Effects of Case Weight Variation on Accuracy

[dsculley]

As Texas10 said, if you are loading on a node the minor variation in case capacity of quality brass should not take you out of the node.
Here is what one member who is apparently very knowledgeable on the subject had to say regarding sorting by case weight in another thread:


KevinThomas

I’m not quite sure where all the conjecture relating to alloy and weight variation comes in, but as a rule, virtually everyone in the industry uses 70/30 cartridge brass for case production. Any other metals involved are little more than impurities, essentially trace elements within that 70/30 alloy. That’s not to say that the brass used by various manufacturers is the same, it most assuredly isn’t. Purity of the alloy, whether its virgin material or recycled blends, the production process that gives the material grain size and structure, all this comes into play as to how well the material will form, and just how good the end product will be. But I’d be shocked to see weight variations of any note being caused by differences in the alloy itself.

While many focus on case weight, it really isn’t a good indicator of capacity at all. Variation in case capacity is controlled primarily by the punches used in drawing the cases. As they come off the presses, the partially formed cases should have virtually identical capacities, assuming there’s nothing changed during that portion of the run. Weight variations in finished cases are the result of other operations that are performed on the case exterior, such as the heading operations that creates the primer pocket, flash hole and cuts the extractor groove. None of these have any bearing on the internal capacity, but very slight variations in how these operations are performed can greatly effect the weight of the finished case.

So why is case weight variation such a hot topic? Because on the face of it, it makes sense that it should be indicative of some difference, and internal capacity would seem to be a likely candidate for being that variable. Ani’s their very simple reason is that case weight variation is very easy to check, while actual water capacity is a real pain in the ass. As a result, many folks will take the fast and easy approach, downplaying the fact that it’s not giving you good data.

My advice here is, take note of the case weight when comparing different brands or runs of cases, and take really significant differences as a good reason to check the actual capacity via water. Aside from that,if you’re dealing with quality brass to begin with, that variation probably isn’t going to be a real concern in the finished product.

 

[South Pender]

If you are getting .75 and higher on a Pearson, you run the risk of colinearity. I was not talking about just using the numbers from the case volumes, but also thinking about including other factors that might prove to be predictors. We do so much to the brass as we are getting it ready, I just wonder if something might show up in a more complex analysis. As you say, sample size does not have to be that large to get an idea of what is going on. 50-75 rounds would probably be sufficient.

Collinearity,or multi-collinearity, is sometimes a problem in multiple regression analyses where some of the predictor variables are highly correlated and, thus, contributing highly redundant information to the prediction of the dependent variable. This can cause problems in the estimation of the beta weights. However, in a simple bivariate analysis like that discussed, it is not a problem. Most Pearson rs greater than .75 are simply correct expressions of the strength of relationship between the X-Y variables, as is the case here.

I think that, if we are considering using inferential statistics in our load-testing endeavors, use of single independent variable each time makes more sense than using several in a multivariate analysis. The problem with the latter kind of analysis is the phenomenal number of combinations of independent-variable values that would be needed to test all the independent variables in the analysis. Consider, for example, doing a multivariate analysis with the independent variables polychotomized as: (a) case weight (with 2 or more levels), (b) neck tension (with several levels), (c) seating depth (with several levels), (d) powder-charge weight (several levels), and (e) choice of primer (several levels). You could end up with something like a 2x3x3x3x3 design, or 162 combinations of independent-variable values, each needing, ideally, at least 5 replications--or a total of something on the order of 810 5-shot groups fired. And even if you used only two levels per independent variable, you're looking at 32 conditions each requiring 5 or more groups shot, for a total of at least 160 groups shot.

To my mind it makes more sense to consider each variable singly, if for no other reason than logistical practicality--but also simplicity of interpretation of each variable's influence.

 

[South Pender]

As Texas10 said, if you are loading on a node the minor variation in case capacity of quality brass should not take you out of the node.
Here is what one member who is apparently very knowledgeable on the subject had to say regarding sorting by case weight in another thread:


KevinThomas

While many focus on case weight, it really isn’t a good indicator of capacity at all. Variation in case capacity is controlled primarily by the punches used in drawing the cases. As they come off the presses, the partially formed cases should have virtually identical capacities, assuming there’s nothing changed during that portion of the run. Weight variations in finished cases are the result of other operations that are performed on the case exterior, such as the heading operations that creates the primer pocket, flash hole and cuts the extractor groove. None of these have any bearing on the internal capacity, but very slight variations in how these operations are performed can greatly effect the weight of the finished case.

So why is case weight variation such a hot topic? Because on the face of it, it makes sense that it should be indicative of some difference, and internal capacity would seem to be a likely candidate for being that variable. Ani’s their very simple reason is that case weight variation is very easy to check, while actual water capacity is a real pain in the ass. As a result, many folks will take the fast and easy approach, downplaying the fact that it’s not giving you good data.

Kevin Thomas's central point here has been seen to be incorrect. In fact, case weight is a good indicator of capacity. Ned Ludd's analyses--particularly the -.75 and higher correlation between the two--establishes this fact.

 

[Ned Ludd]

I think the key here is exactly what the user intends to get out of the exercise of sorting cases by weight. Despite the obvious linear relationship between case weight and case volume, or perhaps I should say, because of the outliers, using case weight as a surrogate for volume with expectations for accurately estimating the internal volume of specific individual cases is a fruitless exercise. For that purpose, even minor outliers will not yield the desired result. This may be what Kevin Thomas was referring to.

However, if a substantial number of cases, let's say 100 or more, are sorted on the basis of weight into three or four weight groups from light to heavy, then it will be almost a mathematical certainty that the overall case volume range within any single weight group will be smaller than overall case volume range of the entire sample group of cases before they were weight-sorted. In other words, within sorted weight groups, the cases will have more consistent internal volume than if they had not been sorted at all. Even better, it will never become less consistent by weight sorting. These are simple statements, based on simple statistic analyses, and are well-supported by empirical data. I really don't understand the resistance to accepting the concept by some. Nonetheless, the more important question as I mentioned previously is whether the small benefit achieved by weight-sorting cases is enough to make an appreciable difference. That can only be decided by the individual and will likely also depend on a number of other factors.

 

[nso123]

Collinearity,or multi-collinearity, is sometimes a problem in multiple regression analyses where some of the predictor variables are highly correlated and, thus, contributing highly redundant information to the prediction of the dependent variable. This can cause problems in the estimation of the beta weights. However, in a simple bivariate analysis like that discussed, it is not a problem. Most Pearson rs greater than .75 are simply correct expressions of the strength of relationship between the X-Y variables, as is the case here.

I think that, if we are considering using inferential statistics in our load-testing endeavors, use of single independent variable each time makes more sense than using several in a multivariate analysis. The problem with the latter kind of analysis is the phenomenal number of combinations of independent-variable values that would be needed to test all the independent variables in the analysis. Consider, for example, doing a multivariate analysis with the independent variables polychotomized as: (a) case weight (with 2 or more levels), (b) neck tension (with several levels), (c) seating depth (with several levels), (d) powder-charge weight (several levels), and (e) choice of primer (several levels). You could end up with something like a 2x3x3x3x3 design, or 162 combinations of independent-variable values, each needing, ideally, at least 5 replications--or a total of something on the order of 810 5-shot groups fired. And even if you used only two levels per independent variable, you're looking at 32 conditions each requiring 5 or more groups shot, for a total of at least 160 groups shot.

To my mind it makes more sense to consider each variable singly, if for no other reason than logistical practicality--but also simplicity of interpretation of each variable's influence.

I understand what you are saying in terms of using a single variable to try and isolate things, but let's say hypothetically that no statistical significance is found by weight sorting, but then you add neck tensions to the model and suddenly weight sorting becomes significant. At that point, we might infer that weight sorting was only significant when neck tensions of a certain level were present. I think my basic question concerns whether there might be something else to be found through some advanced methods. If, someone had the time and resources, do you think there would be anything to learn?

 

[Bc'z]

I understand what you are saying in terms of using a single variable to try and isolate things, but let's say hypothetically that no statistical significance is found by weight sorting, but then you add neck tensions to the model and suddenly weight sorting becomes significant. At that point, we might infer that weight sorting was only significant when neck tensions of a certain level were present. I think my basic question concerns whether there might be something else to be found through some advanced methods. If, someone had the time and resources, do you think there would be anything to learn?

Always something to learn, from what I'm gathering. Your results may vary from my results as to methods of measure, loading technique rifle, shooter.
Only way to know is go through the process.
As they say the proof is in the pudding.
I like butterscotch.

 

[South Pender]

To those who say that sorting on case weight fails to provide a sorting on case volume, let me pick up with the −.75 correlation reported earlier by Ned Ludd. I've taken 20 hypothetical 6mm. PPC cases and recorded their weight in grains and their volume of water in grains. The 20 case weights ranged from 104.0 to 105.9 grains, and the case volumes ranged from 30.1 to 31.9 grains of water--numbers which seem reasonable. I made up the numbers to simulate a correlation of −.75. Here's the bivariate graph (called a "scatterplot") showing each of the 20 cases plotted by weight (X axis) and volume (Y axis).

The Correlation between Case Weight and Case Volume = −.75.

Now, if we wished to separate these 20 cases into the 10 most voluminous cases and the 10 least voluminous, we could accomplish this by selecting those that weigh less than 105.0 gn. as the 10 most voluminous (these would all have a volume of 31.0 gn. or greater), and those cases that weigh 105.0 gn. and greater as the 10 least voluminous (these, with one exception, would have a volume of less than 31.0 gn.) In so doing, we'd miss-classify only one case--that weighing 105.4 gn. and which has a volume of 31.2 gn.

Here we have an imperfect negative correlation, albeit a high one of −.75. So even falling short of a perfect linear relationship (which would be −1.0), a weight sort of cases provides a useful weight sort of volumes. Most bivariate analyses involving a correlation of −.75 would provide scatterplots much like the one presented here.

In fact, my guess is that, with more analysis of these variables, we'd find correlations approaching −.90. These would provide a closer sort of case volume based on weight.

 

[South Pender]

I understand what you are saying in terms of using a single variable to try and isolate things, but let's say hypothetically that no statistical significance is found by weight sorting, but then you add neck tensions to the model and suddenly weight sorting becomes significant. At that point, we might infer that weight sorting was only significant when neck tensions of a certain level were present. I think my basic question concerns whether there might be something else to be found through some advanced methods. If, someone had the time and resources, do you think there would be anything to learn?

Yes, that's a good point. I guess I'd go about it in a slightly different manner. I'd record the neck tensions of the original rounds segregated by case weight and then, in a second analysis, covary out the effects of neck tension in the 2-group analysis (near identical case weights in Group 1; widely varying case weights in Group 2). If the original analysis was nonsignificant, but the covariance analysis was significant, I'd conclude that case weight is a significant factor only if neck tension is held constant.