Re: ANOVA and regression
Hi On 29 May 2001, Alex Yu wrote: Does anyone know any book/paper/website about teaching the relationship between ANOVA and regression? I have Data Analysis for Research Designs by Keppel. I also seached www.jstor.org but could not find anything. I am interested in seeing what approaches have been used to illustrate how ANOVA can be expressed in regression and vice versa in a teacher's perspective. Thanks in advance. A good brief introduction is A. L. Edwards 1979 Multiple Regression and the Analysis of Variance and Covariance by W. H. Freeman. I believe I also had a second edition, although I don't see it anywhere on my shelves. Perhaps in the mid 1980s? 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: The False Placebo Effect
Hi On 24 May 2001, David Heiser wrote: Be careful on your assumptions in your models and studies! --- Placebo Effect An Illusion, Study Says By Gina Kolata New York Times (Published in the Sacramento Bee, Thursday, May 24, 2001) ... He and Gotzsche began looking for well-conducted studies that divided patients into three groups, giving one a real medical treatment, one a placebo and one nothing at all. That was the only way, they reasoned, to decide whether placebos had any medical effect. They found 114, published between 1946 and 1998. When they analyzed the data, they could detect no effects of placebos on objective measurements, like cholesterol levels or blood pressure. Was there some reason that they did not include studies with only 2 groups: no treatment and placebo? Only those two groups are necessary to determine whether placebo differs from no treatment. 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: A regressive question
Hi On 15 May 2001, Alan McLean wrote: The usual test for a simple linear regression model is to test whether the slope coefficient is zero or not. However, if the slope is very close to zero, the intercept will be very close to the dependent variable mean, which suggests that a test could be based on the difference between the estimated intercept and the sample mean. Would this not depend on the scale being used? If the predictor was some scale on which the normal range of values was quite large (e.g., GRE scores?), then the value at 0 might be some distance from the mean of Y even given a very shallow slope. So the test would somehow have to adjust for this; that is, the standard error of the difference from the mean of Y would have to vary as a function of the distance of 0 from the mean of X. And presumably the test should produce the equivalent results to the normal test of the slope. It would be interesting to see if there is such a test. Could it be related to the equations for confidence interval for predicted Y given X? There are separate formulas for individual and group predictions and the widths do vary with distance from the mean of X. 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: errors in journal articles
Hi On 3 May 2001, Warren Sarle wrote: Joel Best is a professor of sociology and criminal justice at the University of Delaware. This essay is excerpted from _Damned Lies and Statistics: Untangling Numbers From the Media, Politicians, and Activists_, just published by the University of California Press So the prospectus began with this (carefully footnoted) quotation: Every year since 1950, the number of American children gunned down has doubled. I had been invited to serve on the student's dissertation committee. When I read the quotation, I assumed the student had made an error in copying it. I went to the library and looked up the article the student had cited. There, in the journal's 1995 volume, was exactly the same sentence: Every year since 1950, the number of American children gunned down has doubled. This quotation is my nomination for a dubious distinction: I think it may be the worst -- that is, the most inaccurate -- social statistic ever. Full text: http://chronicle.com/free/v47/i34/34b00701.htm Here is the progression, culminating in 35 trillion children being gunned down in 1995, far beyond the population of the world since its inception, as Best points out in the original article. In the article he describes tracking down the original basis for the statistic. At some point, doubling _since_ 1950 got translated into doubling every year since 1950. Year# Children Gunned Down 1950 1 1951 2 1952 4 1953 8 1954 16 1955 32 1956 64 1957 128 1958 256 1959 512 1960 1,024 1961 2,048 1962 4,096 1963 8,192 1964 16,384 1965 32,768 1966 65,536 1967 131,072 1968 262,144 1969 524,288 1970 1,048,576 1971 2,097,152 1972 4,194,304 1973 8,388,608 1974 16,777,216 1975 33,554,432 1976 67,108,864 1977 134,217,728 1978 268,435,456 1979 536,870,912 1980 1,073,741,824 1981 2,147,483,648 1982 4,294,967,296 1983 8,589,934,592 1984 17,179,869,184 1985 34,359,738,368 1986 68,719,476,736 1987 137,438,953,472 1988 274,877,906,944 1989 549,755,813,888 1990 1,099,511,627,776 1991 2,199,023,255,552 1992 4,398,046,511,104 1993 8,796,093,022,208 1994 17,592,186,044,416 1995 35,184,372,088,832 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: Artifacts in stats: (Was Student's t vs. z tests)
Hi On 25 Apr 2001, Alan McLean wrote: I agree - although students do need tables in (written) exams... But we use a computer program called Tuteman in our teaching and testing, so the natural way to find critical values or p-values is via the computer - we use Excel mainly. In general, I emphasise the use of p values - in many ways it is a more natural way than using critical values to carry out a test. The p value is a direct measure of 'strength of evidence'. Paul W. Jeffries wrote: But this approach made me think about artifacts in statistics. What are list members views on teaching students to use tables. In the computer age, tables are an anachronism. The vast majority of students will never use a t table. They will just rely on the computer to print the p value. The following article by Dawson in 1997 described how it would be possible to have improved tables (i.e., more p values) that were more compatible with the probability approach. http://www.amstat.org/publications/jse/v5n2/dawson.html 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: FW: Student's t vs. z tests
Hi On 24 Apr 2001, Mark W. Humphries wrote: I concur. As I mentioned at the start of this thread, I am self-learning statistics from books. I have difficulty telling what is being taught as necessary theoretical 'scaffolding' or 'superceded procedures', and what one would actually apply in a realistic case. I would love a textbook which walks through a realistic analysis step by step, while providing the 'theoretical scaffolding' as insets within this flow. Its frustrating to read 50 pages only to find that 'one never actually does it this way'. My gut feeling is that this would be a terribly confusing way to _teach_ anything. Students would be started with a (relatively) advanced procedure and at various points have to be taken aside for lessons on sampling distributions, probability, whatever, and then brought back somehow to the flow of the current lesson. There is a logic to the way that statistics is developed in most intro texts (although some people might not agree with that logic in the absence of a direct empirical test of its efficacy). It would be an interesting study of course, and not that difficult to set up with some hypertext-like instruction. Students could be led through the material in a hierarchical manner or entered at some upper level with recursive links to foundational material. We might find some kind of interaction, with better students doing Ok by either procedure (and perhaps preferring the latter) and weaker students doing Ok by the hierarchical procedure but not the unstructured (for want of a better word) method. At least, that is my prediction. Start of Dennis's comments (I believe) the problem with all these details is that ... the quality of data we get and the methods we use to get it ... PALE^2 in comparison to what such methods might tell us IF everything were clean DATA ARE NOT CLEAN! but, we prefer it seems to emphasize all this minutiae .. rather than spend much much more time on formulating clear questions to ask and, designing good ways to develop measures and collect good data I for one was not saying anything at all about how much time was spent on various topics. And it seems likely to me that more effective methods of instruction (for whatever) leave more time for other material, and not less. we pay NO attention to whether some measure we use provides us with reliable data ... the lack of random assignment in even the simplest of experimental designs ... seems to cause barely a whimper Speak for yourself. How can you know what else is done in a class from a narrow discussion of how best to teach one particular component? we pound statistical significance into the ground when, it has such LIMITED application I think that reading the scientific literature would disabuse one about the limited application of statistical significance. My students tell me that learning about statistical inference greatly increases their capacity to read primary literature. Perhaps it is different in your discipline. but yet, we get in a tizzy (me too i guess) and fight tooth and nail over such silly things as should we start the discussion of hypothesis testing for a mean with z or t? WHO CARES? ... the difference is trivial at best Perhaps the people who don't care shouldn't get involved in the discussion. Again, you seem to be drawing some pretty broad inferences from a discussion of one topic on a list that is dedicated to teaching statistics. in the overall process of research and gathering data ... the process of analysis is the LEAST important aspect of it ... let's face it ... errors that are made in papers/articles/research projects are rarely caused by faulty analysis applications ... though sure, now and then screw ups do happen ... Perhaps that is because students learned those techniques well. Nor are statistical analysis matters independent of good research design. A number of aspects of design follow from an understanding of statistical tests, such as: the importance of sample size, minimizing noise in the study (e.g., standard testing procedures, homogeneous samples), and having a sufficiently powerful manipulation of the predictor variable. the biggest (by a light year) problem is bad data ... collected in a bad way ... hoping to chase answers to bad questions ... or highly overrated and/or unimportant questions NO analysis will salvage these problems ... and to worry and agonize over z or t ... and a hundred other such things is putting too much weight on the wrong things AND ALL IN ONE COURSE TOO! (as some advisors are hoping is all that their students will EVER have to take!) Then it would seem that your argument should be with the people in your area who have this naive expectation. In psychology, undergraduate students will get a number of courses on data analysis and research methods, depending in part on whether they are majors or honours students. So I have the luxury of focussing
Re: Student's t vs. z tests
Hi On Fri, 20 Apr 2001, dennis roberts wrote: At 10:58 AM 4/20/01 -0500, jim clark wrote: What does a t-distribution mean to a student who does not know what a binomial distribution is and how to calculate the probabilities, and who does not know what a normal distribution is and how to obtain the probabilities? good question but, NONE of us have an answer to this ... i know of NO data that exists about going through various different routes and then assessing one's understanding at the end Just a couple of comments. (1) Not having specific evidence on a pedagogical question does not mean that any approach is just as justified as any other approach. We should base our practice on what information is available, appreciating its possible limitations (e.g., personal experience, cognitive models of concept learning, general principles of teaching, principles of task analysis, logic, feedback from students, ...). Only the very naivest sort of crude empiricism would dictate that specific findings are the only worthwhile factors in a science-based practice. (2) In general I suspect that there is much evidence supportive of a task-analytic approach to teaching mathematics, although I have not looked at the literature for many years. That is, mathematics, perhaps more than many other areas, requires a sensitivity to the kinds of prior knowledge presumed by the new knowledge to be acquired. to say that we know that IF we want students to learn about and understand something about t and its applications ... one must: 1. do binomial first ... 2. then do normal 3. then do t is mere speculation Only if you completely devalue many years of experience teaching a subject matter, a background in cognitive and educational psychology, the possibility that there might be certain logical entailments involved among the topics, and so on. Your statement makes it sound as though one is equally justified to promote any of the 3! = 6 possible permutations of all 3 tasks + the 3x2! = 6 permutations of 2 tasks + the 3 possible single tasks (+ the 1 possible 0 tasks, if one wants to be comprehensive). without some kind of an experiment where we try various combinations and orderings ... and see what happens to student's understandings, we know not of what we assert (including me) This is just too nihilistic a view of knowledge and teaching. There are certain constraints. For example, one normally expects that learning the alphabet is better done before learning words. Would you want an experiment before concluding that presenting the calculus of statistics is probably not the best approach to intro stats in non-mathematical disciplines? off the top of my head, i would say that one could learn alot about a t distribution studying it ... are you suggesting that one could not learn about calculating probabilities within a t distribution without having worked and learned about calculating probabilities in a normal distribution? as far as i know, the way students learn about calculating probabilities is NOT by any integrative process ... rather, they are shown a nice drawing of the normal curve, with lines up at -3 to +3 ... with values like .02, .14, .34 ... etc. within certain whole number boundaries under the curve, and then are shown tables on how to find areas (ps) for various kinds of problems (areas between points, below points, above points) if there is something real high level and particularly intuitive about this, let me know. you make it sound like there is some magical learning here ... some INductive principle being established ... and, i don't see it Of course you left off my starting point. For the binomial distribution, students can readily be shown how to actually calculate the probabilities in the sampling distribution. They do not have to take it purely on faith. Then when we move to the normal or t or F or whatever, we can say that these distributions are produced by more sophisticated mathematical techniques that are beyond our capabilities, but _analogous_ to what students did for the binomial. This is the foundation (with its own foundation in an adequate understanding of probability and counting principles). The normal distribution is the bridge between this foundation and the t-distribution (then F, whatever). I can't speak for other disciplines, but at least in psychology and education, it is probability worth noting that an understanding of the normal distribution is valuable in and of itself, irrespective of its role in hypothesis testing. Examples of normal distributions would occur in testing (e.g., understanding different test score transformations, such as T-scores, computed percentiles, and the like), in understanding certain transformations (e.g., of skewed reaction time distributions), and in perception (e.g., d-prime measures of sensitivity). i don't see one whit of difference between this and ... showing some t
Re: partial correlations
Hi On 7 Apr 2001, Dianne Worth wrote: After several years of frustration with SAS, I am migrating to SPSS. I am currently working on a project in both packages, to ensure accuracy of results as I teach myself SPSS. I would like to obtain 1) the squared semi-partial correlation based on the sequence that predictors are entered into the model statement (SCORR1 in SAS) and 2) SCORR2, which is supposed to show the unique proportion of variance that the predictor explains in Y. You can get part (semi-partial rs) in several ways in SPSS. The ZPP option on the STATISTICS sub-command will report zero, part, and partial correlations for each predictor in the equation. The CHANGE and HISTORY options will show you r^2 change (= part or semi-partial r when single predictor entered at a time). CHANGE reports the value at each step and History reports the r^2 changes at the end. So the commands would be: REGR /VARI = y b1 b2 b3 /STAT = DEFAU ZPP CHANGE HISTORY /DEP = y /STEPWISE (or whatever METHOD of entry you choose to use) 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/ =
Avoiding Linear Dependencies in Artificial Data Sets
Hi I like to use small, artificially generated data sets with integer parameters to introduce analyses. Often, however, I find it difficult to avoid undesirable contingencies among the scores (e.g., linear dependencies in within-subject designs). Is there an algorithmic way to generate such scores and avoid such dependencies? Here is a small example with 4 scores for each of 5 subjects. The following analysis reveals the undesirable linear dependencies. I'm assuming the dependencies arise from the noise vectors that I used to generate the cell scores by adding them to the main effect of the factor and the subject effects. Is there a systematic way to create such noise vectors to avoid linear dependencies? data list free / subj vl lo hi vh begin data 1 3 3 5 52 1 3 7 9 3 6 8 8 10 4 7 8 6 7 5 3 3 9 9 end data manova vl lo hi vh /wsf = conc(4) /print = cell /contr(conc) = poly - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Cell Means and Standard Deviations Variable .. VL Mean Std. Dev. N 95 percent Conf. Interval For entire sample 4.000 2.449 5 .959 7.041 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Variable .. LO Mean Std. Dev. N 95 percent Conf. Interval For entire sample 5.000 2.739 5 1.600 8.400 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Variable .. HI Mean Std. Dev. N 95 percent Conf. Interval For entire sample 7.000 1.581 5 5.037 8.963 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Variable .. VH Mean Std. Dev. N 95 percent Conf. Interval For entire sample 8.000 2.000 5 5.517 10.483 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Tests of Between-Subjects Effects. Tests of Significance for T1 using UNIQUE sums of squares Source of Variation SS DFMS F Sig of F WITHIN CELLS 40.00 4 10.00 CONSTANT 720.00 1720.00 72.00 .001 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Estimates for T1 --- Individual univariate .9500 confidence intervals CONSTANT Parameter Coeff.Std. Err. t-Value Sig. t Lower -95%CL- Upper 1 12.00 1.41421 8.48528 .00106 8.07351 15.92649 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * * * * * * * * * * * * * * * * * A n a l y s i s o f V a r i a n c e -- Design 1 * * * * * * * * * * * * * * * * * Tests involving 'CONC' Within-Subject Effect. Mauchly sphericity test, W = .0 Chi-square approx. = . with 5 D. F. Significance = . Greenhouse-Geisser Epsilon = .40650 Huynh-Feldt Epsilon = .49123 Lower-bound Epsilon = .3 AVERAGED Tests of Significance that follow multivariate tests are equivalent to univariate or split-plot or mixed-model approach to repeated measures. Epsilons may be used to adjust d.f. for the AVERAGED results. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * W A R N I N G * The WITHIN CELLS error matrix is SINGULAR. * * * These variables are LINEARLY DEPENDENT * * * on preceding ones ..* * * T3* * * Multivariate tests will be skipped. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 07:51:26The University of Winnipeg SUN SPARCSolaris * * * * * * * * * * * * * * * * * A n a l y s i s o f V a r i a n c e -- Design 1 * * * * * * * * * * * * * * * *
Re: On inappropriate hypothesis testing. Was: MIT Sexism statistical
Hi On 12 Mar 2001, Radford Neal wrote: Yes indeed. And the context in this case is the question of whether or not the difference in performance provides an alternative explanation for why the men were paid more (one supposes, no actual salary data has been released). In this context, all that matters is that there is a difference. As explained in many previous posts by myself and others, it is NOT appropriate in this context to do a significance test, and ignore the difference if you can't reject the null hypothesis of no difference in the populations from which these people were drawn (whatever one might think those populations are). Personally, I am not interested in the question of statistical testing to dismiss the alternative explanation being proposed; indeed, I suspect that the original claim about gender being the cause of salary differences would not stand up very well either to statistical tests. But there does seem to me to be more than just saying ... "see there is a difference" and that statistical procedures would have a role to play. For example, wouldn't the strength and consistency of the differences influence your confidence that this was indeed the underlying factor? The same difference in means due to one or two outliers would surely not mean the same thing as a uniform pattern of productivity differences, would it? And wouldn't you want to demonstrate that there was a significant and ideally strong within-group relationship between productivity and salary before claiming that it is a reasonable alternative for the between-group differences? Or at least, wouldn't that strengthen the case? I appreciate that in some domains (e.g., intelligence testing), people are reluctant to make inferences about between-group differences on the basis of within-group correlations, but that is the basic logic of ANCOVA and related methods. 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: On inappropriate hypothesis testing. Was: MIT Sexism statistical
Hi On Mon, 12 Mar 2001, Irving Scheffe wrote: Jim: For example, suppose you had a department in which the citation data were Males Females 12220 1298 2297 1102 When I said outlier, I had in mind hypothetical data of the following sort (it doesn't matter to me whether it is the salaries or the citation rates): MalesFemales 170001000 10001000 10001000 10001000 Avg 50001000 vs. Males Females 50001000 50001000 50001000 50001000 Avg 50001000 I would view the latter somewhat differently than the former with respect to differences between these samples of males and females, and with respect to the kinds of explanations I would seek (e.g., somewhat general to males, something specific to male 1). The male with 12220 is, let's imagine, a Nobel Prize winner. The salaries for the 4 people are Males Females 156,880 121,176 112,120 114,324 Of course if the salaries were: Males Females 112,120 121,176 156,880 114,324 You probably might want not to promote the hypothesis of productivity differences explaining the gender differences. That was the point of one of my later comments. As Radford Neal has pointed out succinctly, the argument about outliers is irrelevant, and I want to emphasize with this example that it is irrelevant on numerous levels. First of all, it is not necessarily clear whether, and in which of several senses, our Nobel Prize winner is an outlier in his group. Second, even if he is -- so what? Surely you would not argue that this means he didn't deserve his salary! Assuming a correlation between productivity and salary (or winning of Nobel prizes). In fact, careful examination of the salary data [never made public by the administration] together with the performance data might well have led to the conclusion that it is the male faculty who are underpaid. I'm in perfect agreement with this, although I still think that statistics would play a positive role in identifying the determinants of salary. Although, as Dr. Neal pointed out, it is not logically relevant to the issue, I would like to explore your notion, echoed without justification by Rich Ulrich, that the huge difference in citation performance between MIT senior men and women might be due to "one or two outliers." I don't remember making any such attribution. I asked a question about whether detractors of statistical testing would view equivalently differences due to some outliers and more consistent results, in the sense I showed above. I'm not sure it is any more palatable to have one's motives misconstrued by people arguing against gender-related bias than to have them misconstrued by people arguing for gender-related bias. Take a look at the data again, and tell me which male data you consider to be outliers within the male group, and why. For example, are the men with 2133 and 893 "outliers," or those with 12830 and 11313? Not having taken any position on it, I am not too sure I feel any compulsion to answer your question. I guess I would turn it around and say, would you interpret your results exactly the same as the modified results that I have presented below? The data for the senior men and women: 12 year citation counts: MalesFemales -- 128302719 113131690 106281301 43961051 2133 935 893 --- Average 7032 1539 Modified (Hypothetical ... for pedagogical purposes only ... no hidden agenda results ...) Males Females 34500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 Avg 7000 1500 To me, these data are much less suggestive of general differences in productivity between males and females, would not be an adequate account of widespread (i.e., consistent or uniform across individuals) differences in salaries, and so on. Am I correct to assume that for you the consistency of the differences between the groups (which is what a statistical test measures) is completely irrelevant? Or are you implicitly engaging in inferential-like thinking when you examine the actual distributions? As for the notion of exploring the relationship between salary, gender, and performance -- I'd be more than happy to examine any data that MIT would make available. They will, of course, not make such data available. It is too private, they say. But were the data made available to you, would you use any statistical procedures in the examination? Would you care whether the differences in salary were significant? The differences in productivity? The differences in any number of potential confounding variables? What about the significance and strength of the relationships between predictors and salary? What about whether the gender difference was significant after productivity was
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: AW: eigenvalue: origin of term
Hi On Sat, 20 Jan 2001, Bob Wheeler wrote: I can't find a paper by anyone named Cohen with a title resembling what you give in CIS. Perhaps you can improve the citation. Cohen, J. (1968). Multiple regression as a general data-analytic system. Psychological Bulletin, 70, 426-443. 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/ =
