Re: normal approx. to binomial
It's the proportion of success (x/n) which has approxiatmenly a normal distribution for large n, not the number of success (x). Gary Carson http://www.garycarson.com = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: In realtion to t-tests
On Mon, 9 Apr 2001, Rich Ulrich wrote:
> On Mon, 09 Apr 2001 10:44:40 -0400, Paige Miller
> <[EMAIL PROTECTED]> wrote:
>
> > "Andrew L." wrote:
>
AL> I am trying to learn what a t-test will actually tell me, in
> simple terms. < snip >, but i still dont quite
> understand the significance.
>
PM> A t-test compares a mean to a specific value...or two means to each
> other...
> [ ... ]
>
RU> I remember my estimation classes, where the comparison was
RU> always to ZERO for means.
Yes, that's what Paige said: here the mean (mean difference, to be
precise) is being compared to the specific value zero.
OR "two means to each other", since the allegation "X1 = X2" is
equivalent to the allegation "(X1-X2) = 0"
That the hypothethical expectation is often zero (that is, null) is the
reason why that hypothesis is colloquially called "the null hypothesis";
Lumsden argued that it were better called "the model-distributional
hypothesis", but that apparently is too much of a mouthful for most
folks. There is, however, no formal or logical REQUIREMENT that the
value expected under the model-distributional hypothesis be zero.
RU> To ONE, I guess, for ratios.
RU> Technically speaking, or writing.
Someone else pointed out that if the ratio were of interest, one should
probably be taking logarithms; in which case the comparison of interest
would be to log(1) = 0.
(Unless the ratio of interest were a ratio of variances; but in that
case the relevant distribution would not be a t distribution.)
RU> For instance, if the difference in averages X1, X2 is expected to
RU> be zero, then "{(X1-X2) -0 }" ... is distributed as t .
This is, I believe, technically inaccurate. "{(X1-X2) - 0}" is
distributed normally, or approximately so under a central limit theorem;
in which case "{(X1-X2) - 0}" divided by its estimated standard error is
distributed as t . Again technically, as the standard central t .
("Standard", implying that the mean and standard deviation of the
sampling distribution are 0 and 1 respectively; "central", implying that
the non-centrality parameter is zero.)
RU> It might look like a lot of equations with the 'minus zero'
RU> seemingly tacked on, but I consider this to be good form.
No argument with that. Nor with this:
RU> It formalizes as minus
-- DFB.
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-472-3742
=
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=
US government grants and scholarships for International students.
I would like some information on US government grants and scholarships for International students for 8th grade. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: normal approx. to binomial
one tech issue, one thinking issue, I believe. 1) Tech: if np _and_ n(1-p) are > 5, the distribution of binomial observations is considered 'close enough' to Normal. So 'large n' is OK, but fails when p, the p(event), gets very small. Most examples you see in the books use p = .1 or .25 or so. Modern industrial situations usually have p(flaw) around 0.01 and less. Good production will run under 0.001. To reach the 'Normal approximation' level with p = 0.001, you have to have n = 5000. Not particularly reasonable, in most cases. If you generate the distribution for the situation with np = 5 and n = 20 or more, you will see that it is still rather 'pushed' (tech term) up against the left side - your eye will balk at calling it normal. But that's the 'rule of thumb.' I have worked with cases, pushing it down to np = 4, and even 3. However, I wouldn't want to put 3 decimal precision on the calculations at that point. My personal suggestion is that if you believe you have a binomial distribution, and you need the confidence intervals or other applications of the distribution, then why not simply compute them out with the binary equations. Unless n is quite large, you will have to adjust the limits to suit the potential observations, anyway. For example, if n = 10, there is no sense in computing a 3 sigma limit of np = 3.678 - you will never measure more precisely than 3, and then 4. But that's the application level speaking here. 2)I think your books are saying that, when n is very large (or I would say, when np>5), the binomial measurement will fit a Normal dist. It will be discrete, of course, so it will look like a histogram not a continuous density curve. But you knew that. I think your book is calling the binomial rv a single measurement, and it is the collection of repeated measurements that forms the distribution, no? I explain a binomial measurement as, n pieces touched/inspected, x contain the 'flaw' in question, so p = x/n. p is now a single measurement in subsequent calculations. to get a distribution of 100 proportion values, I would have to 'touch' 100*n. I guess that's OK, if you are paying the inspector. Clearly, one of the draw backs of a dichotomous measurement (either OK or not-OK) is that we have to measure a heck of a lot of them to start getting decent results. the better the product (fewer flaws) the worse it gets. See the situation for p = 0.001 above. Eventually we don't bother inspecting, or automate and do 100% inspection. So the next paragraph better explain about the improved information with a continuous measure... Sorry, I got up on my soap box by mistake. Is this enough explanation? Jay James Ankeny wrote: > Hello, > I have a question regarding the so-called normal approx. to the binomial > distribution. According to most textbooks I have looked at (these are > undergraduate stats books), there is some talk of how a binomial random > variable is approximately normal for large n, and may be approximated by the > normal distribution. My question is, are they saying that the sampling > distribution of a binomial rv is approximately normal for large n? > Typically, a binomial rv is not thought of as a statistic, at least in these > books, but this is the only way that the approximation makes sense to me. > Perhaps, the sampling distribution of a binomial rv may be normal, kind of > like the sampling distribution of x-bar may be normal? This way, one could > calculate a statistic from a sample, like the number of successes, and form > a confidence interval. Please tell me if this is way off, but when they say > that a binomial rv may be normal for large n, it seems like this would only > be true if they were talking about a sampling distribution where repeated > samples are selected and the number of successes calculated. > > > > > > > ___ > Send a cool gift with your E-Card > http://www.bluemountain.com/giftcenter/ > > > > > = > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > = > > > -- Jay Warner Principal Scientist Warner Consulting, Inc. North Green Bay Road Racine, WI 53404-1216 USA Ph: (262) 634-9100 FAX:(262) 681-1133 email: [EMAIL PROTECTED] web:http://www.a2q.com The A2Q Method (tm) -- What do you want to improve today? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: normal approx. to binomial
James Ankeny <[EMAIL PROTECTED]> wrote: : My question is, are they saying that the sampling : distribution of a binomial rv is approximately normal for large n? : It's a special case of the CLT for a binary variable with probability p, taking the sum of n observations = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: In realtion to t-tests
On Mon, 09 Apr 2001 10:44:40 -0400, Paige Miller
<[EMAIL PROTECTED]> wrote:
> "Andrew L." wrote:
> >
> > I am trying to learn what a t-test will actually tell me, in simple terms.
> > Dennis Roberts and Paige Miller, have helped alot, but i still dont quite
> > understand the significance.
> >
> > Andy L
>
> A t-test compares a mean to a specific value...or two means to each
> other...
[ ... ]
I remember my estimation classes, where the comparison was
always to ZERO for means. To ONE, I guess, for ratios.
Technically speaking, or writing.
For instance, if the difference in averages X1, X2 is expected to
be zero, then "{(X1-X2) -0 }" ... is distributed as t . It might
look like a lot of equations with the 'minus zero' seemingly tacked
on, but I consider this to be good form. It formalizes as
minus
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
=
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=
Re: Logistic regression advice
On 6 Apr 2001 13:15:34 -0700, [EMAIL PROTECTED] (Zina Taran) wrote: [ ... on logistic regression ] ZT: "1). The 'omnibus' chi-squared for the equation. Is it accurate to say that I can interpret individual significant coefficients if (and only if) the equation itself is significant? " Confused question. Why do you label it the omnibus test? When you think to use that term, the term is (mainly) a ROLE for the overall test, or for a test that subsumes a coherent set of several tests; sometimes you place use test that way, and sometimes you don't. ZT: "2) A few times I added interaction terms and some things became significant. Can I interpret these even if the interaction variable itself (such as 'age') is not significant? Can I interpret an interaction term if neither variable has a significant beta?" Probably not. Assuredly not, unless someone has used care and attention (and knowledge) in the exact dummy-coding of the effects. [ ... snip, 'Nagelkerke' that I don't recall; 'massive' regression which is a term that escapes me, but I think it means, 'no hypotheses, test everything'; and so I disapprove. ] ZT: "5) I know the general rule is 'just the facts' in the results section, meaning that there should be no explanation or interpretation regarding the results. When writing the results section do I specifically draw conclusions as to whether a hypothesis is supported or does that get left to the discussion?" Do you have an Example that is difficult? - It seems to me that if the analyses are straightforward, there should be little question about what the 'results' mean, when you lay them out in their own, minimalist section. In other words, leave discussion to the discussion; but that should be a re-cap of what's apparent. You hope. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Reverse of Fisher's r to z
Yes, there are reasons for using the transformation frm z to r. And, there are published tables of this. For example, Appendix Table B.19 of Zar, Biostatistical Analysis, 4th ed., 1999. Jerrold H. Zar, Professor Department of Biological Sciences Northern Illinois University DeKalb, IL 60115 [EMAIL PROTECTED] === >>> Will Hopkins <[EMAIL PROTECTED]> 04/09/01 04:29AM >>> It's elementary algebra, Cherilyn. BTW, it's z = 0.5log..., not sqrt. So r = (e^2z - 1)/(e^2z + 1). Will = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Reverse of Fisher's r to z
Thanks-- my algebra (and apparently my eyesight too) has gotten a bit creepy around the edges, so I didn't trust it for something this important Truly appreciate it!!! Best, Cherilyn On Mon, 9 Apr 2001, Will Hopkins wrote: > It's elementary algebra, Cherilyn. BTW, it's z = 0.5log..., not sqrt. > > So r = (e^2z - 1)/(e^2z + 1). > > Will > > = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: In realtion to t-tests
"Andrew L." wrote: > > I am trying to learn what a t-test will actually tell me, in simple terms. > Dennis Roberts and Paige Miller, have helped alot, but i still dont quite > understand the significance. > > Andy L A t-test compares a mean to a specific value...or two means to each other... The reason we do this, if you are comparing two means, for example, is if you get mean of group A is 6.75 and mean of group B is 6.8, we really want to know if this difference is significant -- which is another way of saying is it likely that these two mean values arise purely out of random chance? This is a "layman's" way of describing the t-test. The actual proper statistical description can be found in numerous textbooks. There are some assumptions being made in order to do this ... usually the data is identically normally and independently distributed ... approximately normal is usually okay -- Paige Miller Eastman Kodak Company [EMAIL PROTECTED] "It's nothing until I call it!" -- Bill Klem, NL Umpire "Those black-eyed peas tasted all right to me" -- Dixie Chicks = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Time Series Data. Significant movement
I have a set of measurements (e.g. number of errors, faults, etc) over a period of time (e.g. 9 Months) and measurements are taken weekly. These measurements are graphed on a spreadsheet. I need to select a small number of measurements and graphs then display the measurements and the graphs to my audience. My question is, Is there a statistical way of selecting the set of measurement that show movement up or down other than just eye balling the graphs?? -- Philip [EMAIL PROTECTED] = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Reverse of Fisher's r to z
Cherilyn Young wrote:
> I have an itchy little question about the familiar Fisher's r to z
> transformation: The formula, expressed as z= sqrt (log e ( (1+r)/(1-r))),
> is in pretty much any older stats textbook. Does anyone know of a source
> where the equation is written to solve for r? I know it's a very uncommon
> use (if used at all in this way ), but I've got a very legitimate research
> need (and my brain's doing odd things when I'm trying to rewrite the
> equation).
r.back <- function(x)
{
((2.71828182845905^(2 * x)) - 1)/((2.71828182845905^(2 * x)) + 1)
}
fish.z <- function(x)
{
ifelse(x == 0, 0, 0.5 * log((1 + abs(x))/(1 - abs(x))) * (x/abs(x)))
}
Examples:
> fish.z(.45)
[1] 0.4847003
> r.back(.4847003)
[1] 0.45
> r.back(fish.z(.45))
[1] 0.45
HTH,
Chuck
-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-
Chuck Cleland
Institute for the Study of Child Development
UMDNJ--Robert Wood Johnson Medical School
97 Paterson Street
New Brunswick, NJ 08903
phone: (732) 235-7699
fax: (732) 235-6189
http://www2.umdnj.edu/iscdweb/
http://members.nbci.com/cmcleland/
-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-<>-
=
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=
Re: Regression toward the Mean - search question
>A few weeks ago, I believe on this list, a quick discussion of Galton's >regression to the mean popped up. I downloaded some of Galton's data, >generated my own, and found some ways to express the effect in ways my >non-statistian education friends might understand. Still working on >that part. > >In addition, there was a reference to a wonderful article, which I read, >and which explained the whole thing in excellent terms and clarity for >me. The author is clearly an expert on the subject of detecting change >in things. He (I think) even listed people who had fallen into the >regression toward the mean fallacy, including himself. > >Problem: Now of course I really want that article again, and >reference. I cannot find it on my hard drive. Maybe I didn't download >it - it was large. But I can't find the reference to it, either. Bummer! > >Can anyone figure out who and what article I'm referring to, and >re-point me to it? > >Very much obliged to you all, >Jay > >-- >Jay Warner >Principal Scientist >Warner Consulting, Inc. > North Green Bay Road >Racine, WI 53404-1216 >USA > Trochim's page has a nice description of the problem but with few historical references: http://trochim.human.cornell.edu/kb/regrmean.htm Campbell, D. T. and D. A. Kenny 1999. A primer on regression artifacts. Guilford Press. This book is devoted almost entirely to regression to the mean and what to do about it. Stigler, S. M. 1999. Statistics on the table. Harvard University Press. [Stigler has several essays to the discovery of RTM under the heading "Galtonian Ideas" He also presents a sobering case study of poor Otto Secrist, whose 1933 magnum opus in econometrics is a classic RTM artifact. Eugene Gallagher ECOS UMASS/Boston = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: rotations and PCA
Eric Bohlman wrote: In science, it's not enough to > say that you have data that's consistent with your hypothesis; you also > need to show a) that you don't have data that's inconsistent with your > hypothesis and b) that your data is *not* consistent with competing > hypotheses. And there's absolutely nothing controversial about that last > sentence [...] Well, I'd want to modify it a little. On the one hand, a certain amount of inconsistency can be (and sometimes must be) dealt with by saying "every so often something unexpected happens"; otherwise it would only take two researchers making inconsistent observations to bring the whole structure of science crashing down. And on the other hand there are _always_ competing hypotheses. [Consider Jaynes' example of the policeman seeing one who appears to be a masked burglar exiting from the broken window of a jewellery store with a bag of jewellery; he (the policeman) does *not* draw the perfectly logical conclusion that this might be the owner, returning from a costume party, and, having noticed that the window was broken, collecting his stock for safekeeping.] It is sufficient to show that your data are not consistent with hypotheses that are simpler or more plausible, or at least not much less simple or plausible. -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
No Subject
= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Funding for Posters: European Nutrition and Cancer Conference
Dear All, The European Conference on Nutrition and Cancer will take place in Lyon, France on 21-24 June 2001. An important feature of the conference is 2 large poster sessions on days 2 and 3. As indicated on the programme web site, in the GENERAL INFORMATION section, funds have been set aside to pay for travel expenses and lodging for up to 50 participants presenting posters. Poster abstracts must be submitted by the 30th April, 2001. Posters concerning studies of diet, nutrition, genetics, hormones, epidemiologic and statistical methods or other related areas of research are welcome. The form for submitting abstracts is available on the Conference web site: http://www.nutrition-cancer2001.com For further information send email to: [EMAIL PROTECTED] = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Reverse of Fisher's r to z
It's elementary algebra, Cherilyn. BTW, it's z = 0.5log..., not sqrt. So r = (e^2z - 1)/(e^2z + 1). Will = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Reverse of Fisher's r to z
Hi everyone, I have an itchy little question about the familiar Fisher's r to z transformation: The formula, expressed as z= sqrt (log e ( (1+r)/(1-r))), is in pretty much any older stats textbook. Does anyone know of a source where the equation is written to solve for r? I know it's a very uncommon use (if used at all in this way ), but I've got a very legitimate research need (and my brain's doing odd things when I'm trying to rewrite the equation). Thanks in advance, Cherilyn = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
