Re: What's the Mahanalobis distance?
The Mahalanobis distance (MD) is distance between each observation and the mean of the others. For the obs. i MD(i)*MD(i)=(X(i)-mean(X))*inverse(S)*transpose(X(i)-mean(X)) where mean(X) is the mean of variables X, X(i) is values of variables X for i, S is the variance-covariance matrix of X. A relation with hat-matrix H is MD(i)*MD(i)=(n-1)*(h(ii)-1/n) where n is the number of observations and h(ii) is the ii-th element of diag of the hat-matrix H=X*inverse(transpose(X)*X)*transpose(X). Hope this helps -- === Dr SAULEAU Erik-A. DIM -- Etablissement Public de Santé Alsace Nord 141, Ave de Strasbourg 67170 Brumath Tel : 03-88-64-61-81 E-Mail: [EMAIL PROTECTED] -- Centre Hospitalier d'Erstein 13, Route de Krafft BP F 67151 Erstein Cedex E-Mail: [EMAIL PROTECTED] === Teo [EMAIL PROTECTED] a écrit dans le message : [EMAIL PROTECTED] Anyone knows in what consist the Mahanalobis distance?? I have to measure the distance between two histograms... Thanks, Teo. * Sent from AltaVista http://www.altavista.com Where you can also find related Web Pages, Images, Audios, Videos, News, and Shopping. Smart is Beautiful === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: hyp test:better def
Milo Schield wrote: I agree with Dennis that students need to be exposed to the use of Bayesian priors within the process of teaching classical hypothesis testing. Using Bayesian priors can be very difficult for some students. (Why do we take the uniform prior ??? ) For to teach decission making in the class, I have made some WWW-pages . If you have Netscape 4 or better (this is not for IE-users), pleace look my DHTML-pages http://noppa5.pc.helsinki.fi/koe/dhtml.html and there Making decissions 1 (Critical value) Making decissions 2 (Probability) Some of my students said "it was usefull". Regards Juha Puranen -- Juha Puranen Department of Statistics P.O.Box 54 (Unioninkatu 37), 00014 University of Helsinki, Finland http://noppa5.pc.helsinki.fi === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
The best effect size
I would appreciate feedback on the following from list members. I recently participated in a discussion at a conference that revolved around effect sizes. The discussion had to do with the clinical value of a set of predictors based on field studies. In these studies, the predictors (which were all dichotomous, positive-negative judgments based on a clinical test) were related to a series of criteria, some of which were dichotomous and some of which were quantitative. Pearson correlations were computed for all comparisons, and d statistics were also generated for all comparisons involving quantitative criteria. An important point to keep in mind was that the base rates for the predictors (and many of the criteria) were quite skewed; in general, only about 1 in 15 members of the sample were positive on any one of the predictors. These were field studies, so the skew presumably represents real-world base rates. The basis for the discussion was the extreme difference in conclusions one would draw based on whether you computed correlations or d. Because of the skew, a d value of .71 (generally considered a "large" effect) translated into an r value of .15. A d value of .31 (medium-sized) transformed to an r value of .07. The discussion that followed focused on which is the "better" effect size for understanding the usefulness of these predictors. Some of the key points raised: 1. r is more useful here for several reasons: a. It is generally applicable to both the dichotomous and quantitative criteria. b. The concept of "proportion of overlapping variance" has more general usefulness than "mean difference as a proportion of standard deviation." c. The results of the correlational analyses were more consistent with the results of significance tests, that is, even with large samples (N 1000), many of the expected relationships proved to be nonsignificant. 2. d is more useful precisely because it is relatively resistant to the impact of skew, unless group SDs are markedly different. 3. A third, less important issue, was raised in response to point 2. If effect size measures that are resistant to skew are more desirable, is there one that could be applied to both dichotomous and quantitative criteria? If not, which would be the "better" effect size measure for dichotomous criteria: a. the tetrachoric r: one person recommended this on the grounds that it is conceptually similar to the Pearson r and therefore more familiar to researchers. b. the odds ratio: recommended because it does not require the distributional assumptions of the tetrachoric r. The key issue on which I'd like your input, although please feel free to comment on any aspect, is this. Given there is real-world skew in the occurrence of positives, does r or d present a more accurate picture? Should we think of these as small or medium-to-large effect sizes? - Robert McGrath, Ph.D. School of Psychology T110A Fairleigh Dickinson University, Teaneck NJ 07666 voice: 201-692-2445 fax: 201-692-2304 === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: Data Mining
( how did we get to HERE, from Data Mining?) On 15 Apr 2000 17:50:05 GMT, [EMAIL PROTECTED] (Radford Neal) wrote: In article [EMAIL PROTECTED], Rich Ulrich [EMAIL PROTECTED] wrote: One thing that remains true about stock investment schemes: There may be some overall growth, somewhere, but in a specific, narrow perspective, the whole market makes up a zero-sum game. If someone wins, someone else has to lose. The above is internally contradictory, but the final statement is clearly false. Hey, the final statement is a DEFINITION of zero-sum game. Where is YOUR mind wandering to? I have no objection to wise investments, and that is why I specified tried to specify a different context, that is, "schemes." - Sorry that I Of course, short-term "day trading" is largely a zero-sum game, as the return to be expected over such a short time period is very small. - much of it only becomes zero-sum, when the time period is LONG. There are fortunes made on a soaring market. - actually, I expect there are a few Wise Guys who will extract most of the profit, so techno-stocks will be negative-sum for most investors. There is a LONG history like that: In the 1830s and 1840s investors poured money into building canals in the U.S. and England. The countries benefitted from canals; a few manipulators got rich; most of the companies went broke and most of the investors lost money. Railroads followed the same pattern in the second half of that century. In the 1910s, the "wireless telegraph" had the investors flocking -- the U.S. government got involved in prosecuting traders for fraudulent offerings. But I don't know if that was as big as Railroads, in terms of dollars. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: hyp testing -Reply
At 10:32 AM 4/17/00 -0300, Robert Dawson wrote: There's a chapter in J. Utts' mostly wonderful but flawed low-math intro text "Seeing Through Statistics", in which she does much the same. She presents a case study based on some of her own work in which she looked at the question of gender discrimination in pay at her own university, and fails to reject the null hypothesis [no systemic difference in pay between male and female faculty]. She heads the example "Important, but not significant, differences in salaries"; comments (_perhaps_ technically correctly but misleadingly) that "a statistically naive reader could conclude that there is no problem" and in closing states: the flaw here is that ... she has population data i presume ... or about as close as one can come to it ... within the institution ... via the budget or comptroller's office ... THE salary data are known ... so, whatever differences are found ... DEMS are it! the notion of statistical significance in this case seems IRRELEVANT ... the real issue is ... given that there are a variety of factors that might account for such differences (numbers in ranks, time in ranks, etc. etc.) is the remaining difference (if there is one) IMPORTANT TO DEAL WITH ... === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: hyp testing
On 15 Apr 2000, Donald F. Burrill wrote: (2) My second objection is that if the positive-discrete probability is retained for the value "0" (or whatever value the former "no" is held to represent), the distribution of the observed quantity cannot be one of the standard distributions. (In particular, it is not normal.) One then has no basis for asserting the probability of error in rejecting the null hypothesis (at least, not by invoking the standard distributions, as computers do, or the standard tables, as humans do when they aren't relying on computers). Presumably one could derive the sampling distribution in enough detail to handle simple problems, but that still looks like a lot more work than one can imagine most investigators -- psychologists, say -- cheerfully undertaking. This would not be a problem if the alternative was one-tailed, would it? Sorry, Bruce, I do not see your point. How does 1-tailed vs. 2-tailed make a difference in whatever the underlying probability distribution is? Donald, It was clear at the time, but now I'm not sure if I can see my point either! I think what I was driving at was the idea that a point null hypothesis is often false a priori. But if you have a one-tailed alternative, then you don't have a point null, because the null encompasses a whole range of values. For example, if your alternative is that a treatment improves performance, then the null states that performance remains the same or worsens as a result of the treatment. It seems that this kind of null hypothesis certainly can be true. And I think it is perfectly legitimate to use the appropriate continuous distribution (e.g., t-distribution) in carrying out a test. Or am I missing something? Cheers, Bruce === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: hyp testing -Reply
- Original Message - From: dennis roberts At 10:32 AM 4/17/00 -0300, Robert Dawson wrote: There's a chapter in J. Utts' mostly wonderful but flawed low-math intro text "Seeing Through Statistics", in which she does much the same. She presents a case study based on some of her own work in which she looked at the question of gender discrimination in pay at her own university, and fails to reject the null hypothesis [no systemic difference in pay between male and female faculty]. She heads the example "Important, but not significant, differences in salaries"; comments (_perhaps_ technically correctly but misleadingly) that "a statistically naive reader could conclude that there is no problem" and in closing states: and Dennis Roberts replied: the flaw here is that ... she has population data i presume ... or about as close as one can come to it ... within the institution ... via the budget or comptroller's office ... THE salary data are known ... so, whatever differences are found ... DEMS are it! the notion of statistical significance in this case seems IRRELEVANT ... the real issue is ... given that there are a variety of factors that might account for such differences (numbers in ranks, time in ranks, etc. etc.) is the remaining difference (if there is one) IMPORTANT TO DEAL WITH ... If one can totally explain all contributing factors, so that a model with significantly fewer parameters than there are faculty fits everybody to within a practically significant margin of error, then yes, either the model continues to work with gender removed or it doesn't. If, on the other hand, there are unknown sources of variation (a reasonable assumption in any situation involving people), or more sources of variation than there are data (another good bet if one thought hard enough), one cannot automatically go from the observation (*) "The average pay of female faculty members here is less than that of male faculty members" to the apparently desired conclusion (**) "There is a gender-based _pattern_ of discrimination in faculty salaries" without considering the study as a pseudo-experiment, and analyzing it as such. One would be trying to decide: is the difference between mean male and female faculty salaries greater than one would expect if one took N1 males and N2 females and assigned factors such as experience, rank, skill/luck at negotiating a first contract, demand for specialties, merit pay actually deserved [as opposed to given on a gender basis], etc. at random? This is what Utts and her coauthors were, it seems, trying to do. However, when the tests were not significant at the chosen level they seem to have fallen back on inferring (**) directly from (*). -Robert Dawson === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: cluster analysis in one-dimensional circular space
Since clustering methods begin with pairwise distances among observations, why not measure these distances as minimum arc-lengths along the best-fitting circle (or min chord lengths, or min angular deviations with respect to the centroid, etc)? This is how geographic distances are measured (in 2 dimensions, rather than one) and clustered, and also how distances are measured among observations in Kendall's shape spaces (e.g., Procrustes distances), so there's a well established literature. Rich Strauss At 05:32 PM 4/14/00 +0200, you wrote: Hi everybody. I face the problem of clustering one-dimensional data that can range in a circular way. Does anybody knows the best way to solve this problem with no aid of an additional variable ? Using a well-suitable trigonometric transform ? Using an ad-hoc metric ? Thanks. Carl === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ === Dr Richard E Strauss Biological Sciences Texas Tech University Lubbock TX 79409-3131 Email: [EMAIL PROTECTED] Phone: 806-742-2719 Fax: 806-742-2963 === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: hyp testing -Reply
Response embedded within message: In article [EMAIL PROTECTED], [EMAIL PROTECTED] wrote: The way this world is --- A master's candidate, or a phD candidate, or a professor, or a working scientist, has put a lot into his project. In terms of time, in terms of money, and more important still, in terms of emotional commitment, (S)he has lived with this project for two years or more. That is a source of subjective bias: (S)he WANTS the data to show something, preferably to support the original idea behind the research, but even failing that, to show something. There needs be an objective brake on this wish. An hypothesis test is that a brake. NOT rejecting the null hypothesis means that the data has no information (about whatever aspect of the data the test was designed to look at), STOP THERE; go no further. I hope not to get too off topic here, but sometimes the failure to reject the null hypothesis has more implications than successfully rejecting it. I understand your point here, and certainly have seen it happen both personally and in the literature. However, as long as the experiment has a sufficient sample size to detect a meaningful effect (not necessarily just a null of an effect size of zero), then there is something to say. For example, the literature has been overflowing with reports of "estrogenic compounds" such as DDT/DDE that affect sexual development of exposed animals. If someone found that DDE has little ability to competitively bind to estrogen receptors (which someone has found), at least to an extent necessary to elicit strong estrogenic activity, this would not only mean that the null hypothesis that DDE is estrogenic was rejected, but that something ELSE must be happening; ie. that the known alterations to sexual development after exposure to DDE is not due to estrogenic actvity. I am sure that this sort of thing must be happening in other fields. Without some objective brake, the master's student, etc. will go ahead to say something about the data, even when the test would have told her(im) there is nothing to say. Failure to reject null hypotheses that have been "successfully rejected" in numerous previous experiments, and thus are generally accepted by the scientific community at large, can have big implications, even if the alternative explanations were not tested and thus remain unknown. It may not happen often, but failure to reject a null hypothesis, particularly one that was expected to be rejected, may indicate a poorly executed study, but it may signal that the underlying theory from which the experiment is based upon is wrong. That alone is valuable. Shane de Solla [EMAIL PROTECTED] snip Sent via Deja.com http://www.deja.com/ Before you buy. === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: hyp testing -Reply
At 08:07 PM 4/17/00 +, Charles D Madewell wrote: As a working engineer and part time graduate student I do not even understand why anyone would want to do away with hypothesis testing. I have spent many, many hours of my graduate school life learning, reading, calculating, and analyzing using hypothesis tests. Hypothesis testing is not bad. It is errors in designing the experiment that are bad and this comes from PEOPLE not the math. What is the fuss? Are you guys telling me that all of this knowledge I am being taught will be worthless? Come on, find something else to say some of us find it very difficult ... given how we learned/or were taught a subject matter ... AND how we have been practicing it for dozens and dozens of years ... to come to the realization that perhaps ... what we have been taught ... and what we have practiced ... is disproportional to its benefit and utility ... if we take all the courses that teach (particularly at the more introductory levels) statistical material ... and try to establish some percent of that that deals with hypothesis testing and related matters ... VERSUS time spent on other things ... and then ask: is all that time worth the investment of energy? i think the answer is clearly no ... but, we are so slow to change ... if we change at all ... i grew up like that ... and have spent all these years teaching that (have to fill those students with sufficient statistical info) ... but, the reality is: hypothesis testing the way we do it ... has limited utility ... and is overblown to the nth degree now, that does not mean it is not important ... it is ... just not nearly as important as our expenditure of time suggests ... for us AND for students sure, design is much more important than inferential statistics but we have to share some of the blame ... when we push it so ... and as the ONLY way to go about things ... this is not only using our time unwisely ... but also doing a disservice to students ... === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Finding statistical significance between 2 groups with categorical variables
We have 2 groups reporting on the major problem for attending college. We are trying to see if the different response numbers are statistically significant. For example one group responded with an answer 13 times and the other group 32 times. Since a chi square takes the mean of the two, it doesn't show how to compare one to the other. We have no expected mean since these are opinions. Do we have to assume that equal %s of people will choose each category, even though we categorized them after reading the answers on the surveys? Thank you for your time. einstein * Sent from AltaVista http://www.altavista.com Where you can also find related Web Pages, Images, Audios, Videos, News, and Shopping. Smart is Beautiful === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: split half reliability
At 04:26 PM 4/17/00 -0500, Paul R Swank wrote: I disagree with the statement that the split-half reliability coefficient is of no use anymore. Coefficient alpha, while being an excellent estimator of reliability, does have one rather stringent requirement. The items must be homogeneous. i don't ever seem to recall the coefficient alpha .. REQUIRES homogeneous content ... but rather, the SIZE of it will be impacted BY item homogeneity === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: hyp testing -Reply
Hi, Robert and all -- Yes, there occasionally were discussions in our Air Force research whether or not we were working with the POPULATION or a SAMPLE. As Dennis comments: | | the flaw here is that ... she has population data i presume ... or about | as | close as one can come to it ... within the institution ... via the budget | or comptroller's office ... THE salary data are known ... so, whatever | differences are found ... DEMS are it! | One of my Professors used to use the Invertebrate Paleontologists as his example of a POPULATION. I think at that time there were less than 20 people who were Invertebrate Paleontologists. -- Joe * Joe Ward Health Careers High School * * 167 East Arrowhead Dr 4646 Hamilton Wolfe* * San Antonio, TX 78228-2402San Antonio, TX 78229 * * Phone: 210-433-6575 Phone: 210-617-5400* * Fax: 210-433-2828 Fax: 210-617-5423 * * [EMAIL PROTECTED]* * http://www.ijoa.org/joeward/wardindex.html * - Original Message - From: Robert Dawson [EMAIL PROTECTED] To: dennis roberts [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Monday, April 17, 2000 9:54 AM Subject: Re: hyp testing -Reply | | - Original Message - | From: dennis roberts | At 10:32 AM 4/17/00 -0300, Robert Dawson wrote: | | There's a chapter in J. Utts' mostly wonderful but flawed low-math | intro | text "Seeing Through Statistics", in which she does much the same. She | presents a case study based on some of her own work in which she looked | at | the question of gender discrimination in pay at her own university, and | fails to reject the null hypothesis [no systemic difference in pay | between | male and female faculty]. She heads the example "Important, but not | significant, differences in salaries"; comments (_perhaps_ technically | correctly but misleadingly) that "a statistically naive reader could | conclude that there is no problem" and in closing states: | | and Dennis Roberts replied: | | the flaw here is that ... she has population data i presume ... or about | as | close as one can come to it ... within the institution ... via the budget | or comptroller's office ... THE salary data are known ... so, whatever | differences are found ... DEMS are it! | | the notion of statistical significance in this case seems IRRELEVANT ... | the real issue is ... given that there are a variety of factors that might | account for such differences (numbers in ranks, time in ranks, etc. etc.) | is the remaining difference (if there is one) IMPORTANT TO DEAL WITH | ... | | | If one can totally explain all contributing factors, so that a model | with significantly fewer parameters than there are faculty fits everybody to | within a practically significant margin of error, then yes, either the model | continues to work with gender removed or it doesn't. | | If, on the other hand, there are unknown sources of variation (a | reasonable assumption in any situation involving people), or more sources of | variation than there are data (another good bet if one thought hard enough), | one cannot automatically go from the observation | | (*) "The average pay of female faculty members here is less than that of | male faculty members" | | to the apparently desired conclusion | | (**) "There is a gender-based _pattern_ of discrimination in faculty | salaries" | | without considering the study as a pseudo-experiment, and analyzing it as | such. One would be trying to decide: is the difference between mean male | and female faculty salaries greater than one would expect if one took N1 | males and N2 females and assigned factors such as experience, rank, | skill/luck at negotiating a first contract, demand for specialties, merit | pay actually deserved [as opposed to given on a gender basis], etc. at | random? | | This is what Utts and her coauthors were, it seems, trying to do. | However, when the tests were not significant at the chosen level they seem | to have fallen back on inferring (**) directly from (*). | | -Robert Dawson | | | | === | This list is open to everyone. Occasionally, less thoughtful | people send inappropriate messages. Please DO NOT COMPLAIN TO | THE POSTMASTER about these messages because the postmaster has no | way of controlling them, and excessive complaints will result in | termination of the list. | | For information about this list, including information about the | problem of inappropriate messages and information about how to | unsubscribe, please see the web page
Re: split half reliability
Paul R Swank wrote: I disagree with the statement that the split-half reliability coefficient is of no use anymore. Coefficient alpha, while being an excellent estimator of reliability, does have one rather stringent requirement. The items must be homogeneous. This is not always the case with many kinds of scales, nor should it be. In many cases homogeneity of item content may lead to reduced validity if the consruct is too narrowly defined. Screening measures often have this problem. They need to be short but they also need to be broad in scope. Internal consistency for such scales would suffer but a split half procedure, which is much less sensitive to item homogeneity, would fit the bill nicely. I have four responses to this: 1. Split-half requires the items to be divided into two "equal" halves. How is this to be done? Odd/even? First half/second half? Randomly? Cronbach's alpha does not depend on this arbitrary division into halves. 2. Stanley and Hopkins (1972) demonstrated that Cronbach's alpha was essentially equivalent to the "mean of all possible split-half reliability estimates". DeVellis (1991) demonmstrates that if the items in a scale have similar variances (a condition frequently met in well-designed scales), it can be shown that the value of alpha (called standardised alpha) is algebraically equivalent to the Spearman-Brown formula for estimating split-half. In other words, there is no great difference conceptually between the two. 3. Many writers use the term 'homogeneity' to bolster arguments in discussions of reliability and validity. In a paper I have completed recently which is currently under review for publication, I show that the term has about six different meanings in the literature. Whenever I read the word now, I respond, What exactly does the writer mean by homogeneity here? 4. If, by homogeneity, you mean all the items are measuring a similar construct, i.e. the item scores all inter-correlate with each other because they are indicators of a unidimensional construct, then the assertion that Cronbach's alpha depends on being this being the case is demonstrably untrue. Cronbach's alpha will be high as long as every item in a scale correlates well with at least some other items, but not necessarily all of them. Homogeneity is not a "stringent requirement" for a high Cronbach alpha level at all. Cronbach's alpha is simply a measure of reliability; it is not an indicator of unidimensionality, a point widely misunderstood in the literature. Paul Gardner begin:vcard n:Gardner;Dr Paul tel;cell:0412 275 623 tel;fax:Int + 61 3 9905 2779 (Faculty office) tel;home:Int + 61 3 9578 4724 tel;work:Int + 61 3 9905 2854 x-mozilla-html:FALSE adr:;; version:2.1 email;internet:[EMAIL PROTECTED] x-mozilla-cpt:;-29488 fn:Dr Paul Gardner, Reader in Education and Director, Research Degrees, Faculty of Education, Monash University, Vic. Australia 3800 end:vcard
