Re: Homework Problem
Michael Scheltgen <[EMAIL PROTECTED]> wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... > Suppose X1, X2, X3, and X4 have a multivariate Normal Dist'n > with mean vector u, > and Covariance matrix, sigma. > > (a) Suppose it is known that X3 = x3 and X4 = x4. What is: > > 1)The expected value of X1 > 2)The expected value of X2 > 3)The variance of X1 > 4)The variance of X2 > 5)The correlation of X1 and X2 > > My approach was to find the conditional distribution, then > designate > > E[X1] = u1 from the mean vector of the conditional dist'n > E[X2] = u2 from the mean vector of the conditional dist'n > same with the variance, etc... > > Is this the correct approach? Thank you very much for your > comments :) Looks right to me. Glen = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: convergent validity
I'm coming in at a different slant from what I have seen posted on this thread (in sci.stat.edu). On Thu, 29 Mar 2001 20:30:59 +0200, "H.Goudriaan" <[EMAIL PROTECTED]> wrote: ... > I have 2 questionnaires assessing (physical and emotional) health of > heart patients. The 1st measures present state and it's assessed before > treatment and a couple of months after treatment, so that difference > scores can be calculated. The 2nd questionnaire is assessed after > treatment only, and asks respondents how much they have changed on every > aspect (same aspects as the first questionnaire) since just before > treatment. > Respondents received both questionnaires. Now I would like to > investigate the convergent validity of the two domains assessed with > both questionnaire versions. Is there a standard, straightforward way of > doing this? Someone advised me to do a factoranalysis (PCA) (on the > baseline items, the serially measured change scores and the > retrosepctively assessed change scores) and then compare the > factorloadings (I assume after rotation? (Varimax?)). I haven't got a > good feeling about this method for two reasons: > - my questionnaire items are measured on 5- and 7-point Likert scales, > so they're not measured on an interval level and consequently not > (bivariate) normally distributed; [ snip, about factor loading.] If items were really Likert, they would be close enough to normal. But there is no way (that comes to mind) that you should have labels for "Change" that are Likert: Likert range is "completely disagree" ... "completely agree" and responses describe attitudes. You can claim to have Likert-type labels, if you do have a symmetrical set. That is more likely to apply to your Present-Status reports, than to Changes. At any rate -- despite the fact that I have never found clean definitions on this -- having a summed score is not enough to qualify a scale as Likert. Thus, you *may* be well-advised, if someone has advised you so, to treat your responses as 'categories' -- at least, until you do the dual-scaling or other item analyses that will justify regarding them as "interval." For someone experienced in drawing up scales, or if you were picking up items from much-used tests, that would not be a problem; but people are apt to make mistakes if they haven't seen those mistakes well-illustrated. What is your question about individual items? Are some, perhaps, grossly inappropriate? Or, too rarely marked? If 11 are intended for a "physical factor", there *should* emerge a factor or principal component to reflect it. Ditto, for emotional. Any items that don't load are duds (that would be my guess). Or do you imagine 2 strong factors? Again -- whatever happens should not come as much surprise if you've done this sort of thing before. IF the items are done in strict-parallel, it seems unnecessary and obfuscatory to omit a comparison of responses, item by item. -- 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: rotations and PCA
On Sun, 01 Apr 2001 22:13:18 +0100, Colin Cooper <[EMAIL PROTECTED]> wrote: > ==snip See Stephen Jay Gould's _The Mismeasure of Man_ for more > > details; note that Thurstone adopted varimax rotations because their > > results were consistent with *his* pet theories about intelligence. > Hmm. Gould's book is generally reckoned to be rather partial and not > particularly accurate - see for example JB Carroll's 'editorial review' > of the second edition in 'Intelligence' about 4 years ago. (sorry - > haven't got the exact reference to hand). Comrey & Lee's book is one of A google search on < Carroll Gould Intelligence > immediately hit a copy of the article -- http://www.mugu.com/cgi-bin/Upstream/Issues/psychology/IQ/carroll-gould.html I liked Gould's book. I know that he offended people by pointing to gross evidence of racism and sexism in 'scientific reports.' But he has (I think) offended Carroll in a more subtle way. Gould is certainly partial to ideas that Carroll is not receptive to; I think that is what underlies this critique. After Google-ing Carroll, I see that he is a long-time researcher in "intelligence." To me, it seems that Gould is in touch with the newer stream of hypotheses about intelligence -- ideas that tend to invalidate the basic structures of old-line theorists like Carroll. In the article, Carroll eventually seems to express high enthusiasm for 'new techniques' (compared to what Gould made use of) in factor analysis. I can say, my own experience and reading has not led me to the same enthusiasm. Am I missing something? > the better introductions - Loehlin 'latent variable Models' is good if > you're coming to it from a structural equation modelling background. > > Colin Cooper -- 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/ =
Repeated-measures t test for ratio level data
I would like to start a discussion on a family of procedures that tend not to be emphasised in the literature. The procedures I have in mind are based upon the ratio between two sets of scores from the same sample. To illustrate the discussion, I shall refer to the data from a simple psychological experiment I recently undertook (I have simplified the data, in fact the study involved several IVs). The study was designed to investigate an aspect of visual priming. In this kind of experiment there are two stimuli per trial; the prime and the target. The prime is presented before the target. The target is the stimulus to which the participant responds. The prime is said to be congruent if it similar to the target in some way or other. The prime is said to be incongruent if it dissimilar to the target. In my experiment the target was either a blue or a green shape presented on a computer monitor. The participants responded by pressing one of two keys on the computer keyboard. Participants reaction times (RTs) in milliseconds were recorded. There were forty trials per condition. The DV was the medians of RTs by participant by condition (see below. You can ignore the following technical details if you wish. RTs typically have a right-skewed distribution. A standard procedure for dealing with RTs is to calculate the median RT by participant by condition. A further complication that can be overlooked is that only RTs from correctly identified targets are used to generate these medians. There are procedures designed to ensure that the median is not biased by them being calculated from different numbers observations that I shall not discuss here). The aim of the experiment was to determine what effect if any the prime had on response to the target. In my study the primes were either the same colour (i.e., congruent) or a different colour (i.e, incongruent) to the target. Cong Incong 553.50 637.25563.50 591.00656.88 682.00533.25 537.13719.63 799.75632.25 599.75516.88 538.38765.00 741.00445.50 453.38593.38 606.00478.25 517.00539.25 554.75 My hypothesis was that reaction times will be shorter with congruent primes than with incongruent primes. One way of testing this hypothesis is to use a repeated-measures t test; i.e., calculate difference scores for each participant and perform a one-sample t test to determine whether the observed mean difference score is significantly different from zero. But I had recently heard about some researchers who had used the ratio of the lengths people's index and ring fingers as a variable. "Why a ratio and not a difference?", I wondered. If everyone had the same size hands then there would be no point. However, it is reasonable to expect that the relationship between hand size and the difference in two finger lengths is heteroscedastic. Bigger hands can have bigger finger length differences. Then I wondered whether the similar reasoning could be applied to RT data. RT is a ratio level measurement scale just like finger length. It is reasonable to expect that slower participants will have greater variability in their reaction times. I wondered how I might test my hypothesis using ratios rather than differences. Here's "my" solution. I calculated ratio scores for each participant and perform a one-sample t test to determine whether the observed mean ratio score is significantly different from one. As ratios of interval level variables are meaningless I surmised that the t test on ratios should only be applied to ratio level data. For the above data the results are as follows; one sample t test of ratios t (12) = -2.337, p = 0.039 Mean Ratio = 0.965 (i.e., participants in the congruent condition responded 3.5% quicker than participants in the incongruent condition) 95% Confidence Limits = 0.933 and 0.998 However, I was reinventing the wheel. Later I learned that Howell (1997) describes the procedure on pages 180-181 and was previously used by Kaufman & Rock (1962). My feeling is that the t test for ratios should have a similar status and profile as the repeated measures t test (on differences). I suspect that the t test for differences is often used when the t test for ratios would be more suitable. So why is the procedure not more widely used? Perhaps this is only a problem within psychology where ratio level data is not commonly used. Also I wonder whether the t test of ratios is a more powerful test than the t test of differences. If so then the ratio t test should be used in preference to the difference t test. By the way for the above data there is a significant difference for the t test of ratios but not for the t test of differences; one sample t test of differences t (12) = 2.163, p = 0.053 Mean difference = 21.68 95% Confidence Limits = -0.38 and 43.73 Thinking about these issues has caused me to reassess the assumptions underpinning the use of the repeated measures t test (for dif
Re: Repeated-measures t test for ratio level data
At 06:50 PM 4/2/01 +0100, Dr Graham D Smith wrote: >Thinking about these issues has caused me to reassess the assumptions >underpinning the use of the repeated measures t test (for differences). >For a long time, I have thought that the homogeneity of variance >assumption is meaningless for the RM t test. In other words there is no >point in comparing the variability of scores from one condition with the >variability of scores in the other condition prior to using the test. I >thought this because, once the difference scores are calculated >homogeneity of variance is meaningless. The t test is performed on the >differences not the scores themselves whose variances may differ (so >what?). However, I now wonder whether in fact one should look at >homoscedasticity of the relationship between the difference of the scores >in the two conditions and the sum of the scores in the two conditions; for >example, for my data the relationship between Incong-Cong and Incong+Cong. >(Actually the data from my study were not clearly heteroscedastic). let's say that you do a pre and post study with the same Ss ... say, pretest score and posttest score ... AND, while there is variance at pre ... all Ss master the material and, the variance on scores on the post more or less goes away (a not uncommon problem in mastery learning studies) are you suggesting that the difference in variances at pre and post should be of no concern when doing a dependent t test on the means? = 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)
SAT scores are approximately normal with mean 500 and a standard devotion 100. Scores of 800 or higher are reported as 800, so a perfect paper is not required to score 800 on the SAT. What percent of students who take the SAT score 800? The answer to this question shall be: SAT scores of 800+ correspond to z>3; this is 0.15%. Please help me understand this. I dont understand how I get that z>3??? and that it is 0.15%? Thanks for help = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
SAT z>3 (Was: Re: (no subject))
Everything you need is in what you wrote. You do understand that "z" is the usual shorthand for "a standard score", and that a standard score is the representation of a given raw score as its deviation from the population mean in standard-deviation units? The rest is merely a lookup in a table of the standard normal distribution. (I find it to be somewhat less than 0.15%, though.) -- DFB. On Mon, 2 Apr 2001, Jan Sjogren wrote: > SAT scores are approximately normal with mean 500 and a standard > devotion 100. Scores of 800 or higher are reported as 800, so a > perfect paper is not required to score 800 on the SAT. What percent > of students who take the SAT score 800? > > The answer to this question shall be: SAT scores of 800+ correspond > to z>3; this is 0.15%. > > Please help me understand this. I don't understand how I get that > z>3??? and that it is 0.15%? 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 603-471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: (no subject)
well, this is a tricky sort of ? if in fact, all REAL scores that actually convert to a SAT value ... anything = to or > than 800 are listed as ... 800 ... then, the ? really can't be ... what is the p value for having 800 or more ... has to be what is the p value for 800 but, the question being asked is probably wanting you to assume that scores could go larger than 800 ... so, for all practical purposes ... it amounts to a ? of 800 or more ... minitab would say: MTB > cdf 800; SUBC> norm 500 100. Cumulative Distribution Function Normal with mean = 500.000 and standard deviation = 100.000 xP( X <= x ) 800.0.9987 MTB > let k1=1-.9987 MTB > prin k1 Data Display K10.0013 MTB > let k2=100*k1 MTB > prin k2 Data Display K20.13 ... as a percent ... about .13 of ONE percent ... about the value you have as the answer MTB > At 08:23 PM 4/2/01 +, Jan Sjogren wrote: >SAT scores are approximately normal with mean 500 and a standard >devotion 100. Scores of 800 or higher are reported as 800, so a perfect >paper is not required to score 800 on the SAT. What percent of students >who take the SAT score 800? > >The answer to this question shall be: SAT scores of 800+ correspond to >z>3; this is 0.15%. > >Please help me understand this. I dont understand how I get that z>3??? >and that it is 0.15%? > >Thanks for help > > > > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= _ 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/ =
ASA Biometrics Section Awards
NOMINATIONS SOUGHT FOR 2001 BYAR YOUNG INVESTIGATOR AWARD AND BIOMETRICS SECTION TRAVEL AWARDS Have you (or, perhaps one of your students) submitted an abstract for the 2001 Joint Statistical Meetings (JSM)? If so, please note that the Biometrics Section is seeking nominations for the 2001 David P. Byar Young Investigator Award. This annual award is given to a young investigator for the best paper to be presented at the JSM. The award is in memory of David Byar, an internationally known biostatistician who made significant contributions to the development and application of statistical methods during his career at the National Cancer Institute. The winner will receive a $1,000 cash award. In addition to the Byar Award, the Section may also provide additional travel awards to the authors of other outstanding papers that are submitted to the Byar award competition. Criteria for applicants are: - having held a Ph.D. for less than three years at the time of application OR not in receipt of a Ph.D. (students are eligible) - younger than 40 years of age - member of the ASA Biometrics Section - first author of the paper - scheduled to present the paper at the 2001 JSM in Atlanta For the 2001 competition, the application materials should consist of: 1. A cover letter certifying that the applicant meets the eligibility requirements 2. A current CV 3. Three copies of the paper Applicants are also invited to submit one copy each of supplementary published or in-press papers if they comprise a body of scientific work related to the paper to be presented. The 2001 Awards Committee is chaired by Charles S. Davis, Vernon M. Chinchilli, and Joan S. Chmiel, the 2000-2002 Biometrics Section Chairs, respectively. Information regarding this award is also available on the Section webpage, easily accessed by clicking on "Links & Resources" at the ASA website (www.amstat.org). Applications must be postmarked on or before June 1, 2001 and sent to: Charles S. Davis Chair, 2001 Biometrics Section Awards Committee Department of Biostatistics University of Iowa 2837 Steindler Building Iowa City, IA 52242 Phone: (319) 335-9625 Fax: (319) 335-9200 Email: [EMAIL PROTECTED] Submission of electronic versions of manuscripts is encouraged (preferably as a postscript or pdf file). = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Error term in repeated-measures ANOVA
I do all my repeated measures analyses with mixed modeling in SAS these days, but I get called on to help people who use standard repeated-measures analyses with other stats packages. So here's my question, which I should know the answer to but I don't! In a repeated-measures ANOVA, most stats packages do a test for sphericity, and they provide an associated adjusted p value for overall significance of the repeated-measures factor. If my understanding is correct, the adjustment takes care of non-uniformity in the within-subject error between levels of the factor. Fine, but then you want to do a specific contrast between levels of the within-subject factor, such as the last pre-treatment vs the first post-treatment (with or without a control group--it doesn't matter). Now, the p value you get for that contrast... is it based on the overall adjusted error derived from ALL levels of the repeated-measures factor, or is it nothing more than the p value for a t test of the two levels in question? I realize that some packages attempt to provide a correction for inflation of the Type I error when you have many contrasts, so the analysis will be an ANOVA rather than a simple t test, but what within-subject error term do the packages use for specific contrasts? Supplementary question: can you get meaningful residuals out of a standard repeated-measures ANOVA, so you can see how non-uniform they are when you plot them against predicteds and label points with the different levels of the within-subject factor? I do this sort of thing routinely with Proc Mixed, but I never tried it in the days I was still using RM-ANOVA. 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: stan error of r - Virus
Dr. Knodt, Perhaps you should make an appointment with some nerdy geek in the IR department who can explain to you how viruses get promulgated. It is usually through executables (.exe) files or microsoft macros. Otherwise you will continue to be needlessly worried about non-existent threats. :-) Tom G. [EMAIL PROTECTED] wrote: > This might be a great way to spread virus. > > With all the virus going around, please do not post e-mail with attachments > to the mailing list. > > Send attachments only to those who request them. > > Thanks for your understanding > > Dr. Robert C. Knodt > [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/ > = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
attachments
I checked with a nerdy geek and was told that it is a waste of bandwidth to broadcast attachments to an entire mailing list. Although not every attachment is a virus, NO ASCII text is. Dr. Knodt's suggestion is entirely consistent with email etiquette. - Forwarded message from Thomas Gatliffe - Dr. Knodt, Perhaps you should make an appointment with some nerdy geek in the IR department who can explain to you how viruses get promulgated. It is usually through executables (.exe) files or microsoft macros. Otherwise you will continue to be needlessly worried about non-existent threats. :-) Tom G. [EMAIL PROTECTED] wrote: > This might be a great way to spread virus. > > With all the virus going around, please do not post e-mail with attachments > to the mailing list. > > Send attachments only to those who request them. > > Thanks for your understanding > > Dr. Robert C. Knodt > [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/ > = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = - End of forwarded message from Thomas Gatliffe - -- _ | |Robert W. Hayden | | Work: Department of Mathematics / |Plymouth State College MSC#29 | |Plymouth, New Hampshire 03264 USA | * |fax (603) 535-2943 /| Home: 82 River Street (use this in the summer) | )Ashland, NH 03217 L_/(603) 968-9914 (use this year-round) Map of New[EMAIL PROTECTED] (works year-round) Hampshire http://mathpc04.plymouth.edu (works year-round) The State of New Hampshire takes no responsibility for what this map looks like if you are not using a fixed-width font such as Courier. "Opportunity is missed by most people because it is dressed in overalls and looks like work." --Thomas Edison = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
