Hungry? arnyj
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Re: two sample t
dennis roberts wrote: > when we do a 2 sample t test ... where we are estimating the > population variances ... in the context of comparing means ... the > test statistic ... > > diff in means / standard error of differences ... is not exactly like > a t distribution with n1-1 + n2-1 degrees of freedom (without using > the term non central t) > > would it be fair to tell students, as a thumb rule ... that in the > case where: > > ns are quite different ... AND, smaller variance associated with > larger n, and reverse ... is the situation where the test statistic > above is when we are LEAST comfortable saying that it follows (close > to) a t distribution with n1-1 + n2-1 degrees of freedom? > > that is ... i want to set up the "red flag" condition for them ... > > what are guidelines (if any) any of you have used in this situation? G. E. P. Box says, (a) if n(1) = n(2), treat them as if s(1) = s(2). (b) if s(1)/s(2) (selecting 1 & 2 so ratio is >1) is less than about 3, treat them as if s(1) = s(2). This is approx. equal to running an F test for diff in vars. And I think this is where he gets this from. (c) if n(1) is within 'about' 10% of n(2), go for option (a) above. I have a paper I can't find for (a) and (b), but (c) was a verbal. When you speak of getting 'LEAST comfortable' I think you are saying, how much deviation can you stand. A lot depends on the consequences of deviation - decision 'theory' etc. If you take a non-dichotomous view of 't' testing, the question becomes immaterial, anyway. Cheers, Jay -- 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/ =
Do I need to do a Bonferroni/Dunn test?
Hi, I'm trying to finish my dissertation and a person on my committee raised the question of me having to do a Bonferroni correction. Here is the situation. I have 5 subjects that I have tested at 5 different times for 2 different conditions (cued and uncued). When I do a repeated measures ANOVA, I get the the difference between the two conditions over those 5 seperate times is statistically significant. Now, I also have a baseline condition that I want to compare the cued and uncued conditions to at each of the 5 times individually. For example, I want to compare Baseline value to cued at time 1, then Baseline to cued at time 2, etc. To do these comparisons, I use a paired t-test and a significance level of 0.05. The person on my committee suggests that the p-value should be adjusted to be 0.01 to correct for atleast 5 comparisons of cued, and the same when uncued is compared to baseline. I hope what I said makes sense. I'm not a statistician but I could use help, because from my reading on Bonferroni, I don't think I have to make those corrections. If you have suggestions, please e-mail me at [EMAIL PROTECTED] Thanks, Jason = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: two sample t
On 26 Feb 2001 12:26:19 -0800, [EMAIL PROTECTED] (dennis roberts) wrote: > when we do a 2 sample t test ... where we are estimating the population > variances ... in the context of comparing means ... the test statistic ... > > diff in means / standard error of differences ... is not exactly like a t > distribution with n1-1 + n2-1 degrees of freedom (without using the term > non central t) > > would it be fair to tell students, as a thumb rule ... that in the case where: > > ns are quite different ... AND, smaller variance associated with larger > n, and reverse ... is the situation where the test statistic above is when > we are LEAST comfortable saying that it follows (close to) a t > distribution with n1-1 + n2-1 degrees of freedom? > > that is ... i want to set up the "red flag" condition for them ... > > what are guidelines (if any) any of you have used in this situation? Neither extreme is better than the other. Student's t-test and that Satterthwaite test have their problems in the opposite directions. With unequal Ns and unequal variances, and a one-tailed test, - one t-test will be too small (rejecting, approximately, never) and - the other will be too big (rejecting about twice as often); - making the TWO-tailed versions come out 'robust'! for size. Neither direction is better until you decide what bias you want. -- 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: On inappropriate hypothesis testing. Was: MIT Sexism & statistical bunk
- I want to comment a little more thoroughly about the lines I cited: what Garson said about inference, and his citation of Olkey. On Thu, 22 Feb 2001 18:21:41 -0500, Rich Ulrich <[EMAIL PROTECTED]> wrote: [ snip, previous discussion ] me > > I think that Garson is wrong, and the last 40 years of epidemiological > research have proven the worth of statistics provided on non-random, > "observational" samples. When handled with care. > > From G. David Garson, "PA 765 Notes: An Online Textbook." > > On Sampling > http://www2.chass.ncsu.edu/garson/pa765/sampling.htm > > Significance testing is only appropriate for random samples. > > Random sampling is assumed for inferential statistics > (significance testing). "Inferential" refers to the fact > that conclusions are drawn about relationships in the data > based on inference from knowledge of the sampling > distribution. Significance tests are based on a sampling > theory which requires that every case have a chance of being > selected known in advance of sample selection, usually an > equal chance. Statistical inference assesses the > significance of estimates made using random samples. For > enumerations and censuses, such inference is not needed > since estimates are exact. Sampling error is irrelevant and > therefore inferential statistics dealing with sampling error > are irrelevant. - I agree with most of what he says, throughout; there will be a matter of nuances on interpretation and actions. For enumerations and censuses, a limited sort of statistics on 'finite populations,' he says sampling error is irrelevant. Irrelevant is a good and fitting word here. This is not 'illegal and banned,' but rather 'unwanted and totally beside the point.' Garson > > Significance tests are sometimes applied > arbitrarily to non-random samples but there is no existing > method of assessing the validity of such estimates, though > analysis of non-response may shed some light. The following > is typical of a disclaimer footnote in research based on a > non random sample: Here is my perspective on testing, which does not match his. - For a randomized experimental design, a small p-level on a "test of hypothesis" establishes that *something* seemed to happen, owing to the treatment; the test might stand pretty-much by itself. - For a non-random sample, a similar test establishes that *something* seems to exist, owing to the factor in question *or* to any of a dozen factors that someone might imagine. The test establishes, perhaps, the _prima facie_ case but the investigator has the responsibility of trying to dispute it. That is, it is an investigator's responsibility (and not just an option) to consider potential confounders and covariates. If the small p-level stands up robustly, that is good for the theory -- but not definitive. If there are vital aspects or factors that cannot be tested, then opponents can stay unsatisfied, no matter WHAT the available tests may say. Garson > > "Because some authors (ex., Oakes, 1986) note the use of > inferential statistics is warranted for nonprobability > samples if the sample seems to represent the population, and > in deference to the widespread social science practice of > reporting significance levels for nonprobability samples as > a convenient if arbitrary assessment criterion, significance > levels have been reported in the tables included in this > article." See Michael Oakes (1986). Statistical inference: A > commentary for social and behavioral sciences. NY: Wiley. > Garson is telling his readers and would-be statisticians a way to present p-levels, even when the sampling doesn't justify it. And, I would say, when the analysis doesn't justify it. I am not happy with the lines -- The disclaimer does not assume that a *good* analysis has been done, nor does it point to what makes up a good analysis. '... if the sample seems to represent the population' seems to be a weak reminder of the proper effort to overcome 'confounding factors'; it is not an assurance that the effects have proven to be robust. So, the disclaimer should recognize that the non random sample is potentially open to various interpretations; the present analysis has attempted to control for several possibilities; certain effects do seem robust statistically, in addition to being supported by outside chains of inference, and data collected independently. I suggested earlier that this is the status of epidemiological, observational studies. For the most part, those studies have been quite fruitful. But not always. They have been especially likely to mislead, I think, when the designs pretend that binomial variability is the only source of error in a large survey, and attempt to interpret small effects. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html ===
RE: pizza
Your pizza taste test seems simple enough to me, but I may be missing something. The binomial has four assumptions: 1. N trials of an experiment. 2. Two possible outcomes. 3. Probability of success is the same for each trial. 4. Trials are independent. 1 and 2 are trivial. Using subjects only once and running each subject at a different time would satisfy 4. 3 is true under the null hypothesis. Remember that your null hypothesis is that students cannot determine pizza brands at a rate better than random guessing. The distribution under the alternative might be a bit trickier. For example, some students may be better at distinguishing pizza brands than others. It is my understanding though, that unless there are large variations in the probability of success from trial to trial, the binomial probability formulas are pretty robust to this violation of assumptions. To really make the experiment fun, use beer consumption during the taste test as a second factor or as a covariate. Steve Simon, [EMAIL PROTECTED], Standard Disclaimer. STATS: STeve's Attempt to Teach Statistics. http://www.cmh.edu/stats = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
two sample t
when we do a 2 sample t test ... where we are estimating the population variances ... in the context of comparing means ... the test statistic ... diff in means / standard error of differences ... is not exactly like a t distribution with n1-1 + n2-1 degrees of freedom (without using the term non central t) would it be fair to tell students, as a thumb rule ... that in the case where: ns are quite different ... AND, smaller variance associated with larger n, and reverse ... is the situation where the test statistic above is when we are LEAST comfortable saying that it follows (close to) a t distribution with n1-1 + n2-1 degrees of freedom? that is ... i want to set up the "red flag" condition for them ... what are guidelines (if any) any of you have used in this situation? _ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: pizza
the original post meant that ... there were multiple tasters ... i had just put 10 as an example thus, in the binomial context ... i was assuming (rightfully or wrongfully) that n=10 ... that is, if we SCORE across the 10 ... we could have scores of 0 to 10 ... in terms of how many got the correct orderings now, it was the p that i was most interested in ... since ... in the example ... we have no real idea of how many times the Ss might taste and retaste ... slices and, if multiple ... in what orders ... given that for any particular S ... the way the problem was posted ... the correct order could have been (and only) ... SSD ... SDS ... DSS ... in this sense, there is a 1 out of 3 chance of hitting it correctly ... but, is the p value in this binomial really 1/3??? is this really a true binomial case? does the fact that SSS and DDD are not allowed and, the fact that tasting one surely has some impact on what you decide about tasting another (hence, some dependence in the situation) ... take it out of the binomial? At 09:15 AM 2/26/01 -0600, Mike Granaas wrote: >Upon rereading Dennis' original question he proposed 10 S, not 10 >trials/S. So, my speculations about sequential trials for a given S are >not relevant. That will teach me to try and respond on friday afternoons. > >Michael = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: pizza
On Sat, 24 Feb 2001, Donald Burrill wrote: > On Sat, 24 Feb 2001, Mike Granaas wrote: > > > each of A, B, and C three times and one of those a fourth time. > > This sounds as though you thought each S were going to have ten separate > trials at identifying the "odd pizza out", with a different set of three > pizzas each time. I don't see how else "choosing each of A, B, and C > three times and one of those a fourth time" could mean anything else; > but if I've misunderstood, doubtless your reply will explain. > However interesting such an experiment might be, it's not the experiment > that I thought Dennis described. Upon rereading Dennis' original question he proposed 10 S, not 10 trials/S. So, my speculations about sequential trials for a given S are not relevant. That will teach me to try and respond on friday afternoons. Michael > > < snip, the rest > > -- Don. > -- > Donald F. Burrill[EMAIL PROTECTED] > 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED] > MSC #29, Plymouth, NH 03264 (603) 535-2597 > Department of Mathematics, Boston University[EMAIL PROTECTED] > 111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288 > 184 Nashua Road, Bedford, NH 03110 (603) 471-7128 > > > > = > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > = > *** Michael M. Granaas Associate Professor[EMAIL PROTECTED] Department of Psychology University of South Dakota Phone: (605) 677-5295 Vermillion, SD 57069 FAX: (605) 677-6604 *** All views expressed are those of the author and do not necessarily reflect those of the University of South Dakota, or the South Dakota Board of Regents. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: pizza
On Sat, 24 Feb 2001, Donald Burrill wrote: > On Sat, 24 Feb 2001, Mike Granaas wrote: > > > Interesting point. Yes, if the Ss do something other than a random guess > > the binomial model would be violated. The question then becomes what > > would they do if they are uncertain? I suspect that they would fall back > > on visual inspection...which piece appears to be different than the others > > (less green pepper, more browned, etc) Such information is probably > > relevant often enough that "guessing" would be well above 1/3. > > So what you would then have is evidence that Ss can in fact do better > than "chance", but you might NOT know whether that improvement is due to > their actually being able to perform as claimed, or to some other > factor(s) relevant to identifying the "odd pizza out": a human-cum-pizza > version of "Clever Hans", pehaps? Yes. > > > Using blindfolded Ss will deal with that problem, and gets us back to > > the question that Dennis is asking. I'm guessing that rather than going > > through some sort of a systematic process (e.g. binary decision for the > > first piece, progress to second piece only if first piece was judged > > "same".) > Umm: Logical problems here. > (1) How can _first_ piece be judged "same"? Same as what? > (2) Why would Ss not taste all three pizzas, given the ground rules > Dennis specified (or implied) at the outset? Yes, the Ss would taste all three pieces of pizza, possibly multiple times, before arriving at their judgement. Here "first" refers to the order in which a particular set of three slices was presented to S. Later I refer to them as slices "A", "B", and "C". As I understand Dennis' earlier comment, S, after tasting these three slices to their hearts content, would, if uncertain, tackle the decision making process by starting with the first of the three slices presented. That is they would start by making a binary decision about "A" and only move on to considering "B" if they decide that "A" is not the odd slice. > > > ... Ss will in fact do something more like guessing. Only they > > will condition their guesses such that if they picked slice A as different > > on the previous trial they will first consider slices B and C on the > > current trial (they will actually avoid selecting the same slice position > > on sequential trials). > How did "sequential trials" get into the > scenario? As I read Dennis' description, each S was to taste the three > pizzas presented (perhaps tasting each more than once, but not attacking > a whole 'nother SET of pizzas). My reading was that there would be 10 trials per subject. If each S participates in one, and only one trial, then this speculation is outside of the problem bounds. > > > Furthermore they will try to equalize the number > > of position choices they make across the experiment so that they choose > > each of A, B, and C three times and one of those a fourth time. > > This sounds as though you thought each S were going to have ten separate > trials at identifying the "odd pizza out", with a different set of three > pizzas each time. I don't see how else "choosing each of A, B, and C > three times and one of those a fourth time" could mean anything else; > but if I've misunderstood, doubtless your reply will explain. > However interesting such an experiment might be, it's not the experiment > that I thought Dennis described. Yes, I read the original post as suggesting that there would be 10 replications of the taste test for each S. I'll have to go back and read Dennis' original question again. Michael > > < snip, the rest > > -- Don. > -- > Donald F. Burrill[EMAIL PROTECTED] > 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED] > MSC #29, Plymouth, NH 03264 (603) 535-2597 > Department of Mathematics, Boston University[EMAIL PROTECTED] > 111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288 > 184 Nashua Road, Bedford, NH 03110 (603) 471-7128 > > *** Michael M. Granaas Associate Professor[EMAIL PROTECTED] Department of Psychology University of South Dakota Phone: (605) 677-5295 Vermillion, SD 57069 FAX: (605) 677-6604 *** All views expressed are those of the author and do not necessarily reflect those of the University of South Dakota, or the South Dakota Board of Regents. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat
