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http://www.sciencedaily.com/releases/2008/08/080826135937.htm"...adding that though the sample was small, the results were statistically and clinically significant. "Oh? Why, because it is his study? Seriously question the professor's assertion that anything much can be projected from one ten by ten sample. Maybe so, maybe not. -- Paul Helbert Mid Atlantic Home Roaster's Gatheringhttp://paul.helbert.googlepages.com/midatlantichomeroaster'sgatheringHomeroast mailing list Homeroasthttp://www.sweetmariascoffee.com/gallery/main.php?g2_itemIdx20">http://lists.sweetmariascoffee.com/listinfo.cgi/homeroast-sweetmariascoffee.comHomeroast community pictures -upload yours!) :http://www.sweetmariascoffee.com/gallery/main.php?g2_itemIdx20 |

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Sample size is built into the calculation of all significance tests. In fact, it takes a strong relationship to show significance with small samples. One way to think about the probability value calculated in significance tests is that it shows the probability you are wrong when you say the relationship found in your sample exists in the population your sample is randomly drawn from. Here is how I used to introduce the concept to my stat classes: I tell them we are going to pretend to gamble using a coin toss. I will toss this coin and every time it comes up heads you all owe me a dollar and every time it comes up tails I owe each of you a dollar. I then toss the coin and without showing any of them the coin I call "Heads". I then say that if they are halfway rational they will have a hypothesis in their mind that we can begin to test. That is, Dr. Gundlach is cheating. They don't have to be willing to assert that it is true at this point, but that it is just a possibility. What we can do is calculate the probability that they are wrong when they say I cheated. Given that the coin has two side, there is a fifty-fifty chance that it came up heads as I called it so the probability they are wrong when they say I am cheating at this point is .5. I then introduce the notion of the traditional level of certainty of .05 and that if the probability of being wrong is more than .05 they don't have a statistical leg to stand on when they assert that I am cheating. I then toss the coin again and we calculate the probability of being wrong again which is .5 * .5 or . 25, still more than .05. I toss and call heads a third time and we calculate a probability of .125 so it is still not significant. A fourth time yields a p of .0625, which is close but this is not horse shoes or hand grenades and they need that .05 or less before they will tell the world that their statistics professor is cheating them. A fifth toss with a call of heads yields a p=.03125 which is less than . 05 so they can now go tell my department head, the dean, and even the president that I am cheating and that they have statistically significant evidence to back it up. But to bring this back to the issue of significance with small samples, here with a n of 5, there are significant results. So if studies are done with small samples and show significant results, you should not automatically doubt the results because of the sample size. And, the reality is that in using this teaching tool for over thirty years, at about one and a half times per year on average, I won without actually cheating once, which was about 2.2% of the time. So among the approximately 45 classes that concluded that I was indeed cheating, only one was factually wrong. pecan jim On Aug 27, 2008, at 8:04 AM, Paul Helbert wrote: < |

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Thanks, Jim. I enjoyed that. Possible outcomes for a coin toss = 2. Possible factors influencing human hypertension = ? Surely much greater than two. So, yes, I follow and agree with you that one should not dismiss a study out of hand because of small sample; but unless we can hold all the other (known and unknown) variables constant, we might best enlarge the sample. It took the Harvard Physician's Health Study I http://phs.bwh.harvard.edu/phs1.htm)over twenty years using more than twenty thousand individuals to conclude that aspirin really provided some protection from myocardial infarction. Wonder they didn't just flip a coin ;>) On Wed, Aug 27, 2008 at 10:47 AM, Jim Gundlach wrote: < |

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I didn't go and read the original paper, but this seems to be proving the obvious. Maybe I can get some grant money to prove that water is wet. --mike On 8/27/08, Paul Helbert wrote: < |

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"...grant money to prove that water is wet." < |

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Who knows, maybe ask the guy that discovered that circulation of atmosphere affected Mediterranean climate 20,000 years ago. |

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Actually reminds me of Day 1 in Physics 101 class at Bradley U with Dr. Ernst Ising. "You have just one thing to learn all year, F" he said. The Ising Effect came later, but it took the whole first year to plumb the elementary possibilities of F for us Freshmen would-be EE's. 25 years later, Dad and I met Dr. Ising at a Victor Borge concert, and he still remembered my innovative (erroneous) solution to a problem involving the centripetal force on a line as it unwound a ball from a pole + angular speed, angle of the line as a function of time. Now I can build a Heck of a Door Bell! Never had statics (math) by itself, only with dynamics- more physics... Cheers, Mabuhay -RayO, aka Opa! Got Grinder? On Wed, Aug 27, 2008 at 8:47 AM, Jim Gundlach wrote: < |

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Ray, your story reminds me of a guy I met the other day with a shirt that read 2 + 2 = 5 for very large values of 2 It made me smile. :) On 8/28/08, raymanowen wrote: < |

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another way to see it: 2+2=5, when 2 'tends' to infinite :-) |