• Important Executive Director Announcement from the NAWCC

    The NAWCC Board of Directors is pleased to announce that Mr. Rory McEvoy has been named Executive Director of the NAWCC. Rory is an internationally renowned horological scholar and comes to the NAWCC with strong credentials that solidly align with our education, fundraising, and membership growth objectives. He has a postgraduate degree in the conservation and restoration of antique clocks from West Dean College, and throughout his career, he has had the opportunity to handle some of the world’s most important horological artifacts, including longitude timekeepers by Harrison, Kendall, and Mudge.

    Rory formerly worked as Curator of Horology at the Royal Observatory, Greenwich, where his role included day-to-day management of research and digitization projects, writing, public speaking, conservation, convening conferences, exhibition work, and development of acquisition/disposal and collection care policies. In addition, he has worked as a horological specialist at Bonhams in London, where he cataloged and handled many rare timepieces and built important relationships with collectors, buyers, and sellers. Most recently, Rory has used his talents to share his love of horology at the university level by teaching horological theory, history, and the practical repair and making of clocks and watches at Birmingham City University.

    Rory is a British citizen and currently resides in the UK. Pre-COVID-19, Rory and his wife, Kaai, visited HQ in Columbia, Pennsylvania, where they met with staff, spent time in the Museum and Library & Research Center, and toured the area. Rory and Kaai will be relocating to the area as soon as the immigration challenges and travel restrictions due to COVID-19 permit.

    Some of you may already be familiar with Rory as he is also a well-known author and lecturer. His recent publications include the book Harrison Decoded: Towards a Perfect Pendulum Clock, which he edited with Jonathan Betts, and the article “George Graham and the Orrery” in the journal Nuncius.

    Until Rory’s relocation to the United States is complete, he will be working closely with an on-boarding team assembled by the NAWCC Board of Directors to introduce him to the opportunities and challenges before us and to ensure a smooth transition. Rory will be participating in strategic and financial planning immediately, which will allow him to hit the ground running when he arrives in Columbia

    You can read more about Rory McEvoy and this exciting announcement in the upcoming March/April issue of the Watch & Clock Bulletin.

    Please join the entire Board and staff in welcoming Rory to the NAWCC community.

Understanding Standard Deviation

Alex Hamilton

NAWCC Member
Jan 29, 2021
8
0
1
60
Carolina Beach
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Hi all,
I have read about using a standard deviation calculator in analyzing timegrapher testing results and for the life of me still am not sure how it relates to watch timing accuracy.
As an example I just serviced a Stowa PUW 560.
The results are as follows in 10 positions:
DU= 10
DD=11
0=-5
1=-2
2=0
3=-5
4=-11
5=-9
6=-7
7=-5
When plugged into the standard deviation calculator I come up with standard deviation of 3.58
Can anyone shed some light on this statistic means in watch timing or is it really meaningless.
Thanks in advance, Alex
 

Chris Radek

NAWCC Member
Apr 13, 2014
769
305
63
Lincoln, NE, USA
timeguy.com
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If the standard deviation is high, it means your values are more spread out. If it's lower, it means your values are clustered tightly near the mean (average) value. That would mean the watch's positional adjustment (independent of regulation) is better.

That being said, I think you don't have the standard deviation calculated right, it should be more like 7.

Your mean value (average of measured positions) is -2.3, so you can think about the standard deviation meaning that your values are mostly within 7 of that (-9.3 ... 4.7) and the values outside that range are the extreme/unusual ones.
 

Alex Hamilton

NAWCC Member
Jan 29, 2021
8
0
1
60
Carolina Beach
Country
If the standard deviation is high, it means your values are more spread out. If it's lower, it means your values are clustered tightly near the mean (average) value. That would mean the watch's positional adjustment (independent of regulation) is better.

That being said, I think you don't have the standard deviation calculated right, it should be more like 7.

Your mean value (average of measured positions) is -2.3, so you can think about the standard deviation meaning that your values are mostly within 7 of that (-9.3 ... 4.7) and the values outside that range are the extreme/unusual ones.
Hey Chris,
Thanks for that answer.
I reentered the numbers into the calculator, this time entering the negative numbers as -5,-2 etc and came up with 7.4xxxxxxx which lines up to what you thought it should be.you
A mean time value seems pretty good but if I understand you correctly, ideally you would want the mean value and deviation value closer together.
 

Chris Radek

NAWCC Member
Apr 13, 2014
769
305
63
Lincoln, NE, USA
timeguy.com
Country
Well you ideally want the average (average and mean are different words for the same thing) to be around 0 and the standard deviation to be small.

For example say you test some positions and get values of -100, -50, 0, 50, 100. It's easy to see the average is 0, but the standard deviation is very high, 79 in this case. The regulation of the watch is as good as possible, centered on 0, but the watch isn't going to keep great time because the positions vary so much.

Now you adjust the balance wheel and hairspring and make the same tests and get numbers much more tightly clustered: -3, -1, 0, 1, 3. This has the same average of 0, which means the regulation is set to be as good as possible, but now the standard deviation is much lower at around 2. You can imagine that this watch will now keep much better time in use.

See how the standard deviation is a single number that pretty well represents the quality of the positional adjustment of the watch?
 

Alex Hamilton

NAWCC Member
Jan 29, 2021
8
0
1
60
Carolina Beach
Country
Well you ideally want the average (average and mean are different words for the same thing) to be around 0 and the standard deviation to be small.

For example say you test some positions and get values of -100, -50, 0, 50, 100. It's easy to see the average is 0, but the standard deviation is very high, 79 in this case. The regulation of the watch is as good as possible, centered on 0, but the watch isn't going to keep great time because the positions vary so much.

Now you adjust the balance wheel and hairspring and make the same tests and get numbers much more tightly clustered: -3, -1, 0, 1, 3. This has the same average of 0, which means the regulation is set to be as good as possible, but now the standard deviation is much lower at around 2. You can imagine that this watch will now keep much better time in use.

See how the standard deviation is a single number that pretty well represents the quality of the positional adjustment of the watch?
Perfect. Now it makes sense.
Thanks Chris
 

Paul_S

NAWCC Member
Mar 27, 2015
188
7
18
North Carolina
Country
As someone who does data science as his day job, I suggest additionally looking at the "mean absolute deviation" as an especially practical statistics for watch adjusting. This is simply how far away the positions are from zero (whether fast or slow), on average.

For the 10 rates in this example, the standard deviation is 7.44, and mean absolute deviation is 6.50. Each position is, on average, 6.5 seconds away from zero in any direction. It has a more intuitive interpretation, I think.

No one single metric best captures performance, and I suppose it is easy to overthink these things. The old "straight limits" discussed in the old watchmaking books (a straight limit of 15 means no position can be more than 20 seconds from zero) have a certain appeal in their practical simplicity. In practice, I tend to focus on straight limits.

For this particular watch, what stands out is a "hanging/lying" or "horizontal/vertical" disparity. The two horizontal rates (DU/DD) are appreciably faster than all eight vertical ones. This can be vexing to deal with and is discussed in the Kleinlein and Jendritzki books on watch adjusting.

# in the off chance someone reading this uses R for statistics, some code
# start

library(DescTools)
example <- c(10,11,-5,-2,0,-5,-11,-9,-7,-5)
MeanAD(example, center = 0, na.rm = FALSE)
sd(example)

# end
 

DeweyC

NAWCC Member
Feb 5, 2007
2,338
912
113
Baltimore
www.historictimekeepers.com
Country
Hi all,
I have read about using a standard deviation calculator in analyzing timegrapher testing results and for the life of me still am not sure how it relates to watch timing accuracy.
As an example I just serviced a Stowa PUW 560.
The results are as follows in 10 positions:
DU= 10
DD=11
0=-5
1=-2
2=0
3=-5
4=-11
5=-9
6=-7
7=-5
When plugged into the standard deviation calculator I come up with standard deviation of 3.58
Can anyone shed some light on this statistic means in watch timing or is it really meaningless.
Thanks in advance, Alex
As a card carrying statistician, I have never seen standard deviation used this way. As you probably know already SD is used to estimate the sample spread around the mean for that sample in order to assess if the sample mean is a good indicator of the true mean for the population being studied. Each of the different positions represent a new type of sample (population) and the use here is like measuring apples and oranges.

In horology, SD was used in chronometer trials to estimate the variability of the rate over the 7 day (one observation for each of the 7 days) trials in the various temps. This stability of rate factored into the scoring. In fact I believe this stability of rate was the most heavily weighted factor in the score. These trials included at least 30 observations and some lasted for 3 months.

In positional timing, the only factor I have ever see or been exposed to is the "positional error rate". This is the largest rate difference between any two positions.

Your watch has a positional error of 11 seconds (positions 2 and 4). This is actually almost Rolex standards (was 10 last time I looked). From the factory Hamilton specified a 6 second positional error. This means the maximum error rate when worn will be -11 seconds and given it not will stay in one position when worn, that error rate will be considerably less. It is this human element that required watches to be regulated by the watchmaker after one or two weeks of use.
 
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Paul_S

NAWCC Member
Mar 27, 2015
188
7
18
North Carolina
Country
I think metrics like standard deviations, average absolute deviations, or fancier alternatives (e.g., entropy measures) are most useful for comparison purposes, such as comparing a watch to itself over time (e.g., how each round of adjusting affects the rates, or how a watch varies across a set of days) or comparing watches to each other.

But as appealing as fancy-pants statistics are, often the simplest ones are the best, such as the tried-and-true "range" Dewey notes (the gap between the fastest and slowest position).

For practical purposes, it can get even simpler. The distances between specific positions might be the target, such as when watches were adjusted to 2 or 3 positions instead of all 6.

Likewise, a good set of rates (with a low SD, for example) can nevertheless be non-ideal in the specific positions. A "positional error" (range) of 10 for pocket watch, for example, is better when it is between dial-up and pendant-down (an uncommon position for a pocket watch) than dial-up and pendant-up (both common positions in the real world).

This Stowa watch is an example of the metrics obscuring an adjusting issue. The two horizontal positions have an average of +10.5. The eight vertical ones listed have an average of -.5.5. All vertical positions are slower than the horizontal ones. The hanging/lying range is 15, which is nearly as high as the range for all 10 positions you recorded (22).

So while the rates as a set aren't that far from zero, the low variance obscures a "hanging/lying" error (albeit a minor one for that kind of watch).
 

Al J

Registered User
Jul 21, 2009
635
86
28
Canada
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Region
I've never seen standard deviation used in bench watchmaking - not included in any instructions I've had in school or in brand training. Typically watch companies will give tolerances in terms of average rate over a number of positions, and then the Delta (difference between the fastest and slowest position). Add in numbers for isochronism (full wind rates compared to 24 hours after full wind typically), and that's really all you need practically when working on a watch.

Of course you will look for other things in the timing - relationship of horizontal to vertical readings, opposite vertical readings being very far apart indicating a possible poise error, etc. But personally for working on one specific watch, I don't think standard deviation is particularly useful.

Cheers, Al
 
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DeweyC

NAWCC Member
Feb 5, 2007
2,338
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www.historictimekeepers.com
Country
I've never seen standard deviation used in bench watchmaking - not included in any instructions I've had in school or in brand training. Typically watch companies will give tolerances in terms of average rate over a number of positions, and then the Delta (difference between the fastest and slowest position). Add in numbers for isochronism (full wind rates compared to 24 hours after full wind typically), and that's really all you need practically when working on a watch.

Of course you will look for other things in the timing - relationship of horizontal to vertical readings, opposite vertical readings being very far apart indicating a possible poise error, etc. But personally for working on one specific watch, I don't think standard deviation is particularly useful.

Cheers, Al
There are two issues with this attempt to quantify rate variance using SD.

The first is very basic information theory. What information is gained by this "metric"? I can see none. All the information required is in the positional rates. The gain "could" come if the observer recorded the means of each positional rate over time. Say 30 days (5 days in each position). Then compute the means and SD for each position to see how variable the rate is in that position. That adds information and is what was done in trials. It was called "recovery". Knowing the stability of rate in each position does add information. Not sure how much is useful in wathces such as RRG watches, but for navigation (where there is not always means to immediately verify the dial reading) it adds value. But this latter and correct use of SD is not what the OP asked about.

The SD as proposed merely tells you what you already know from your direct observations. That the spread of rates is high or low. There is no added information. Even the mean of the positional rates is useless since that mean does not take into account the time spent in each position during use. Statistics derived from that mean (SD) would then also be useless.

The second issue is that it does not change the behavior of the watchmaker/customer. There is a positional rate difference. Unavoidable. But the watch takes different positions for varied amounts of time. Depending on the wearer.

The watch will still have to be regulated after a couple weeks of wear. Rather than spend time trying to compute, why not just spend the time to get the rates as close possible? Once the positional rates are under 6 seconds (Hamilton RRG) the watch should be very close to 30 seconds per week out the door.
 
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