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  1. Y

    Statistics for differentiating between groups?

    Returning to this: it doesn't matter how many groups you shoot. Groups with fewer shots will always average smaller sizes than groups with more shots. If you shoot more groups and take the average, you'll get a better average, but you'll still only be measuring the average size of your n-shot...
  2. Y

    Statistics for differentiating between groups?

    OK.
  3. Y

    Statistics for differentiating between groups?

    This is a bit ironic to say only a few posts after telling me to spend more time practicing my technique and less time worrying about ammo.
  4. Y

    Statistics for differentiating between groups?

    How does the situation change with more groups?
  5. Y

    Statistics for differentiating between groups?

    And yet here you are, commenting on a stats thread :ROFLMAO:
  6. Y

    Statistics for differentiating between groups?

    Apologies if I was tearing down a straw man. The issue I'm getting at, which from what I can tell is widely misunderstood in the shooting world, is this: We shoot practice/testing groups in order to try and figure out how confident we can be that we'll hit our target when push comes to shove...
  7. Y

    Statistics for differentiating between groups?

    No, you have to do it my way. Ya know, once I figure out my way from talking to people on the internet.
  8. Y

    Statistics for differentiating between groups?

    You were warned in the OP ;)
  9. Y

    Statistics for differentiating between groups?

    You're not limiting the amount of environmentally induced variance by shooting fewer shots in each group. You're simply not observing the variance, which is basically like saying ignorance is bliss. This is, in point of fact, one of the most widespread and dangerous misunderstandings I...
  10. Y

    Statistics for differentiating between groups?

    Ah, I see what you're getting at Brent. I am thinking of this from a different angle though. Let's say I buy a few boxes of Nosler e-tip factory ammo (load A) and a few boxes of Hornady superformance CX factory ammo (load B) for my 7mm-08. For the sake of argument, let's say I have an indoor...
  11. Y

    Statistics for differentiating between groups?

    I'm not sure how you're differentiating between testing groups and testing loads here. Can you elaborate or provide an example?
  12. Y

    Statistics for differentiating between groups?

    I finally came back around to this, and I'm curious what you mean by needing more groups. Can you elaborate? So far the best option I can see for comparing two groups of n shots is to measure the radius of each shot and then compare the two distributions with a Wicoxon Rank Sum test, which...
  13. Y

    Statistics for differentiating between groups?

    I'd love to read that essay, if you still have a copy. I've forgotten how to do a proper power calculation to figure out how many samples need to be taken for the CLT to apply in any given case, but I remember the rule of thumb was thirty samples. So, we're talking about 60 rounds per load in...
  14. Y

    Statistics for differentiating between groups?

    I had not heard of WEZ or the Houston Warehouse. Thanks!
  15. Y

    Statistics for differentiating between groups?

    Most shooters have, myself included. This is exactly the issue that's motivating me to put all this info together (I am a research economist, after all). My goal is to write up a statistically valid method of how to tell if your ammo/load is good enough, and how to tell if you're chasing...
  16. Y

    Statistics for differentiating between groups?

    Thinking more on this, you're certainly correct that mean of the group size across many different groups follows a normal distribution. That's the Central Limit Theorem. Still, testing ammo based on a method that relies on the limiting behavior of the CLT is, uh, too rich for my blood. That...
  17. Y

    Statistics for differentiating between groups?

    Radius is certainly not normally distributed. To avoid confusion, it's worth carefully stating that the mean radius of a single group does not have a distribution–its a single number. The radius, which we can compute for every shot, does have a distribution—the Hoyt distribution...
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    Statistics for differentiating between groups?

    No nitpicking intended. Just trying to work out a valid test between groups.
  19. Y

    Statistics for differentiating between groups?

    I'm not sure about this. For a set of groups, does the diameter (aka group size) follow a normal distribution? I have a hard time buying that, since the groups (viewed as a set of xy coordinates) are samples from a bivariate normal distribution. The probability is highest in the middle, so I...
  20. Y

    Statistics for differentiating between groups?

    The issue here is that the distance from center (I.e., the radius) does not follow a normal distribution and thus the t test is invalid. The distance from center follows something called a Nakagami-q aka Hoyt distribution, and it's unclear to me if there are established hypothesis tests for such...
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