UAH Global Temperature Update for May, 2024: +0.90 deg. C

The 2nd tells you nothing about the accuracy of the data points being used to evaluate the r^2 value. The slope of the trend line has to be conditioned by the measurement uncertainty of the data points. The measurement uncertainty simply can’t be ignored as bellman and climate science does.

Even in 1) the random variation has to be conditioned by the measurement uncertainty of the data points used to establish the variation (I am assuming you are talking about the standard deviation). The uncertainty in the minimum and maximum values in the data set change the variance calculated for the data set using only the stated values and *increases* the amount of variation (i.e. the standard deviation).

You simply can’t just ignore measurement uncertainty in anything to do with measured values. Garbage in, garbage out.

“ I have no memory of you telling Monckton you didn’t believe his pause becasue of the huge measurement uncertainty in his preferred data set.”

Your lack of reading comprehension is showing again. The pause DOES exist in the data he is using – the same data climate science uses. So you have two choices, 1. if CoM is wrong then so is climate science or 2. that it is impossible to know what is happening.

“I remember you attacking me for daring to suggest there was any uncertainty in the trend.”

Your memory skills are as bad as your reading comprehension skills.

What I have *always* said, and which you seem to be unable to comprehend because of your lack of reading comprehension ability, is that what is happening is part of the GREAT UNKNOWN. The data has such inherent measurement uncertainty that it is impossible to identify temp differences less than the units digit. That makes knowing the actual trend of the “global temp” impossible to know. It’s part of the GREAT UNKNOWN.

As usual your cognitive dissonance is right at the forefront. You want your cake and to eat it too and so you say whatever you have to in the moment. As I said, you have two choices, either CoM’s pause is correct and climate science can calculate anomalies in the hundredths digit or CoM’s pause is unknowable and climate science can *NOT* calculate anomalies in the hundredths digit and their conclusions are unknowable garbage.

Pick one and stick with it!

“We are not talking about the difference between two values – we are talking about a least squares regression through 100 different data points.”

Why do you ALWAYS make such idiotic assertions? The slope of a linear regression line DEFINES the difference between two consecutive values on the line! The slope of that line is based on minimizing the residuals between the given measurements and the line (the difference between two values)!

“You don’t need to know the true slope to know what the best fit is”

But the best-fit metric depends on the values of the data, including their measurement uncertainty! There simply is no true value for the best-fit metric if there is no true value for the data points!

You keep getting stuck in the paradigm of measurements being “true value +/- error” that the international community abandoned 50 years ago. You simply can’t let that paradigm go because in your statistics training all data is 100% accurate. So you just ignore the uncertainty of the data. You were never taught how to integrate data uncertainty into statistical analysis and you stubbornly refuse to learn how to do it today! Instead you just claim that sources like the GUM, Taylor, Bevington, and Possolo are all wrong. You can’t admit, even to yourself, that Possolo in TN1900, Ex 2, had to assume that all measurements were 100% accurate with no measurement uncertainty. For you, making that assumption is just standard practice for *everything*. Right down to stating that you *can* find the “true value” of the slope of a linear-regression line for a set of measurements. And then you want to turn around and claim that CoM can’t do the same thing!

“Still waiting for you to tell me if you think my uncertainty is too big or too small.”

It’s neither. You just assume it’s always ZERO!

The measurement uncertainty over time for *any* set of temperature data is at least in the units digit because that is how the data has been recorded. Even in the current NWS ASOS system the temperature is recorded by rounding the measurement to the nearest units digit in Fahrenheit and then converting to Celsius in the tenths digit. That alone introduces measurement uncertainty that will be in the units digit, quoting the Celsius value in the tenths digit is is adding resolution that you simply can’t know!

“then we can see if you still agree with me that the uncertainty means there is no significant difference between the short term pause, and the long term trend.”

There is no significant difference BECAUSE YOU CAN’T KNOW EITHER ONE IN ORDER TO COMPARE THEM!

He is so brainwashed by the antiquated meme of “true value +/- error” that he believes the treatment of measurements and measurement uncertainty in the GUM is wrong. It all comes back to the basic meme of “all measurement uncertainty is random, Gaussian, and cancels”. Therefore random sampling as in an MC simulation can tell you the “true value”.

They are 50 years out of date and can’t admit it.

It wasn’t out of date. His original book was pioneering in changing metrology from the meme of “true value +/- error” to “stated value +/- uncertainty”.

His copyright is 1982 and 1997.

As usual you are cherry picking without reading for meaning. If you would read his preface to the second addition you would find that he didn’t change anything in his approach to “stated value +/- uncertainty”.

“And ignored the context. Quote the entire sentence.”There’s a straight forward equation based on assumptions that there is a trend with random independent error.””

So what? You are still saying you assumed all measurement uncertainty is random, Gaussian, and cancels! What else is “random independent error”? BTW, because of measurement uncertainty the “ERROR” is impossible to know unless you know the “true value”. Do *YOU* know the true value?

“The simple equation, as explained by Taylor, is based on those assumptions.”

Once again, you have *NEVER*, not once studied Taylor in order to understand what is he doing. You’ve never done the examples in order to learn something.

Taylor’s equations in Chapter 3 assume PARTIAL cancellation, not complete cancellation. *YOU ARE ASSUMING COMPLETE CANCELLATION*. I.e. random, Gaussian, and cancels.

” If you’d ever paid any attention, you would know that the assumption of independence is not correct in cases like this”

It’s not the assumption of independence, it is assuming that all measurement uncertainty is random, Gaussian, and cancels!

“You keep jumping from the concept of a simplifying assumption”

This is the excuse of a blackboard mathematician/statistician who doesn’t care about whether the assumptions mean anything in the real world!

“to claiming that everyone believes those assumptions are always correct.”

When you make the assumption EVERY SINGLE TIME that all measurement uncertainty is random, Gaussian, and cancels it’s pretty damn hard to do anything other than assume you believe that assumption is always correct!

“ I do not.”

Of course you do. Like when you say the standard deviation of the stated values can be used to determine measurement uncertainty. You can only do so by assuming measurement uncertainty is 0 (zero). You can only assume it is zero if you assume it is random, Gaussian, and cancels. Just as Possolo did in TN1900, Ex. 2!

You *always* assume measurement uncertainty is random, Gaussian, and cancels in every thing you do. EVERY SINGLE TIME. Apparently you don’t even realize that do.

Taylor and Chapter 8? You are cherry picking again! You didn’t understand anything Taylor says in Chapter 8. You didn’t even look at Fig 8.1(b)!

In Chapter 8 Taylor is trying to find out if the relationship between x& y is linear. He says: “The second question that must be asked is whether the measured values (x1,y1), …, (xn,yn) do really bear out our expectation that y is linear in x.”

No where in Section 8 does he state what the linear relationship *is*, i.e. the *true value* of the slope of the linear line, only that if it is within the error bars that it can then judge visually if the relationship is linear.

Note that in Section 8.2 (finding constants A and B) he says:

“If we knew the constants A and B the, for any given value of x_i (which we are assuming has no uncertainty), we could compute the true value of the corresponding y_i, …”

“The measurement of y_i is governed by a normal distribution centered on this true value, with a width parameter of σ_y.” (tpg note: normally distributed implies random uncertainty only)

“In the now familiar way, we will assume that the best estimates for the unknown constants A and B, based on the given measurments, are those values of A and B for which the probability Prob_A,B(y1, …, yn) is maximum …”

————————————–

As I said, you are CHERRY-PICKING again.

In Section 8.3, Uncertainty in the Measurements of y:

“Remember that the numbers y1, …,, yn are not N measurements of the same quantity. … Thus we certainly do not get an idea of their reliability by examining the spread in their values.”

“Nevertheless, we can easily estimate the uncertainty σ_y in the numbers y1, …, yn. The measurement of each y_i is (we are assuming) normally distributed about its true value A +Bx_i with a width parameter σ_y”

As Taylor stated in Chapter 4, most of the rest of the book assumes random uncertainty only, no systematic uncertainty. That is certainly the case in Chapter 8. That’s what the words “normally distributed about its true value” means!

Someday you *really* need to stop cherry-picking stuff hoping it will validate you misunderstandings about measurement uncertainty!

Rule 1: Measurement uncertainty in field applications cannot be assumed to be “normally distributed” when you are measuring different things using different things.
Rule 2: Measurement uncertainty always grows, you can’t reduce it through averaging.
Rule 3: Systematic uncertainty is not amenable to statistical analysis.

Resign yourself to this and maybe you’ll see some light on the subject.

You lack of math understanding is demonstrated by your continued dependence on the meme of “all measurement uncertainty is random, Gaussian, and cancels” so that you can ignore it.

1. You’ve been shown the graphs showing standard deviation as positive from the mean and negative from the mean.
2. Rectangular distributions are SYMMETRIC, just like Gaussian. I’ve told you at least a dozen times that when I use the term Gaussian that I am talking about symmetric distributions. Your memory is as bad as your understanding of measurement uncertainty.
3. You fail to understand that selecting samples at random will *always* give a Gaussian distribution of the sample means. If the Monte Carlo simulation selects values from a population at random that is no different than *YOU* selecting samples at random from a population. As usual your cognitive dissonance is on display. You want us to believe that YOU selecting samples at random follows the CLT theory but a Monte Carlo simulation selecting samples from a population at random does not. And that isn’t even addressing how the Monte Carlo algorithm actually picks the random values (does it do so using a Gaussian distribution as a psuedo-random generator?)

Nothing you ever assert makes any physical sense at all. You are either saying what you need to say in the moment or you are displaying cognitive dissonance.

1. No kidding! You won’t even recognize that when it comes to measurement uncertainty! There *IS* a reason uncertainty is given as a positive and a negative value, +/-! When combining measurement uncertainty the negative side of the uncertainty gets bigger, it ADDS. Same with the positive side of the measurement uncertainty, it gets bigger, it ADDS. It simply doesn’t matter if you are adding two measurements or subtracting two measurements and get either a positive or negative value – THE MEASUREMENT UNCERTAINTY ADDS IN EVERY CASE! IT GETS *BIGGER*.
2. I’ve TOLD YOU MULTIPLE TIMES HOW I AM USING THE WORDS. *YOU* are the one that chooses to ignore that.
3. When it comes to MC you have no idea of what you are talking about. You *do* want us to believe the CLT applies in one case but not in another one – cognitive dissonance at its finest. You are beyond help if you don’t believe sampling of even a skewed distribution can result in a Gaussian distribution of the sample means. It simply doesn’t matter if YOU do it personally or have a computer do it. But you want us to believe that it does matter. Unfrekaingbelievable.

You’ll never get it, will you?

1.Standard deviation of the stated values will ONLY give you the measurement uncertainty IF AND ONLY IF you assume all measurement uncertainty is random, Gaussian, and cancels.

Why do you think Possolo assumed all measurement uncertainty was 0 (zero) in TN1900, EX 2?

It was so he wouldn’t have to condition the standard deviation of the stated values by a measurement uncertainty value!

No.2: I have told you repeatedly that when I say Gaussian that is to indicate a symmetric distribution. Your memory is *YOUR* problem, not mine.

The CLT does *NOT* only apply to Gaussian distributions. It applies to *ANY* distribution, be it Gaussian or skewed. No one has ever disputed this. The issue is that the CLT doesn’t help with statistical analysis of a skewed or multi-modal distribution where the average and the median are different. You can’t seem to get that into your head no matter how many times you are told it.

“What it says is that the sampling distribution will tend to a Gaussian distribution as sample size increases.”

And what does that Gaussian distribution of sample means imply for a non-Gaussian parent distribution? Ans: Very litle, certainly *not* the accuracy of the mean!

You keep trying to rationalize to yourself that you can somehow decrease measurement uncertainty merely by assuming it is all random, Gaussian, and cancels.

You can’t. Resign yourself to that.

The uncertainty of the trend *IS* also conditioned by the measurement uncertainty of the data points used to determine the trend. A fact you stubbornly refuse to admit.

A trend line is made up of segments between adjacent data points. If those adjacent data points are uncertain then so is the slope of the line between the two adjacent data points. A linear slope is nothing more than finding a line with a common slope for each segment. But if the slope of the line between the segments is uncertain then so will the linear line with a common slope.

You “uncertainty of the trend” is nothing more than the best fit to the stated values of the data points while ignoring the measurement uncertainty of the data points. A common tactic in climate science. “All measurement uncertainty is random, Gaussian, and cancels”

The slope of that linear line with a common slope is just as uncertain as the measurement uncertainty of the individual data points.

“Er, no. That would just be a wibbly wobbly line.”

YES! A linear regression is just a way to straighten out the wobbly line!

But it is the segment to segment differences that determine what the linear regression will be!

“Here’s the question for you. I’ve asked it many times before so I don’t expect an answer. When you do your calculation of the uncertainty of the trend, taking in all the uncertainties and systematic errors in UAH, do you expect it to be bigger or smaller than what I would estimate ignoring all those uncertainties?”

The problem is not that you haven’t been answered. The problem is that you won’t accept the answer because of your dogmatic belief that all measurement uncertainty is random, Gaussian, and cancels.

The “uncertainty of the trend” is ONLY A METRIC FOR HOW THE LINE FITS THE STATED VALUES!

You *still* don’t understand measurement uncertainty! The problem is that the TRUE trend line is part of the GREAT UNKNOWN!

If you had answered my previous question concerning what the trend line between 3 +/- 0.5 and 4 +/- 0.5 actually is you might get a glimmer of understanding. Instead you just ignore it because it doesn’t fit your dogma.

The actual trend line could be anywhere in the universe of 2.5 to 4.5 and 3.5 to 3.5. Or a slope somewhere between 0 and 2. What it actually is just can’t be determined!

*YOU* would answer that the slope of the trend line is 1. And the R^2 value is 1. Perfect fit. All residuals = 0. An uncertainty of 0.

So your “uncertainty of the trend line” is *far bigger than what you would calculate! The uncertainty becomes a +/-1 from an individual uncertainty of +/- 0.5. A direct addition of the measurement uncertainty. And totally different from your “uncertainty of the trend line” equaling zero.

When you change each individual data point to its possible reasonable value plus/minus then the distance from the resulting data point to the “best fit line” is going to increase! x^2 gets BIGGER for each data point! And that is assuming that the slope of the trend line calculated from only the stated values is the *true* trend line. The real issue is that you simply don’t know that even the slope of the line best fitting the stated values is the slope of the true trend line. IT’S ALL PART OF THE GREAT UNKNOWN!

Stop saying this has never been explained to you. It’s been explained MULTIPLE TIMES. You’ve even been provided graphs to emphasize the point. And you *always* fall back on the meme that all measurement uncertainty is random, Gaussian, and cancels and the stated values are 100% accurate.

I tried to explain to him that if he went to the lumber yard to get material to build a deck using an average uncertainty that was less than the element uncertainties that he would be going back at some point to get some more boards. Either that or scabbing some together.

Went right over his head because he thinks you can decrease measurement uncertainty by averaging it.

“I didn’t say they do. I said it was wrong to claim the concept of error had been abandoned 50 years ago”

It *was* abandoned 50 years ago. When I was studying electrical engineering at college in 1968 we were taught “estimated value +/- uncertainty” and *NOT* “true value +/- error”. That’s more that 50 years ago. When analyzing results from circuits in introductory lab we were using equipment that was not calibrated except at random intervals. We were using parts with manufacturing tolerances of as much as +/- 20%. There was *no* expectation of knowing what the “true value” was for any circuit built and measured at a lab station.

Jeesh, we were even taught that in Chem Lab 101! When titrating a solution you simply couldn’t depend on a “drop” from the pipette being exactly 1ml so you were limited to how many significant digits you would use! It was all “estimated value +/- uncertainty”, not “true value +/- error”. You simply couldn’t depend on every one having the “true value” at any station, even if measuring extracts from the same solution!

“I also think it’s wrong to claim the GUM as proof that it was abandoned at all. They are simply expressing a preference, not insisting that the term should be abandoned.”

You are *still* cherry picking. You have not read Annex D in the JCGM in any manner, shape, or form.

“The term true value (B.2.3) has traditionally been used in publications on uncertainty but not in this Guide for the reasons presented in this annex. Because the terms “measurand”, “error”, and “uncertainty” are frequently misunderstood, this annex also provides additional discussion of the ideas underlying them to supplement the discussion given in Clause 3. Two figures are presented to illustrate why the concept of uncertainty adopted in this Guide is based on the measurement result and its evaluated uncertainty rather than on the unknowable quantities “true” value and error.” (bolding mine, tpg)

YOU NEED TO STOP CHERRY PICKING AND READ EVERY SINGLE WORD IN THE JCGM AND MEMORIZE THEM AND THEN TRY TO UNDERSTAND THE CONCEPTS BEING EXPLAINED.

You mouth the word “uncertainty” but you don’t understand it at all. It’s like you trying to equate the SEM with measurement uncertainty by calling the SEM the “uncertainty of the mean”.

It all comes back to your ingrained meme of “all measurement uncertainty is random, Gaussian, and cancels”. That meme colors everything you say and you refuse to admit it. But it just keeps coming out in everything you say.

It’s like NONE of the CAGW advocates have *ever* actually built anything or designed anything in the physical world. Even something as simple as the railing on a deck is subject to measurement uncertainty and you can’t decrease that by taking an average of a bunch of boards. You’ll wind up with a gap at one end that the nails through the vertical supports can’t reliably hold!

It’s because the “average” is not a measurement. It is a statistical descriptor. Dependence on it as a measurement is just wrong. The average might be useful in calculating the number of board-feet in order to get a total price estimate but you better condition that to make up for the shorter boards that won’t cover the spans you need to bridge on your deck – meaning you’ll have to go back and buy more boards or scab pieces together (that looks real good don’t you know!).

You don’t even understand what the words “true value” and “normal distribution” mean and imply when it comes to measurements.

That’s because you ALWAYS assume that all measurement uncertainty is random, Gaussian, and cancels. You say you don’t but it just shines through in everything you post!

“You keep claiming things like this yet never actually link to where you quoted it.”

I don’t have a link from Taylor to provide. I HAVE HIS BOOK! I QUOTED RIGHT OUT OF HIS BOOK!

“I can see nothing in Taylor where he claims the y_i measurements are “true values””

That’s because you can’t read! You can only cherry pick.

I quoted you the text from Fig 1 of his book.

Here’s from the text (again!):

“If we knew the constants A and B, the, for any given value x_i (which we are assuming has no uncertainty), we could compute the true value of the corresponding y_i,

(true value for y_i) = A + Bx_i.

The measurement of y_i is governed by the normal distribution centered on this true value, with width parameter σ_y. Therefore the probability of obtaining the observed value y_i is ….” (bolding and italics mine, tpg)

If you can’t see the words “true value” in Taylor’s book then you simply can’t read. If you don’t understand how “true value” and “normal distribution” are related then you simply haven’t read Taylor’s book.

Taylor told you in Chapter 4 that the rest of the book was primarily based on the assumption of no systematic bias in the measurements. This lead to the ability to assume the average of the measurement’s stated values is the “true value” – but this also requires that the random bias be Gaussian.

His Chapter 8 is based on these assumptions.

There are none so blind as those who will not see.

“I didn’t ask for a link to the book, just to where you quoted him as assuming “that you have a TRUE VALUE for the measurements.”.”

I gave you the direct quotes from the book. I can’t help it if you can’t read!

“Why do you think there is a normal distribution if it si the true value?””

Because Taylor SAYS IT IN THE TEXT!

“The measurement of y_i is governed by the normal distribution centered on this true value,”

What in Pete’s name do you think the words “normal distribution” MEANS?

Ans: It means you have a random, Gaussian distribution which cancels leaving the mean as the true value!

Neither of these assumptions apply to the real world measurements of temperature! The distributions are almost guaranteed to not be oormal and, therefore, the mean is not a true value.

I’ll say it again: YOUR PROBLEM IS THAT YOU CAN’T OR WON’T READ!

“You say that Taylor assumes the y measurements are true values, and your evidence is that he says they are from a normal distribution centered on the true value. If you can’t see the difference then you are really beyond hope.”

ROFL!!!

In your view saying you have a normal distribution centered on a true value means you do *NOT* have a normal distribution centered on a true value?

Your cognitive dissonance is showing again.

The force of gravity will cause rising temps to have a different variance from falling temps. Yet climate science never even mentions this, let alone tries to calculate it!

“True if you ignore all the times I assume it’s none of those things.”

If you didn’t assume that then you would have to admit that you don’t even know the sign for the slope of a trend line where the measurement uncertainty is larger than the differences the trend line is supposed to highlight.

If you didn’t assume that all measurement uncertainty is random, Gaussian, and cancels then you would have to admit that climate models, trained on uncertain past data, are garbage. You would have to admit that the baseline temps used to calculate anomalies simply can’t identify differences smaller than the unit digits and the “warmer than last year by 0.01C is just garbage.

So, do you reject the climate science as it is formulated today or are you going to stick with the meme of all measurement uncertainty is random, Gaussian, and cancels?

“I was playing with theStan and Bmrs packages a couple of weeks ago, and if you ask nicely I might see what happens if you assume non-Gausian distributions. Not that it will help as you seem to be rejecting all MC methods as well.”

As usual you are cherry picking. It isn’t an issue of non-Gaussian distributions. It’s an issue of measurement uncertainty adding – ALWAYS. It doesn’t matter if the data distribution is non-Gaussian or if the measurement uncertainty is asymmetric.

Sampling error assuming no measurement uncertainty in the data is *NOT* the accuracy of the population mean. A linear regression assuming no measurement uncertainty is *NOT* the true trend. And an MC choosing random values does nothing more than generate a Gaussian distribution per the CLT.



“Sorry G’s. That happens to be definitively true. And your mind bending “example” has nada to do with what’s actually under discussion.”

Sorry bud, but what I said is true. The linear regression only works if you assume all data points are 100% accurate. Otherwise you simply cannot identify the “true” linear regression line slope.

If you had actually bothered to work out the example I gave you then you would understand that. When the slope of the possible linear regression lines can range from 1 to 2 because of measurement uncertainty then it is impossible to tell which slope is “true”.

“To treat measurement uncertainty in trending, you randomly sample each of the measurement distributions”

Nope. If the measurements are given as “stated value +/- measurement uncertainty” then a random sample of the stated values is useless. The standard deviation of the stated values has to also be conditioned by the measurement uncertainty.

“Standard error” is nothing more than identifying the sampling error. The sampling error is *NOT* a metric for the accuracy of anything. The accuracy is defined by the measurement uncertainty.

Until you and bellman understand that you can get a very precisely calculated mean (i.e. the standard error) from terribly inaccurate data due to measurement uncertainty you will never understand measurement uncertainty.

I can measure crankshaft journals on an engine with a micrometer that is terribly out of calibration and get a very small standard error (i.e. a very small variation in measurements) – but when I order a new set of crankshaft bushings they won’t work! You’ll either lock up the engine or have no oil pressure!

Neither you or bellman are apparently able to grasp that simple concept, a concept a six year old can figure out!

Random sampling simply can’t reduce uncertainty.

Bevington: “The accuracy of an experiment, as we have defined it, is generally dependent on how well we can control or compensate for systematic errors, errors that will make our results different from the “true” values with reproducible discrepancies. Errors of this type are not easy to detect and not easily studied by statistical analysis. They may result from faulty calibration of equipment or from bias on the part of the observer.”

Taylor: “As noted before, not all types of experimental uncertainty can be assessed by statistical analysis based on repeated measurements. For this reason, uncertainties are classified into two groups: the random uncertainties, which can be treated statistically, and the systematic uncertainties, which cannot. This distinction is described in Section 4.1. Most of the remainder of this chapter is devoted to random uncertainties.” (tpg note: bellman has yet to understand this. He believes that all of the Taylor examples in Chapter 4 and later chapters apply to *all* measurements, whether they have systematic uncertainty or not).

Now come back and tell us how they are wrong and sampling (a statistical analysis tool) *can* result in determining a “true value”.

Again, you are stuck in the meme of all measurements being “true value +/- error” and that all error is random, Gaussian, and cancels.

Why don’t you join the rest of us in the 21st century?

“So, unless you have the magical condition of systemic error for millions of measurements slowly, evenly, going from one side to the other, over a 30+ year period, enough to quaitatively change the trend you – well, I already made my case…”

Your lack of understanding of how electronic components drift is showing.

An example is that the drift of a thin-film resistor (such as in an SMD component) is a complex equation of time and operating temperature. At a typical operating temperature the value can change by as much as 0.5% in less than a year. And the change will go up from there. That may not seem like a lot but when you are trying to identify temp differences in hundredths digit it can make a big difference. And the change does not have a +/- value. It is only shown as </= 0.5%. So assuming that some will go lower in value and some will go up in value is probably not a valid assumption.

Think of it this way. What does heat do to most materials? Resistance is a function of the resistivity of the material. Even in metal the resistivity *increases* as you heat it. Whether it returns to its original resistivity is a function of the hysteresis curve for the material.

What this means is that you can expect most measurement devices to drift in the same direction as it is used and the drift will increase with age. That means the drift is *not* random nor will it cancel out over multiple devices. That’s why measurement uncertainty can’t be assumed to be random, Gaussian, and cancels.

I make make sterling silver jewelry for sale and sew apparel for sale. Most of my time is spent on these endeavors. I don’t have time to try and educate people like you and the rest on multiple forums about measurement uncertainty and the properties of materials.