Stn Dev vs 2 Sigma

[Baron23]

@Ledzep and any others who still remember statistics (which I did squeak thru barely and at 69 I'm successfully purged that from my memory!! haha).

We talk about Standard Deviation (or one sigma) in reloading as really the prime indicator of MV consistency.

Now, if I understand it correctly, Stn Dev, the way we use it; 1) assumes we have the total population vice sampling (which we do); 2) assumes a normal distribution (which I don't know is valid or not); and 3) my main point is that it only includes 68% of the population. That is, the Stn Dev numbers we get from chrono'ing our ammo (and let's say from a pop of 50 shots to ensure we have a statistically valid sample) is really telling us only that 34% will be plus and 34% will be minus our average MV and 32% will be outside of this boundary. That 32% seems like a lot to my ignorant self.

My first question is; two sigma, which will include 95% of our data population, is just 2 x Stn Dev, correct? So, if I have a Stn Dev of 11 fps, 95% of my shots MV will fall into a 22 fps range centered on the average. Right?

And, I guess my next question is why do we only focus on Stn Dev and not a a tighter criteria like 2 sigma which seems more meaningful to me.

And yes, I have too much time on my hands! haha

Thanks for considering my uniformed and ignorant questions! haha

 

[Dogtown]

Let me just preface that stats is not my jam. I have an education in it and use a variety of sampling techniques in my job, but I'm by no means an expert.

Yes, we should assume a normal distribution and 2 sigma would mean that 95% of the population is within that distribution and 5% are on the outlying edges of the distribution. The higher the sigma value the lower the odds that a given result is outside of the range of distribution. That's why in Physics, for example, you tend to see 6 sigma as the gold standard, but for what we're doing that's nuts. It's kind of like trying to measure powder charges to +/- 0.0005 grains; those kind of fluctuations are insignificant to what we're doing.

So that dark portion above is 1 sigma and from what I'm gathering from your questions, you're thinking that we should instead be looking at the lighter wider 2 sigma section? What we're generally looking for with low 1 sigma SD values in shooting is to get an idea of how spread out the velocity values are from the mean. Why not do 2 or 3 sigma? Honestly I don't know - the math isn't necessarily harder. I suspect it's just that for the small sample sizes we tend to test with (n < 10 or n < 30) a higher sigma probably doesn't really contribute more.

 

[Bmghunter]

Not an expert here, but I did take statistics too. Knowing the std dev gives you one or two or three sigma values already, as you mentioned 2x, 3x, etc. Yes 2x std dev captures a higher amount of your shot velocities, but at the end of the day, you are still looking for the std value that gives you the most consistent velocity. Whether you use 2 sigma or one std dev, it's the same effect, smaller std dev means more consistent velocity. Knowing one gives you the value of the other. Using the same terminology keeps it easier to compare different values.

 

[TheOfficeT-Rex]

And, I guess my next question is why do we only focus on Stn Dev and not a a tighter criteria like 2 sigma which seems more meaningful to me.

It's all in how you want to use it. Dogtown has a good example above - physics may require a higher degree of confidence, but for me to judge one load or process against another, comparing SD against SD is fine. If you wanted to move towards 2 sigma, why not just compare extreme spreads? You're 95% of the way there...

If you want to work out long range hit percentages, and the impact of SD on hit probability, I'd recommend Lit'z book. I have a copy here and it dives a lot deeper into mathematical modeling. For everyone else to PP wave on the internet about how awesome their loads are, just using SD is fine.

 

[Dogtown]

Yup, 6 sigma is a tough standard to work to, but in physics research it’s vital that a result being anomalous be to a very very tiny percentage. The folks working at the LHC started seeing hints of the Higgs field right away in the first few data collecting runs but they waited a few years until they were at 6 sigma before they were confident that what they were seeing was very real and wasn’t some quantum fluctuation that just happened to appear periodically (coincidences happen all the time in research, especially when you don’t have huge n values).

On a side note about statistical sampling, I seem to remember Litz (AB) having software that basically does quasi-monte carlo simulations of impacts at distance based on typical ballistic data. The result is a similar distribution of expected impacts on or near the target to help the user get a rough educated estimate of load performance. I’m a bit surprised tools like that aren’t as popular.

 

[Ledzep]

1. Generally speaking, and assuming normal distribution, most of what's been posted is correct regarding how SD is often used.

2. I'll look through my data pile, but it seemed to me that, while the data I've collected generally produces "bell curves" the distribution wasn't exactly normal. Long-term data seemed to suggest 4 sigma encompassed more than 95% of the data. I'll double check tomorrow if I remember.

3. SD is only a useful tool for comparing/contrasting if it's given a large enough sample size. Otherwise the "error bars" on the number your chrono spits out can be large enough to make determinations muddy-- and rightfully so. 16-18 is the FLOOR according to the data I've collected. I shoot a lot of 20-shotters, but will occasionally still do 35-50 depending on what I'm looking at/for. Put another way, the more shots you put in the sample, the less deviation you'll see in repeating the same test over and over again. The fewer shots in a sample, the more deviation you'll see from test to test of the "exact" same thing.

 

[Baron23]

@Ledzep @Dogtown @TheOfficeT-Rex @Bmghunter

HI guys - sorry for opening a question thread and then disappearing.....but family and Labor Day hijacked me for the duration yesterday! haha

I want to thank everybody for their input and replies. I find that here in the reloading forum, you get serious answers from knowledgeable and willing people.

Let me reply to some of your input and again demo my ignorance! haha

Yes, we do assume a Gaussian distribution (how about that word bubbling up from the memory tar pit! haha) but tbh I think we do that just as a mathematical convenience and I'm not aware of any proof that this is actually true. I'd be interested in what Ledzep says if he looks at his data more but 4 sigma to capture 95% of the data population may be "bell shaped" but is def not a "normal" distribution. But I get it....what else are we really to do.

And I am familiar with the image showing the curve and sigma points but thank @Dogtown for publishing it in this thread.

I do think I did get answers to my main question which is that if we have the entire population in the data set (vice sampling and extrapolating) then yes, 2 sigma, 3 sigma, etc are indeed 2x, 3x, etc the SD (i.e. 1 sigma).

I do not necessarily agree (but may well be wrong) that if looking at 2 sigma, then we may as well look at ES as they would be mostly equivalent. This goes back to my suspicion that, while we assume normal distribution, this may well not be the case. Let's say that Roger Reloader is really on his game and reloading very consistent ammo....for the most part (that last part is important). The plot of his 50 shot plus chrono data set (and yes, Ledzep, I agree that we need a goodly sized data set for any validity) may well be much tighter/narrower than a normal distribution. BUT like us all, Roger is human and just really fucked up a load or two that resulted in a large ES while SD remains very small (and again, this assumes a significant sample size sufficient to bury the noise ).

I seem to remember Litz (AB) having software that basically does quasi-monte carlo simulations of impacts at distance based on typical ballistic data. The result is a similar distribution of expected impacts on or near the target

This is sort of what I was getting at. Yes, SD seems to be handy for comparison of one load (or change in loading process/technique) to another. Its a well defined figure of merit and does facilitate comparisons, right? All good.

But I think of Circular Probability Error as used by the military, that looks at the probability that 50% of the projectiles/missiles will impact within a certain radius, and think to myself, wow...50% ain't all that good.

So, when we look at long range first hit probabilities, is SD....defining a group of shots with MV within +/- 34% of mean average, good enough? If I really, really, really want to know the circular error with really, really, really high hit probability, then we would have to look at 2 or 3 sigma....yes/no???

And yes, this is mostly mental masturbation and I cop to that! haha

Cheers

Thanks again, hope all had a fun and safe Labor Day, and again...I do appreciate your taking the time to reply.

 

[Dogtown]

It feels a bit like splitting hairs at this point. The good news is most chronos will compute either or both ES and SD, and while SD is a quick gauge of how consistent your ammo is, I shoot a lot of ELR distances so I tend to focus on ES a bit more.

 

[Baron23]

It feels a bit like splitting hairs at this point. The good news is most chronos will compute either or both ES and SD, and while SD is a quick gauge of how consistent your ammo is, I shoot a lot of ELR distances so I tend to focus on ES a bit more.

haha...yes, splitting hairs. I agree.....

But your focusing more on ES for ELR (which I have not shot) does seem go to the core of my interest in these questions.

Thanks and best of luck

 

[Ledzep]

Here's some data from a "vanilla" 6.5 Creedmoor ladder test. 35 shots per test. 140gr ELD-M, H4350, 2.80" COAL, Fed210, Hornady cases.

41.3gr
Min: 2753
Max: 2784
Avg: 2765
ES: 31
SD: 8
2 Sigma: 16
4 Sigma: 32
6 Sigma: 47
(all inside 4 sigma)


41.6gr
Min: 2770
Max: 2796
Avg: 2781
ES: 26
SD: 8
2 Sigma: 16
4 Sigma: 32
6 Sigma: 48
(all inside 4 sigma)


41.9gr
Min: 2782
Max: 2823
Avg: 2799
ES: 41
SD: 9
2 Sigma: 19
4 Sigma: 37
6 Sigma: 56
(1 shot outside of 4 sigma, high)



42.2gr
Min: 2807
Max: 2851
Avg: 2826
ES: 44
SD: 9
2 Sigma: 18
4 Sigma: 37
6 Sigma: 55
(1 shot outside of 4 sigma, high)

So what I've noticed across most of this testing is that even if I do fairly large samples, very rarely are there 'outliers' that are outside of +/- 2.5 sigma. Most everything fits inside of 4.5 sigma. The bell shape is very similar to a 'normal' distribution, but it's a tighter spread. I used to know but I'm not hip anymore on the various distributions because I believe there was a correction factor for such a thing. So typically we look at a 20 shot string and you would expect 1 shot (5%) to be outside of 4 sigma, and more often than not it's not the case. Even above, with 35 shot samples you only have 1 shot ea. outside 4 sigma on the two samples that do go outside 4 sigma, 1.4% of the total 140 rounds. Some of this could be because the tails get pretty short past a certain point, but even at 2 sigma benchmark, more than 68% is included. 74% for example on the 41.9gr sample.

The other thing I've noticed... a caveat on me saying "normal bell shaped", is that there seems to be *generally* a higher propensity to have lower velocities than higher velocities. It's skewed a bit. The fewer number of shots that go above average, tend to go farther above the average. This leaves a majority of shots below the average.

 

[Ledzep]

My distribution looks a little a little more like this (totally free-hand MS painterized, not exactly to scale, etc..).

 

[Baron23]

Here's some data from a "vanilla" 6.5 Creedmoor ladder test. 35 shots per test. 140gr ELD-M, H4350, 2.80" COAL, Fed210, Hornady cases.

41.3gr
Min: 2753
Max: 2784
Avg: 2765
ES: 31
SD: 8
2 Sigma: 16
4 Sigma: 32
6 Sigma: 47
(all inside 4 sigma)


41.6gr
Min: 2770
Max: 2796
Avg: 2781
ES: 26
SD: 8
2 Sigma: 16
4 Sigma: 32
6 Sigma: 48
(all inside 4 sigma)


41.9gr
Min: 2782
Max: 2823
Avg: 2799
ES: 41
SD: 9
2 Sigma: 19
4 Sigma: 37
6 Sigma: 56
(1 shot outside of 4 sigma, high)



42.2gr
Min: 2807
Max: 2851
Avg: 2826
ES: 44
SD: 9
2 Sigma: 18
4 Sigma: 37
6 Sigma: 55
(1 shot outside of 4 sigma, high)

So what I've noticed across most of this testing is that even if I do fairly large samples, very rarely are there 'outliers' that are outside of +/- 2.5 sigma. Most everything fits inside of 4.5 sigma. The bell shape is very similar to a 'normal' distribution, but it's a tighter spread. I used to know but I'm not hip anymore on the various distributions because I believe there was a correction factor for such a thing. So typically we look at a 20 shot string and you would expect 1 shot (5%) to be outside of 4 sigma, and more often than not it's not the case. Even above, with 35 shot samples you only have 1 shot ea. outside 4 sigma on the two samples that do go outside 4 sigma, 1.4% of the total 140 rounds. Some of this could be because the tails get pretty short past a certain point, but even at 2 sigma benchmark, more than 68% is included. 74% for example on the 41.9gr sample.

The other thing I've noticed... a caveat on me saying "normal bell shaped", is that there seems to be *generally* a higher propensity to have lower velocities than higher velocities. It's skewed a bit. The fewer number of shots that go above average, tend to go farther above the average. This leaves a majority of shots below the average.

Thank you for taking the time to dig this out and publish it here.

What I have been doing this summer is collecting chrono data on reloads with two charge weights that I picked out for further testing. I have been adding the new data points to the older set and continuing to calc ES/SD in Excel. Yeah, not the same day/temp but pretty much similar (that is, hot as hell in Maryland this summer).

I have, for example, a bit over 100 shots for one charge weight and, as you have said, after a bit (eh, maybe 50 shots) the SD became pretty stable as new data points were added.

And, as a new reloader (and who the hell else but a new reloader would be wrapped up in this hair splitting! haha) I'm rather gratified as I'm getting ES of 57 and SD of 11 and looking at your numbers I don't seem to be doing that badly (and I really am very new to reloading metallic).

I think if I want to try to improve these figures more, I may well have to get into neck bushings and mandrels to see if I can tune up neck tension (my Reddining FL die is giving me a fairly consistent .003 of tension...so, not bad to my mind, really) and move away from Hndy brass to something a bit more consistent (and mo' $$ haha).

Thanks again for the data.

 

[TheOfficeT-Rex]

So, when we look at long range first hit probabilities, is SD....defining a group of shots with MV within +/- 34% of mean average, good enough? If I really, really, really want to know the circular error with really, really, really high hit probability, then we would have to look at 2 or 3 sigma....yes/no???

When we look at modeling first hit probabilities, using SD is fine because it is an input to the equation. What I mean is, assuming a normal distribution, the monte carlo(esque) simulations for hit probability would model the same population if you told it the average was 3000, with an SD of 10 or an average of 3000 with a 2sigma of 20. The equation would count either the SD, or 2sigma, as the same indication of randomness in the equation - your hit probability outcome would be nearly identical.

From a practical standpoint, Litz's book "Accuracy and Precision for Long Range Shooting" looks at modeling the effect of MV, wind speed estimation, rifle precision, target size, and range estimation on hit percentage. I think the book covers a lot of what you are driving towards with modeling, although it can be a dense read in sections. Heck, this is the first time I've picked it up since I finished it, you can have my copy if you want to slog through it.

The real question is, are you trying to make a model for hit percentage, and to what end? The end is what should really drive your analysis. With respect to SD, I will say this - lower is better, and target size/range matter. SD is going to cause few misses on a full size IPSC, statistically. 10" circle at 1000? SD matters more, but how much it matters is dependent on MV.

If your SD over 100 rounds is 11, I'd consider that a win and probably wouldn't specifically chase it - but my shooting is either short range benchrest-esq or PRS practical style. YMMV.

 

[Doom]

To the OP, I'll try and answer your questions/ But I would recommend that you go to the precision rifle blog and read the three part series on statistics.

Now, if I understand it correctly, Stn Dev, the way we use it; 1) assumes we have the total population vice sampling (which we do); 2) assumes a normal distribution (which I don't know is valid or not); and 3) my main point is that it only includes 68% of the population. That is, the Stn Dev numbers we get from chrono'ing our ammo (and let's say from a pop of 50 shots to ensure we have a statistically valid sample) is really telling us only that 34% will be plus and 34% will be minus our average MV and 32% will be outside of this boundary. That 32% seems like a lot to my ignorant self.

First, when we test we are testing a sample out of a population. It is important to make this distinction. If we run 3 samples across a chronograph and calculate a standard deviation, then by the nature of the derivation of the SD formula, 68% of the data lies in +/-1 SD and 95% lie in +/-2SD, and so on. Obviously three shots is difficult to divide into that classification. If more shots are sampled then the the numbers become more normal. As to whether or not a distribution is normal or not is often debated but scientific research has proven that most data exhibits a normal distribution. Understand though that when we talk of standard deviation, that covers the range of percentages since all are calculated off of SD.

My first question is; two sigma, which will include 95% of our data population, is just 2 x Stn Dev, correct? So, if I have a Stn Dev of 11 fps, 95% of my shots MV will fall into a 22 fps range centered on the average. Right?

Not quite. The SD obtained for a test (sample) applies ONLY to the sample. It matters not whether its 3 shots, 5 shots, or 200 shots. So yes in your case the 95% is 22fps. This does not mean that it applies directly to the population , meaning other rounds loaded the same of which the sample is meant to represent. To apply the sample SD to a larger population is an exercise in probability. The articles I mentioned in the PRB explain this in detail. If you test 3 rounds and obtain a mean(average) value of 2600 and a SD of 11, then there is 95% confidence that the population mean would be between 2573 and 2627 fps, and that the standard deviation of the population would be between 5.7 and 69.1 fps. SO a three round test is not very informative, especially when looking at SD. If ten rounds are sampled, the mean confidence interval is 2586 and 2614, and the SD is 6.6 and 31.6. For 10 rounds its 2592 and 2608, and 7.6 and 20.1. All based on 2600 mean and 11 SD. Also, you should note that the mean will typically be normally distributed in large samples and populations, but standard deviation is not normally distributed. There is a limit as to how small the SD can be. Note that it is also a calculated value and not a measured value.

And, I guess my next question is why do we only focus on Stn Dev and not a a tighter criteria like 2 sigma which seems more meaningful to me.

As noted earlier the SD is the basic statistic for any criterion, be it the 2 sigma, 3 six sigma, or the dreaded 6 sigma. so a discussion of just SD conveys the base information.

Go to post #28 on https://www.snipershide.com/shooting/threads/stats-for-velocities-and-groups.7085562/#post-9614553 and you can see some data applications and how samples and population vary and what they ultimately mean.

 

[Baron23]

To the OP, I'll try and answer your questions/ But I would recommend that you go to the precision rifle blog and read the three part series on statistics.

First, when we test we are testing a sample out of a population. It is important to make this distinction. If we run 3 samples across a chronograph and calculate a standard deviation, then by the nature of the derivation of the SD formula, 68% of the data lies in +/-1 SD and 95% lie in +/-2SD, and so on. Obviously three shots is difficult to divide into that classification. If more shots are sampled then the the numbers become more normal. As to whether or not a distribution is normal or not is often debated but scientific research has proven that most data exhibits a normal distribution. Understand though that when we talk of standard deviation, that covers the range of percentages since all are calculated off of SD.



Not quite. The SD obtained for a test (sample) applies ONLY to the sample. It matters not whether its 3 shots, 5 shots, or 200 shots. So yes in your case the 95% is 22fps. This does not mean that it applies directly to the population , meaning other rounds loaded the same of which the sample is meant to represent. To apply the sample SD to a larger population is an exercise in probability. The articles I mentioned in the PRB explain this in detail. If you test 3 rounds and obtain a mean(average) value of 2600 and a SD of 11, then there is 95% confidence that the population mean would be between 2573 and 2627 fps, and that the standard deviation of the population would be between 5.7 and 69.1 fps. SO a three round test is not very informative, especially when looking at SD. If ten rounds are sampled, the mean confidence interval is 2586 and 2614, and the SD is 6.6 and 31.6. For 10 rounds its 2592 and 2608, and 7.6 and 20.1. All based on 2600 mean and 11 SD. Also, you should note that the mean will typically be normally distributed in large samples and populations, but standard deviation is not normally distributed. There is a limit as to how small the SD can be. Note that it is also a calculated value and not a measured value.


As noted earlier the SD is the basic statistic for any criterion, be it the 2 sigma, 3 six sigma, or the dreaded 6 sigma. so a discussion of just SD conveys the base information.

Go to post #28 on https://www.snipershide.com/shooting/threads/stats-for-velocities-and-groups.7085562/#post-9614553 and you can see some data applications and how samples and population vary and what they ultimately mean.

Thank you...I will look at PRB and find those articles....I had not seen them before but almost everything on that blog is outstanding and informative.

I guess my only question...and you seem to have a much greater grasp of statistics than I, is whether we have the full population or a sample.

For example, if doing production testing and pulling a sample out of every ten items off of the line producing 100 items, then we have a sample and the full population is 100. I took a look at some equations for SD and there seems to be a slight diff in how you calculate for a sample subset of the data vs having all data points and hence a full population.

However, if I shoot 40 rounds and have data on every round, then I do believe that I have the full population. It is not a sample, it is the full data set. And I do understand that projecting the results of this analysis to future data (mo' shots) is a probabilistic function. But, I still think (and am prob wrong) we have the full data set of 40 shots hence the full population. I do this in Excel and use STDEV.P (P for full population) which is predicated on inputing the full data set as the argument for the function....which, if I have 40 shots and enter the range that includes the MV for all 40 shots, it still seems to me that we do indeed have the full population and STDEV.P is the appropriate function. But, please do correct me if I am wrong as my grasp of statistics seems to have died with some of my very old brain cells.

Oh, and I do not do 3 round tests and take that SD as being at all significant....I'm calc SD off of 40-100 consecutive data points.

And I book marked your linked post and will read it later. Thank you for that.

Thanks again and I will re-read your post again and see if I can glean more meaning...there is a lot in there.

 

[Ledzep]

I would say most of the time your testing is a sample, and the population would represent the useful/steady barrel life of a particular load.

Another way to look at it:

Imagine a 1000yd indoor tunnel where your barreled action is bolted to a 2-ton block of granite, you pick a load and seating depth and proceed to fire the useful barrel life of that load down range at blank paper at 1000yd. After say 2800 rounds from a 6.5 Creedmoor, you can evaluate the dispersion and MV ES/SD of the population.

Unfortunately... now your barrel is toast! So the name of the game is to get as much information as possible out of as few rounds as possible to make conclusions about which load is better so that the population ends up being as good as possible. However there is no cheating statistics. As Doom pointed out, small sample size means inconclusive results when the potential error in the test result is greater than the difference between two tests.

 

[Baron23]

I would say most of the time your testing is a sample, and the population would represent the useful/steady barrel life of a particular load.

Another way to look at it:

Imagine a 1000yd indoor tunnel where your barreled action is bolted to a 2-ton block of granite, you pick a load and seating depth and proceed to fire the useful barrel life of that load down range at blank paper at 1000yd. After say 2800 rounds from a 6.5 Creedmoor, you can evaluate the dispersion and MV ES/SD of the population.

Unfortunately... now your barrel is toast! So the name of the game is to get as much information as possible out of as few rounds as possible to make conclusions about which load is better so that the population ends up being as good as possible. However there is no cheating statistics. As Doom pointed out, small sample size means inconclusive results when the potential error in the test result is greater than the difference between two tests.

So, you think I should be using STDEV.S vice STDEV.P in Excel (if you know??). I ran STDEV.S and 11 SD turned into 10.7 on a hundred round data set so...close enough for government work.

I do get the idea of sample....but its only a sample if you try to apply/project it to the larger future collected data population of...say, total barrel life # of rounds. But taking the chrono info I have as a discrete and complete data set, and including all data points in that set, it seems to me that this is the entire population and the calculated SD for full pop would apply....to this data set only. Or am I an idiot (well, yes, I'm an idiot and I think I've gotten in over my head on statistics....and for perhaps no productive or practical reason)

I will re-read @Doom post above and the one he linked and look for the PRB articles on this subject that he referred me to.

But, its been a long day, my head hurts, and I'm probably very wrong....but perhaps close enough for practical rifle shooting! haha

Thank you, ledzep. I have enjoyed your informed contributions to this subject...particularly in the long thread about the chimeric, non-existent, velocity nodes

 

[Ledzep]

Yes, if you want to use a discrete population and analyze that population you can do that.

I tend to think it's more useful to think of it as a sample and use the data from the sample to predict the performance of the population, but analysis of the population is also possible. The difference in the equations is not very big from what I recall. something like dividing +1 or -1 from the total number of 'specimens' depending on which you use. So the bigger the sample size the less difference there is. I data dumped most of probability and statistics as soon as I saw I passed the class, though...

 

[Doom]

Ouch! Now my head hurts. Normally we consider anything we test as a sample of the population. However, let’s say you are using a LabRadar and you are measuring every shot. Then every shot measured is the population. Think of it as an production line where every piece is weighed and loaded into a 500 piece box. You would know the SD of the average weight of the pieces (population) in the box. Now if you want to use that SD and average to predict the weight of the next box of 500 coming off the line then the first 500 is a sample. In my example post, the 10 rounds tested were used as a population;the 3 and 5 rounds were samples of that population. It was also a sample of the 500 rounds in the brick.

As for STDEV.P and STDEV.S, the difference in the formula is (n-1) and n, so the difference in the small, for n=10, you are talking about dividing 10 vs 9. A difference of 11%.

As you noted, the difference is small. In my work, we typically used 60 discreet measurements of things like pressures and temperatures that were considered primary (important). Often times we would find small differences in data reduction and analysis and would find that one person used .P and the other used .S. Which was correct? It was the one specified by the Test Code!