Re: Two sided test with the chi-square distribution?
On Thu, 8 Feb 2001, jim clark wrote in part: We all agree that it is confusing, but I do believe that the use of one-tailed and two-tailed to refer to directional vs. non-directional hypotheses (rather than uniquely to one or two tails of a distribution) is very wide-spread and quite common. There would not be a problem if the hypotheses in question were STATED. It's this sloppy habit of saying "F test" or "chi square test", with no hint of WHICH "F test" or "chi square test" one is talking about, that impedes communication. That is probably what led to the posting that initiated this thread. Yes. "I thought the chi-square test was always two-sided", or words to that effect, the querent wrote. He she or they have not, in all the correspondence since, said what the hypothesis being tested was. I had written: It is still possible to use the F _statistic_ to test the null hypothesis that Var1 = Var2, in circumstances where it is entirely possible that Var1 Var2, Var1 = Var2, or Var1 Var2. In such cases _both_ tails of the F distribution are of interest, not just the upper tail. --- and Jim replied: Right, but if one calculates F_larger/F_smaller, then one is only looking at the upper tail of the F distribution even though one is doing a non-directional test (i.e., two-tailed in the vernacular). The appropriate critical value for a non-directional test would be F_.05. Whoops! Not if you want to test at the usual 5% level! For a non-directional test of the null hypothesis that two variances are equal, the critical value would be F_(alpha/2). If you made a directional hypothesis and predicted which variance was going to be larger (as implied in F's use for anova and regression), then you would compare the obtained value of F to F_.10, not F_.05. I'll agree with you if you halve those subscripts! (Or acknowledge that you wanted to test at the 10% level...) You state that using F in ANOVA and regression imply that one had a _prediction_ of which variance would be larger. This is not how I understand the idea of "predicting", which I take to imply that one could have predicted something in the opposite direction. In ANOVA the null hypothesis _of interest_ is commonly expressed as "all the means are equal" (in some language or other), vs. "some of the means differ", and the alternative hypothesis is indeed non-directional -- in the metric of the subgroup means. But the hypothesis actually _tested_ (using F) is the null hypothesis that a particular variance component is zero, vs. the alternative that it isn't, and since a variance component cannot be negative, the alternative really is that the variance component in question is positive: thus in the metric of variances the alternative hypothesis is one-sided. This is a matter of algebra, not of "predicting" the direction of an effect. However, perhaps others are more willing to use "predict" in this rather sloppy (from my point of view ;-) fashion. You are using the upper tail (i.e., one-tail) of the distribution to test a directional (i.e., "one-tailed") hypothesis. Yes. Because a result in the _lower_ tail would tend to confirm the null hypothesis, not reject it. Like Don, I hope that language can become clearer on these issues, but my suspicion is that it will be a long, long time before one- vs. two-tailed stops meaning directional vs. non-directional alternative hypotheses for most people. I have no problem with that. I just wish that people would say what they're talking about: if it's a hypothesis test that is of concern, what is the hypothesis and what is the test statistic, for example. To say only "chi-square test" or "F test" or "z test" is simply insufficient. -- 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/ =
Re: Two sided test with the chi-square distribution?
On Tue, 6 Feb 2001, jim clark wrote in part: The problem is that one-tailed test is taken as synonymous with directional hypothesis (e.g., Ha: Mu1Mu2). This causes no confusion with distributions such as the t-test, because directional implies one-tailed. This correspondence does not hold for other statistics, such as the F and Chi2. The statement is not correct. The correspondence certainly holds for F and chi-square _statistics_. What it seems not to hold for is certain particular hypothesis tests for which those statistics are the commonly used test statistics. The "large F" Jim speaks of below celarly refers to an analysis of variance (and one with only two groups, at that!). In that context, while the hypotheses _of interest_ are the null hypothesis that the several means Mu_j are identical, vs. the two-sided alternative hypothesis that some of them are different, the formal hypothesis tested by the F statistic is the null hypothesis that a certain variance component equals zero, vs. the alternative hypothesis that it does not equal zero; and since a variance component cannot be negative, the _test_ is one-sided, in the metric of variances: one rejects only for F sufficiently greater than 1 for the result to be improbable under the null hypothesis. It is still possible to use the F _statistic_ to test the null hypothesis that Var1 = Var2, in circumstances where it is entirely possible that Var1 Var2, Var1 = Var2, or Var1 Var2. In such cases _both_ tails of the F distribution are of interest, not just the upper tail. Similarly, one may use Chi-square to test the null hypothesis that a variance has a specified value, and wich to reject if the evidence leads one to believe that the true value is LESS, OR if the true value is GREATER, than the value specified. One can get a large F by either Mu1Mu2 or Mu1Mu2 (or by positive or negative R, ...). Therefore the one-tail of the distribution corresponds (normally) to a two-tailed or non-directional test. However, there is absolutely nothing wrong with making the necessary adjustment to make the test directional (i.e., equivalent to the one-tailed t-test), and therefore referring to it (confusingly, of course) as a one-tailed test. On this point, one must agree with Thom: such a use of language can only be confusing, as you acknowledge. "Newspeak", it was called in "1984". -- 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/ =
Re: Two sided test with the chi-square distribution?
Incorrectly? Would you please expand your thought. The only thing that might be called an error in his laws, that comes immediately to mind, is the fact that he didn't allow for the small problem of two genes being on the same chromosome -- but then he didn't know about chromosomes. Is this what you meant? Your supposition is interesting, but all of his data exhibits a too good fit. "Robert J. MacG. Dawson" wrote: Rich Strauss wrote: Your point is well taken, and I didn't mean to imply dishonesty either -- the term "fudged" was a poor choice, but I meant it in the sense of manipulation or filtering, not necessarily conscious, and I mentioned that it was an assertion. I don't see any reason to suppose that it wasn't _conscious_, but there is no reason to suppose that it was _malicious_. One obvious hypothesis is that Mendel used his model (incorrectly, as we now know) to guide his classification of a few dubious cases. -Robert Dawson -- Bob Wheeler --- (Reply to: [EMAIL PROTECTED]) ECHIP, Inc. = 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 sided test with the chi-square distribution?
Bob Wheeler wrote: Your point is a good one, but as a side issue, let me object to the word "fudged." It implies chicanery, which is not something that even Fisher cared to imply. No one will ever know why Mendel's results appear as they do, but It was not necessarily with an intent to mislead. An argument can be made, that his intent was to call attention to the regularities involved just as one does by showing a line on a plot instead of the scattered points from which it is calculated. Attitudes about data were different then. [snip the rest] Even Sir Isaac Newton, in correspondence with his publisher, discussed what we call 'massaging' of data until it fit right. Nonetheless, I spend a fair amount of time in an UG metallurgy lab emphasizing that _they_ cannot adjust and discard embarrassing points to fit preconceptions. 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/ =
Re: Two sided test with the chi-square distribution?
Hi On Tue, 6 Feb 2001, Thom Baguley wrote: Donald Burrill wrote: Well, it _might_ be. Depends on what hypothesis was being tested, doesn't it? And so far "rjkim" hasn't deigned to tell us that. Yes, though I think the vocabulary can obscure what goes on. To me a "one-tailed" test should refer to the distribution to retain the meaning of "tail" and hence is a confusing term if used without further explanation. The problem is that one-tailed test is taken as synonymous with directional hypothesis (e.g., Ha: Mu1Mu2). This causes no confusion with distributions such as the t-test, because directional implies one-tailed. This correspondence does not hold for other statistics, such as the F and Chi2. One can get a large F by either Mu1Mu2 or Mu1Mu2 (or by positive or negative R, ...). Therefore the one-tail of the distribution corresponds (normally) to a two-tailed or non-directional test. However, there is absolutely nothing wrong with making the necessary adjustment to make the test directional (i.e., equivalent to the one-tailed t-test), and therefore referring to it (confusingly, of course) as a one-tailed test. To make F directional, one simply halves p from the statistical output or looks up the critical value of F with 2*alpha (e.g., .10). The same would hold for Chi2 and is presumably what happened with the paper referred to initially (assuming knowledge of statistics). That is, the Chi2 under many applications would be insensitive as to the direction by which observed values differed from expected values, making it a non-directional/two-tailed test without some adjustment. But such adjustment would be appropriate if the direction of differences was predicted, just as for the F. Best wishes Jim James M. Clark (204) 786-9757 Department of Psychology(204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark = 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 sided test with the chi-square distribution?
would this be like the F being less than 1 ... in a regular anova??? mean difference not even varying like we would expect them to by chance if null were true? = 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 sided test with the chi-square distribution?
I think some of this is a matter of vocabulary. Do you say 'one tailed test' or 'one sided test'? (Ditto for 'two'.) People seem to use the two phrases fairly interchangeably. In this context, it does not matter whether you think of the F distribution as having two 'ends' - and you can use one or both of them in a test - or two tails (one very short and stubby, one long and skinny) - and you can use one or both of them in a test. I used the term 'one-tailed' in my previous email. If you prefer, change this to 'one sided'. dennis roberts wrote: distributions are inherently TWO ended ... at least i have never seen one that had, say ... an upper end but no lower end ... how a particular significance TEST uses a distribution ... one end or both ... is a function of how the test statistic is defined It is not the test statistic, but the test hypotheses that determine whether a test is one or two sided. Alan -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102Fax: +61 03 9903 2007 = 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 sided test with the chi-square distribution?
Your point is well taken, and I didn't mean to imply dishonesty either -- the term "fudged" was a poor choice, but I meant it in the sense of manipulation or filtering, not necessarily conscious, and I mentioned that it was an assertion. Rich Strauss At 06:13 PM 2/5/01 -0500, you wrote: Your point is a good one, but as a side issue, let me object to the word "fudged." It implies chicanery, which is not something that even Fisher cared to imply. No one will ever know why Mendel's results appear as they do, but It was not necessarily with an intent to mislead. An argument can be made, that his intent was to call attention to the regularities involved just as one does by showing a line on a plot instead of the scattered points from which it is calculated. Attitudes about data were different then. The scatter in this sort of data is large, and quite confusing. Look at the difficulties and puzzlements of the three individuals who rediscovered the phenomenon 50 years later -- their data are very confusing, and none of the three got it quite right until they found Mendel's paper. Dr Richard E Strauss Biological Sciences Texas Tech University Lubbock TX 79409-3131 Email: [EMAIL PROTECTED] (formerly [EMAIL PROTECTED]) Phone: 806-742-2719 Fax: 806-742-2963 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
