The correct interpretation of these words is now obvious: 10 +/- 10 km/s was a "clear null result" for their expectation to find 10 km/s. Harald |
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Harry:
Recently there was a discussion about experimental null results. I noticed a discrepancy between the meaning of "null result" in one old paper, and the suggested meaning in the FAQ: http://hermes.physics.adelaide.edu.a.../experiments.h tml The FAQ states about The Kennedy-Thorndike Experiment: "Their null result is consistent with SR." With SR is specifically meant Einstein's version of the Special Relativity Theory. Some time ago that statement fooled me into thinking that the K-T results supported the null hypothesis. I am aware of no good reason to add "null" to "result", as that adds no useful information but may instead mislead the reader, and the following claim that the result is "consistent with SR" may increase the misunderstanding as the results do not clearly favour SR. (My suggestion now for the FAQ: just replace by "Their results are not inconsistent with SR".) No, the correct way to state the result was as it was stated. One would only state the result as being "not inconsistent" with the hypothesis, if one was trying to claim a non-null result for an experiment for which the error bars made the result consistent with a null hypothesis. Your definition below is somewhat confusing as in the way it's stated. ------ http://en.wikipedia.org/wiki/Null_result: " Generally, a null result is the consequence of an analysis or experiment that does not detect a proposition or principle original to the analysis or experiment. In science, it can be a result that shows none of the data which would have been expected. It is a value of testable information. It is literally a product of an investigation that is a quantity of no importance. In statistics, specifically, a null result occurs when there are non-significant differences between experimental and control conditions. While some differences may in fact be observed, they are below the threshold set prior to testing. The cutoff for these significance values varies, but is often .05. This is considered evidence for the null hypothesis. ------ The way I read that means a null result for a null hypothesis is a result which doesn't satisfy a null hypothesis. I think the following quantifies what it means to test a null hypothesis, without the addit- ional confusion of throwing in the term "null result" and trying to figure out negations of negations. An experiment for which the hypothesis is null, is one in which the difference between the data points and the values predicted from theory is null. Null hypothesis: (predicted value - data) = 0 In order to determine whether the null hypothesis is consistent with the data, you need the residuals of the fitted data. The residuals are what define the goodness of the fit to the data points (not the predicted values). This is what connects the fitted data to the predicted value, so that you can make the comparison between theory and experiment and specify an uncertainty. residual = (fit of data - data) The fitted data points are said to agree with the fitted data if the residuals approximate the (random) statistical errors in the experiment. residuals random error =~ (fit of data - data) +/- random errors The residuals can also give additional information (further below). Then, the difference between a null hypothesis and the residuals is: \delta = (predicted value - data) - (fit of data - data) +/- random errors = (predicted value - fit of data) +/- random errors So, an experiment is said to be consistent with a null hypothesis if: \delta = (predicted value - fit of data) =~ +/- random errors What you could also say is that the experiment is not inconsistent with a different theory which predicts values which are different than the theory from which the null hypothesis of this experiment was formed, if the values lie within the random errors of this experiment. However, you cannot say any more than that about the alternative theory, because you did not construct the experiment to null out the predicted values for the alternative theory. An experiment which tests a null hypothesis for a given theory is not necessarily equivalent to a different null hypothesis obtained from a different theory. In principle that would be true, but in practice, the experiment must be designed to eliminate the sources of systematic errors. In the csae where the experiment is a test of special relativity, the experiment is designed to eliminate the sources of systematic error that would occur from some general asymmetry in the apparatus. If you were testing an ether theory as a null hypothesis, you would first need the predicted values from the ether theory because the experiment would need to be designed in order to insure that the sources of systematic error were minimized so that the experiment was optimized to determine whether or not the data agreed with the prediction of the _particular_ ether theory in question. It would be nice if one hypothesis was the complement of any other hypothesis for a given experiment, but the reality is that a source of systematic error can only be identified if you know where to look for it. In general, knowing where to look for it means looking where the experiment will most affect your null hypothesis. The residuals can give additional information about the structure of the errors, because there should be no structure in the residuals if the residuals approximate the random errors in the experiment. However, it is not possible to associate non-random errors with anything but a potential future experiment desgined to investigate that structure. For example, if you have a data set with values that are all within the experimental uncertainty, but the errors show a non-random variation, then a new experiment could be designed to insure the non-random variation was not due to the apparatus. One then designs new apparatus to insure the non-random variation is not a systematic effect of the apparatus. In physics, the results of the Michelson-Morley experiment, which did not detect the aether, was of this type. This experiment's famous failed detection, commonly referred to as the null result, caused the aether theory to be abandoned. Shortly after was formed the basis of Albert Einstein's theory of relativity, in which the aether was not included. The michelson-morely experiment was. by neccessity, an experiment constructed by assumption that there would be no variation in the data from any ether drift, since no ether theory was able to predict values of that drift such that the experiment could be constructed to look precisely for the direction and magnitude of a predicted effect. Thus, "null result" can simply mean that the expected effect could not be confirmed. That a certain effect was not found does *not* necessarily mean that no effect was found! There was no _specific_ effect which was being tested, i.e., they did not have any null hypothesis for an experiment such that (theory-data) = 0 except the case where the theory would predict no effect. In order to have a null hypothesis for an ether theory, they would have needed a theory that gives the hypothesis (ether theory - data) = 0. It's obvious that they could not address every possible scheme one could imagine that would be consistent with the result they obtained, because they had no way of knowing anything that wasn't quantified by a particular theory. A "null hypothesis" expresses the expectation that no difference will be found between two values. Right, but no ether theory predicted any specific value. The rest of the argument that was made is the earth's lack of a priviliged location and velocity with respect to the ether frame. In physics, experimental results which hinge on a very specific fluke of nature favorable to a general theory about nature are frowned upon. This is the primary reason that everyone believes there is a deeper connection between the parameters in the standard model. Each of those parameters is so close to being a critical value for that parameter, that it's inconceivable that each of them has the value it does due to random chance. If \alpha differed by even a fraction of a percent, the universe would be vastly different. - In the SR context, the "null hypothesis" for MMX is that no significant signal difference should be found for different orientations. - In M-M's context of stationary ether theory, failure to detect an "ether wind" of =30 km/s could be a "null result". The point is that the experiment did not address any issue regarding any specific ether theory. Everyone at the time believed _any_ ether theory should result in some drift, so the most the experiment could do is give a limit on _any_ drift based upon the sensitivity of the experiment to _any_ drift. Everyone too the results to be a problem simply because there was no reason to believe that the earth had some priviliged status as being at rest in the ether to within the uncertainty of the experiment. Your figure requires the sun to essentially be at rest in the ether frame. |
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#6
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"Bill Rowe" wrote in message ... In article , (Harry) wrote: Tom Roberts wrote in message ... But, as I stated in the FAQ, their null result is consistent with SR. And my suggested change was already a compromise in your direction in which I allowed for the same bias as in the overall presentation. Better would be: "Their results are not necessarily inconsistent with SR". not inconsistent with SR = consistent with SR, that is a double negative (a less than optimum way of expression) is logically equivalent to a positive. So, what is the problem? The problem is the "lacking middle ground" related to "grey zones". It is an often made error in statistics and reasoning. For example, if P(A) + P(B) = 1, and P(A) = ca. 0.5, it can't be claimed that P(B) 0.5 but one may claim that P(B) is NOT 0.5. The usual meaning of consistent is: In agreement; compatible. Now one could propose that if for example someone measures 10 +/- 5, that is consistent with 20, because there is a slight chance that they don't disagree. Obviously that is not the way "consistent with" is understood, and all measurements would be consistent with everything! To have the right to claim that a result is in agreement, one should be well inside the 50% confidence interval. Note that I may be mistaken on this point, so that everyone but me uses "consistent with" for "inside 50% confidence interval", and "inconsistent with" for "outside 50% confidence interval". If so, then the statement in the FAQ should be: "Their results are inconsistent with SR". Harald |
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"Bilge" wrote in message ... Harry: Recently there was a discussion about experimental null results. I noticed a discrepancy between the meaning of "null result" in one old paper, and the suggested meaning in the FAQ: http://hermes.physics.adelaide.edu.a...SR/experiments. h tml The FAQ states about The Kennedy-Thorndike Experiment: "Their null result is consistent with SR." With SR is specifically meant Einstein's version of the Special Relativity Theory. Some time ago that statement fooled me into thinking that the K-T results supported the null hypothesis. I am aware of no good reason to add "null" to "result", as that adds no useful information but may instead mislead the reader, and the following claim that the result is "consistent with SR" may increase the misunderstanding as the results do not clearly favour SR. (My suggestion now for the FAQ: just replace by "Their results are not inconsistent with SR".) No, the correct way to state the result was as it was stated. One would only state the result as being "not inconsistent" with the hypothesis, if one was trying to claim a non-null result for an experiment for which the error bars made the result consistent with a null hypothesis. Your definition below is somewhat confusing as in the way it's stated. Well, your above definition sounds rather blurred to me, but no doubt you specify more below. ------ http://en.wikipedia.org/wiki/Null_result: " Generally, a null result is the consequence of an analysis or experiment that does not detect a proposition or principle original to the analysis or experiment. In science, it can be a result that shows none of the data which would have been expected. It is a value of testable information. It is literally a product of an investigation that is a quantity of no importance. In statistics, specifically, a null result occurs when there are non-significant differences between experimental and control conditions. While some differences may in fact be observed, they are below the threshold set prior to testing. The cutoff for these significance values varies, but is often .05. This is considered evidence for the null hypothesis. ------ The way I read that means a null result for a null hypothesis is a result which doesn't satisfy a null hypothesis. I think the following quantifies what it means to test a null hypothesis, without the addit- ional confusion of throwing in the term "null result" and trying to figure out negations of negations. An experiment for which the hypothesis is null, is one in which the difference between the data points and the values predicted from theory is null. Null hypothesis: (predicted value - data) = 0 In order to determine whether the null hypothesis is consistent with the data, you need the residuals of the fitted data. The residuals are what define the goodness of the fit to the data points (not the predicted values). This is what connects the fitted data to the predicted value, so that you can make the comparison between theory and experiment and specify an uncertainty. residual = (fit of data - data) The fitted data points are said to agree with the fitted data if the residuals approximate the (random) statistical errors in the experiment. residuals random error =~ (fit of data - data) +/- random errors To what level of confidence, or how many sigma? The residuals can also give additional information (further below). Then, the difference between a null hypothesis and the residuals is: \delta = (predicted value - data) - (fit of data - data) +/- random errors = (predicted value - fit of data) +/- random errors So, an experiment is said to be consistent with a null hypothesis if: \delta = (predicted value - fit of data) =~ +/- random errors What you could also say is that the experiment is not inconsistent with a different theory which predicts values which are different than the theory from which the null hypothesis of this experiment was formed, if the values lie within the random errors of this experiment. However, you cannot say any more than that about the alternative theory, because you did not construct the experiment to null out the predicted values for the alternative theory. An experiment which tests a null hypothesis for a given theory is not necessarily equivalent to a different null hypothesis obtained from a different theory. Interesting remark. That point is generally ignored... In principle that would be true, but in practice, the experiment must be designed to eliminate the sources of systematic errors. In the csae where the experiment is a test of special relativity, the experiment is designed to eliminate the sources of systematic error that would occur from some general asymmetry in the apparatus. If you were testing an ether theory as a null hypothesis, you would first need the predicted values from the ether theory because the experiment would need to be designed in order to insure that the sources of systematic error were minimized so that the experiment was optimized to determine whether or not the data agreed with the prediction of the _particular_ ether theory in question. Exactly. It would be nice if one hypothesis was the complement of any other hypothesis for a given experiment, but the reality is that a source of systematic error can only be identified if you know where to look for it. In general, knowing where to look for it means looking where the experiment will most affect your null hypothesis. The residuals can give additional information about the structure of the errors, because there should be no structure in the residuals if the residuals approximate the random errors in the experiment. However, it is not possible to associate non-random errors with anything but a potential future experiment desgined to investigate that structure. For example, if you have a data set with values that are all within the experimental uncertainty, but the errors show a non-random variation, then a new experiment could be designed to insure the non-random variation was not due to the apparatus. One then designs new apparatus to insure the non-random variation is not a systematic effect of the apparatus. In physics, the results of the Michelson-Morley experiment, which did not detect the aether, was of this type. This experiment's famous failed detection, commonly referred to as the null result, caused the aether theory to be abandoned. Shortly after was formed the basis of Albert Einstein's theory of relativity, in which the aether was not included. The michelson-morely experiment was. by neccessity, an experiment constructed by assumption that there would be no variation in the data from any ether drift, since no ether theory was able to predict values of that drift such that the experiment could be constructed to look precisely for the direction and magnitude of a predicted effect. Exactly (if I understand you well!). Instead they simply looked for an "ether wind" of 30 km/s for half a year, but with in mind the alternative but badly specified hypothesis of some amount of drift. Thus, "null result" can simply mean that the expected effect could not be confirmed. That a certain effect was not found does *not* necessarily mean that no effect was found! There was no _specific_ effect which was being tested, i.e., they did not have any null hypothesis for an experiment such that (theory-data) = 0 except the case where the theory would predict no effect. ???!! To the contrary, they and K-T tested for a very specific effect, see above! They only expected an unknown offset value. But that can be dealt with in statistics. Sorry to say Bilge but clearly Partrick is right, you should read some history. And watch out, "history" as you can find in science books is unreliable, for many don't give a ****. Read the original papers instead. SNIP A "null hypothesis" expresses the expectation that no difference will be found between two values. Right, but no ether theory predicted any specific value. SNIP - In the SR context, the "null hypothesis" for MMX is that no significant signal difference should be found for different orientations. - In M-M's context of stationary ether theory, failure to detect an "ether wind" of =30 km/s could be a "null result". The point is that the experiment did not address any issue regarding any specific ether theory. Incorrect as explained, and not the only point. Main point was, as you noted yourself, that they did not test for "SRT". Everyone at the time believed _any_ ether theory should result in some drift, so the most the experiment could do is give a limit on _any_ drift based upon the sensitivity of the experiment to _any_ drift. Everyone too the results to be a problem simply because there was no reason to believe that the earth had some priviliged status as being at rest in the ether to within the uncertainty of the experiment. Your figure requires the sun to essentially be at rest in the ether frame. No, you did not understand it. I hope now you do! Harald |
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Correction, when I wrote:
I am sure that I'm not the only one who has been misled by that kind of statements, see the Google groups thread starting from Message-ID: et I meant the part of the thread starting with one or two postings lower: Sorry if you couldn't find it! Harald |
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#9
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PS Bilge, I now realise that you did not back up your main point:
SNIP The FAQ states about The Kennedy-Thorndike Experiment: "Their null result is consistent with SR." With SR is specifically meant Einstein's version of the Special Relativity Theory. SNIP No, the correct way to state the result was as it was stated. One would only state the result as being "not inconsistent" with the hypothesis, if one was trying to claim a non-null result for an experiment for which the error bars made the result consistent with a null hypothesis. SNIP. Bilge, as I emphasised: in the FAQ the results are not mentioned, there is no reference to further analysis, and the predicted value lies outside the error bars. Please show how it can be scientifically correct and not misleading to simply state that that result is a "null result" and consistent with the theory. Thanks. Harald |
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#10
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Harry:
PS Bilge, I now realise that you did not back up your main point: SNIP The FAQ states about The Kennedy-Thorndike Experiment: "Their null result is consistent with SR." With SR is specifically meant Einstein's version of the Special Relativity Theory. SNIP No, the correct way to state the result was as it was stated. One would only state the result as being "not inconsistent" with the hypothesis, if one was trying to claim a non-null result for an experiment for which the error bars made the result consistent with a null hypothesis. SNIP. Bilge, as I emphasised: in the FAQ the results are not mentioned, there is no reference to further analysis, and the predicted value lies outside the error bars. Please show how it can be scientifically correct and not misleading to simply state that that result is a "null result" and consistent with the theory. I'm assuming that "null result" means that null hypothesis is true, rather than the confusing way your wikipedia reference defines it, which I read to mean the opposite. If I construct a null hypothesis, then the only null hypothesis I can construct is that the ether drift is zero (unless you can give a specific magnitude and direction for the ether drift so that the statistical analysis is with repect to a specified fringe shift other than zero). That was why I gave a definition for null hypothesis and avoided the term "null result". The comparison of the data is to no fringe shift, not a predicted shift. The experimental data is consistent with a prediction of no fringe shift. It could also be consistent with an experiment which looked for a specific fringe shift, but apparently there was no predicted value to use for a null hypothesis so the null hypothesis was determined by using the valude zero. What is misleading? The experiment is consistent with its null hypothesis. I'm not going to debate the semantics of "null result" since I don't think your reference is very clear or at least it's not clear that your reference defines it as it's used in the faq. |
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