Statistical Jargon....

[Haywire Haywood]

Below is an excerpt from the help file from my new CED Millennium Chrono.  Can someone translate this to lamen’s terms for me?  Also can someone give me an explaination for Standard Deviation and how it's used?  
Here's some sample numbers from 14 Aguila .22 "Colibris" (similar to BB caps):
 
High: 406.2  
Low: 370.6  
Extreme Spread: 35.6
Avg: 395.0
S.D.: 10.8  
95%: ±6.0

Thanks,
Ian

The “Add 95% Probability” option will add a reliability factor for each group.  “95% Probability” means at least 95% of all shots should produce a velocity no greater or less than the average velocity plus/minus this amount.  Unlike SD, the “95% Probability” number is weighted by the number of shots in each string so you can better compare groups with a different number of shots.  For any Statisticians who are interested, the “95% Probability” is calculated using Chebyshev’s theorem for small samples.

[Deadeye47]

Haywire..thats the same problem I have reading and UNDERSTANDING the directions on my new chrony... I can't!!  :x  Good luck...

[Mac11700]

Below is an excerpt from the help file from my new CED Millennium Chrono.  Can someone translate this to lamen’s terms for me?  Also can someone give me an explaination for Standard Deviation and how it's used?  
Here's some sample numbers from 14 Aguila .22 "Colibris" (similar to BB caps):
 
High: 406.2  
Low: 370.6  
Extreme Spread: 35.6
Avg: 395.0
S.D.: 10.8  
95%: ±6.0

Thanks,
Ian



The “Add 95% Probability” option will add a reliability factor for each group.  “95% Probability” means at least 95% of all shots should produce a velocity no greater or less than the average velocity plus/minus this amount.  Unlike SD, the “95% Probability” number is weighted by the number of shots in each string so you can better compare groups with a different number of shots.  For any Statisticians who are interested, the “95% Probability” is calculated using Chebyshev’s theorem for small samples.

Well I'll give it a shot... :wink:  :wink:  Actully this is for my Beta Master Chrony but should help you...at least I hope it does.

FORMULAS
The computer in your Beta Chrony or Gamma Chrony calculates shot-string statistics in a manner similar to the simple methods shown below:
Average (Mean) Velocity (-Av-)       Where V is velocity and n is the number of shots.

Total all shots in a string and divide by the number of shots in the string, e.g.,
(2990 + 3010 + 2996 + 3004) ÷ 4 = 3000 FPS

Standard Deviation, population, (-Sd-)    
Multiply the square of the average velocity by the number of shots and deduct it from the sum of the squares of all shot velocities, then divide this total by the number of shots minus 1, and then take the square root of this figure. For example:
[(29902 + 30102 + 29962 + 30042 - 4 x 30002) ÷ (4-1)]½= 9 FPS

Standard Deviation is a measure of how close each shot’s velocity is to the "average" shot. It is called STANDARD because it is computed in such a way that it has a standard meaning when compared to the NORMAL CURVE. Nearly all things we measure fit a normal curve [e.g., the height of people, the diameter of (supposedly) identical motor pistons, and the velocity of (supposedly) identical cartridges]. The NORMAL CURVE shows that all variables occur more frequently at or near the average, and less frequently as they deviate further from the average. We use a STANDARD DEVIATION measure so that all things we measure can be compared with each other and to this curve [68% of all things we measure falls between one Standard Deviation above or below average, 95.4% falls between two Standard Deviations above and below the average, and 99.7% falls between three Standard Deviations above and below the average]. Thus, Standard Deviation is a universal method in statistics and measurement for dealing with and interpreting data.

Therefore, if the bullets are travelling at an average muzzle velocity of 3000 feet per second, and they have a Standard Deviation of 20, then 68% of the shots fired will fall between 2980 and 3020 fps, and 95.4% will fall between 2960 and 3040 fps. Nearly all of them (99.7%) will fall between 2940 and 3060 fps.

Since Standard Deviation is the most important information your chronograph can give you, it is useful to understand the reason for this. At least ten (10) shots are required to obtain a reliable average and Standard Deviation. Fewer shots (such as 3 or 5) are typically "small samples", and are considered unreliable when measuring anything variable.
Extreme Spread (-ES-)    Hi - Lo
Subtract the slowest shot from the fastest. For example: 3010 - 2990 = 20 FPS

ENERGY CALCULATION:
Average velocity X Average velocity X Weight of bullet in grains ÷ 450 240 = _____ft. lbs.


I hope that wasn't to technical for you...when I first got my chronograph I had to read it about 30 times before it sunk in my thick head...

Watch your extream spread too...this figure will show you things about your load...like how consistant all of your components and loading technics are...the lower the numbers you get for  your E.S.- and your S.D. the better...that's the key. Standard deviation is your averages off the normal velocities...the lower the number of the  deviation the better it is...you want your velocities to be the same from shot to shot...some loads will give you real low figures...others won't...then you get to factor in the tempreature differences for the same load and you can see why the powder manufactures are striving to make them as consistant as possiable...namely Hodgdons Extream powders...

Have a Good One

Mac

[Haywire Haywood]

WHEW  :shock: ... when I get back from work tonight, I gotta have a couple beers, close one eye and read that again a couple dozen times.  Everything is crystal clear except for the SD stuff...  I guess I just need to accept that it's a measure of consistancy, that the lower the value the  better, and not to worry about the details of how it's calculated.

Thanks Mac,
Ian

[Brett]

Thanks Mac, very good explanation. You just gave me a flash-back to college stat's class some 23 years ago.   Naturally back then when I was first struggling to understand this stuff, I was thinking "what the %$# am I ever going to use this $#@ for?"  Go figure.   Of course if my college prof. had used bullets in his examples instead of "widgets" I may have caught on a lot quicker.  :lol:

Brett

[Mac11700]

Haywire:

Here's the easiest way to remember what S.D. is...

Standard Deviation is a measure of how close each shot’s velocity is to the "average" shot.

It is easier for me to look at it this way than anyother way.

We strive to make each handloaded round to be the same...and to have the exact same velocity for each round. When we measure the velocity of a group called a shot string..we come up with a average velocity for the group...the larger the number of shots in a string(group) to be able to average them all...the better...once we have the average velocity of the shot string(group)...then any velocity different than than average for the string(group) is the "Deviation"....

The way mathmeticians figure things...all things...they have to fall into different groups of percentages and they devise all kinds of formulas to explain things...in this case.. it  is velocities...and they can tell what percentage will be in what group(deviation)..by devising different fourmulas that have different  rationals to explain why those figures happen...believe when I say they have formulas for just about everything...even chaos.. and most of it is GREEK to me :wink:

The end of your initial post goes into it a little bit  with the" pecentage of probability" theroum by Chebyshev" Even among the worlds greatest mathmeticians they are split into groups...much like the our own group who argue over the 45-70 and the 450M :-D

Mac

[Deadeye47]

The theroum by Chebyshev is exactly why my theroum on why I hate math  is the way it is... :shock:  My theroum is that I hated it when I was in school cause I didn't understand it and I hate it just as much now for the same reason.... :bye:

[JPH45]

Mac11700 is  very close. He is however describing the "average average". SD (standard deviation) is the "standard" amount of variation from the average. More simply, if a load produces a standard deviation of 20, then we can say that any sample we test will deviate from the average by at least 20. Average the amount of difference from the average of your test sample and you will get a number different from the SD.

Chebyshev is correct, we cannot predict with 100% accuracy what a test sample is going to do, we can only use the data to PREDICT, and prediction comes only with a fudge factor. He is saying, in your example, that the next sample will fall into the parameters extablished by your test group with a 95% probability +/- 6. This means he will BET that the next shot will do that if you give him a fudge factor of 89-101 points of certainty. Blah, Blah, Blah.....

We want to know this because we want to know how to sight in our guns. We want ot be able to predict that the next shot we make will be close enough in velocity to those before it, that our sight settings will be correct for the velocity....Blah, Blah, Blah....

It may well be, that our chronographs tell us more about our loading practices and compatability of components rather than how "good " a load actually is. I have fired some fantastic loads that gave numbers a statician dreams about.....only to have it not print on a newspaper. Conversely, I have seen  terrible stats loads that shot like a house afire.

I have seen SD's as low as 8 several times with 13 grains of Unique and 400 grain bullets in my 45-70. Velocity is about 1100 fps. Is this a good hunting load?? It'll do ANYTHING one would expect a 44 magnum revolver  to be capable of, with practically identical trajectories. I just can't bring myself to load this up this coming season in the hopes of poking one through a buck. There is more to statistics than statistics.

Never forget Mark Twains great quote....."There are lies, damned lies, and statistics"

[Haywire Haywood]

if a load produces a standard deviation of 20, then we can say that any sample we test will deviate from the average by at least 20.

Hmm... the way I understood it (until a few seconds ago that is), the above should have read "no more than 20" instead of "at least 20".  :?  If it is correct as written, then what I thought I had started to grasp just flew out the window. ---putting back the beer and getting the Jägermeister out---

Ian

[JPH45]

Haywire, Unfortunately, a bell curve as described for normal groups will usually cover 3 standard deviations either side of "0" or the norm.  Load up about 50 or 75 rounds of something to play with. It doesn't really matter what. fire every round of it over your chronograph. You can do this as 5 hot or ten shot groups (I prefer 5 shot strings) or you can fire the sample as one group. Be sure to record the velocity of every shot. Do the math.

While I have a lot more data available on this load, my favorite 357 Max plinking load is 11 grains of 5744 and the Lee 158 grain RF boolit. This is a typical 10 shot string:

967.8
971.8
976.7
976.4
964.4
996.5
973.1
965.9
987.8
987.4

SD= 10.10
Avg. Vel = 976
Avg Dev (Average Deviation, average from average) 8.2
Extreme spread 22

Note that the extreme spread is just over 2 times the standard deviation, and is 2.5 times (and a little more) of the Average Deviation, while the SD and the AD are actually quite close (in this example anyway)

Now 20 rounds of my favorite 44 plinking load, 8.6 grains of Blue Dot produced these figures:

SD = 23.49
Avg. Dev. = 16.8
Avg. Vel. = 820
Extreme Spread = 112

Both of those loads will shoot into 1.25" at 75 yards. Yet neither load shoots significantly better than the other.

If we take the 44 data, and center the average velocity in the extreeme spread (rarely how it actually happens) we would have a high velocity of 882 and a low of 748, the actual figures are 869 and 757.  

Always remember that every shot you fire over your chrono is making a prediction, and the more predictions you have, the higher your confidence in what the next shot is going to do, and that is what we want to know.

In collage I took a statistics course. The instructor came in each morning with a cardboard box filled with the entire workings of a pocket watch. Each morning he would dump this out on the desk, look at it, sweep it back into the box and continue class. At the end of the semister he did this and before sweeping the contents back into the box said to us "Statistically, it is possible that I can dump this box out on my desk and the parts will fall into working order. I have done this 4 times a day for 22 years and it hasn't happened yet. Please remember Mr Twains words as you embark on your life with statistics....There are lies, damned lies, and stastistics." (Yes, I am aware I repeat myself)

[Mac11700]

JHP45:

Since Haywire was asking for a laymans explanation I gave him just that...if you look at my earlier explaination..you'll see the the more detailed eplaination and the formula for getting the  S.D.

Haywire...

You can crunch numbers all day long and arrive at  different  results...most of which goes out the window thanks to Mr.Murphy...

Rule of thumb...Haywire...the more consistant your loads are... gennerally the more accurate they can be...

While you can get very small S.D's and have Ho-Hum  groups..... most of the time it's not that way...same for the extreme spread.

While a extreme spread of 112 for  a subsonic load such as JPH45's  357 can be acceptable...look at the benchrest shooters shooting a 308 utilizing a 180 gr. matchking hp at 2600fps... while the difference of bullet drop due to a -100 fps difference in the spead is only a 1/4" at 100 yards...move that out to normal match ranges of 500-600-and 1K and the variance becomes dramatic.,enough so you'll never win.

I guess this is where some will  ask"how accurate do you need...hunting accuracy for me is a Minute of (put your own animal here...)  or " I never shoot past 100-200 yards,those figure don't really matter...for me I look at it this way if I had to take a shot at a long range...would my ammo be good enough? ...I work my butt off making my ammunition that I reload as consistant as possible...this takes a big variable out of any problems getting it to group,at most any range I choose to shoot.

When I reload I strive to make everything consistant...and when I succeed...all of those figures are very small and most the time... single digit.That's the difference between me and a-lot of other people...I want match accuracy from all of my rifles...if I can't get it...I keep trying till I do...even if it takes having them reworked or as a last result trade it off.

While the S.D. gives you approximation...it isn't the only thing to be concerned about...and I say approximation because if your extreme spreads can't be more consistant than 100 fps...then your figures will always be changing...and you need to find the cause for that by changing components or loading technics.

Mac

[Longcruise]

Never forget Mark Twains great quote....."There are lies, damned lies, and statistics"

I also like to remember what my college stat prof said on the first day of class:  "Statistics don't lie, but Statisticians do."

Not his original quote but since the class was focused on statistics for the Sociologist, it was more than a little bit pertinent.