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*VV0VccV2Under penalty of perjury, I Elliot M. Cramer do hereby declare:
I am Elliot M. Cramer. I am Professor Emeritus in the L. L. Thurstone Psychometric Laboratory of the Department of Psychology at the University of North Carolina at Chapel Hill. I am an applied statistician and quantitative psychologist and am a Fellow of the Association for Psychological Science. I was previously a Fellow of the Division on Evaluation, Measurement, and Statistics of the American Psychological Association. I am also a member of the American Statistical Association.
My background
I received a B.S. degree in mathematics from the Massachusetts Institute of Technology and went on to receive an M.A. degree in Experimental Psychology at the Johns Hopkins University. I then spent two years as a mathematician at the Biometrics Branch of the National Institutes of Health, serving as their first scientific computer programmer. I worked with virtually every statistician there and, as a result, decided on a change of specialization. I returned to Johns Hopkins for a year as an NIH fellow, receiving a PhD in Experimental Psychology but immediately began a career in Applied Statistics. I was a Professor in the Psychology Department of the University of North Carolina for 29 years where I taught and did research, primarily in applied statistics. I have taken many advanced training courses in Statistics and was a visiting scholar for a semester at the Stanford University Department of Statistics. I have published in major statistical journals including Biometrics, Journal of the American Statistical Association, Technometrics, The American Statistician, and Psychometrika.
I have been a consultant in statistical methods to many organizations and individuals involving psychological and other applications. I have been a legal consultant and have been qualified as an expert in statistics and psychology in a number of cases, testifying for both plaintiff and defendant. I have testified in three sexually violent predator civil commitment trials and expect to testify in at least two more this year. I am a manuscript reviewer for the journal Sexual Abuse.
At the University of North Carolina I taught a required graduate course in advanced statistical methods as well as courses for those specializing in quantitative methods. In the course of teaching hundreds of clinical psychology PhD students, it has been my experience that among psychology graduate students, clinical students have the least interest in statistical methods, being more oriented towards clinical practice rather than research. Their typical training consists of one or two courses in statistics.
R. K Hanson and the STATIC99
I am very familiar with the STATIC99 scale developed by R. Karl Hanson and have relied on his work in my court testimony. In his 1999 paper, STATIC 99: Improving Actuarial Risk Assessments for Sex Offenders, he "compared the predictive accuracy of three sex offender risk assessment measures", noting that the "STATIC99 showed moderate predictive accuracy for both sexual recidivism" and violent recidivism with a correlation of .33. This correlation is moderate at most, accounting for only about 10% of the variation in sexual recidivism. It is comparable to the predictive validity of the SAT in predicting first year college scores. This suggests that the STATIC99 would be useful as a screening device but not as a selection device.
My first reaction to the STATIC99 scale was that it was quite crude, with most of the items such as age being dichotomous. I was very interested to see Hanson's later 2006 paper, "Does STATIC99 Predict Recidivism Among Older Sexual Offenders?" which I first read under the earlier more appropriate title "The Validity of STATIC99 with Older Sexual Offenders." In this paper he looked at a sample of 3,425 sexual offenders, three times as many as his original 1999 paper where he had only 1301 cases. Obviously this later paper is substantially more reliable than the earlier paper. Hanson stated "Recent research has suggested that its (STATIC99) methods of accounting for the offenders' ages may be insufficient to capture declines in recidivism risk associated with advanced age. ... Older offenders, however, had lower sexual recidivism rates than would be expected based on their STATIC99 risk categories. Consequently, evaluators using STATIC99 should consider advanced age in their overall estimate of risk." I do not see how anyone could disagree with this conclusion. His colleague and coauthor, David Thornton, recently said "It is generally accepted that on average, recidivism rates decline with age. This effect isn't fully allowed for by Static99. Hanson (2006) demonstrates this in a large multisample analysis."
In addition to providing estimated recidivism rates, the 2006 paper gave confidence intervals, providing a margin of error for these rates, similar to what is stated in election polling. Clearly this is the definitive paper on the STATIC99. I was puzzled by Hanson's statements in his paper that "Evaluators using STATIC99 should consider advanced age as one factor in their overall estimate of risk. How best to consider age remains unresolved by the current study. ... the stability of these estimates are unknown until they have been replicated in independent samples." Evidently Hanson does not realize that the purpose of the confidence intervals which he has provided (evidently for the first time in his work on the STATIC99) IS to provide evidence of stability. In his Declaration, Dr. Wollert states that he was told by Hanson that "he did not think the confidence interval approach was very helpful for SVP statutes." Evidently these confidence intervals were computed by someone else with more expertise.
It is obvious to me (as it would be to any statistician) "how best to consider age." One should "consider age" by using the tables that Hanson has provided in his 2006 paper. The tables in the original STATIC99 paper are obsolete because they are based on a much smaller sample and because they do not take age into account. My opinion has been reinforced by Richard Wollert's replication using independent data and Bayesian methods; he has obtained virtually the same results as Hanson.
I think that Hanson's work in developing and validating the STATIC99 is excellent, but I am appalled by his recent criticisms of the work of Dr. Richard Wollert. Hanson is a clinical psychologist and my understanding is that his graduate student interests were in psychotherapy and psychopathology. Reviewing his resume, it is apparent that he has been quite prolific but he has never published in the statistical literature nor is there evidence that he has expertise in statistics. His criticism are all the more surprising since Wollert's paper confirms the results given by Hanson in his 2006 paper on the effects of age on recidivism. Contrary to Hanson's statements, Wollert's work is very sound from a statistical point of view. I see no evidence that Hanson has the statistical competence to criticize Wollert's work. This is confirmed by Hanson's statistical errors in his declaration to the Court.
Dr. Hansons criticisms of Dr. Richard Wollert
I first learned of Dr. Richard Wollert's work when I was doing research for my first commitment trial. I was impressed by his evident statistical sophistication and I have kept in contact with him during the past year. He has a remarkable knowledge of statistical methods for a clinical psychologist as demonstrated in his publications. He has considerable statistical facility which is particularly reflected in his use of Bayesian methods. I have found his papers interesting and instructive, but they have served primarily to reinforce my views of the limited predictability of the STATIC99 and the importance of taking age into account in making evaluations. This view was derived from Hanson's own work. For someone age 4050 scoring in the high range on the STATIC99, Hanson's results show that about 25% of those convicted will recidivate in five years. In other words, three individuals will be misidentified for every one that is correctly identified. For someone in the moderately high group this ratio becomes six to one.
Hanson's naivete with regard to statistics is illustrated by the 2007 metaanalysis paper he cites. Hanson's 1999 paper on the STATIC99 states that the STATIC99 has only "moderate predictive accuracy" as evidenced by a correlation of .33 with sexual recidivism. Similarly, the STATIC99 coding manual (2003) states that "The weaknesses of the STATIC99 are that it demonstrates only moderate predictive accuracy". In the more recent metaanalysis paper, Hanson now claims that "it is possible to conduct psychologically informed risk assessments ... of high predictive accuracy". This contradiction between what he said before (and has repeated) and what he says now is explained by his lack of expertise in statistics resulting in errors and misleading statements. In his metaanalysis paper, Hanson writes "The d statistic was selected because it is less influenced by recidivism base rates than correlation coefficients  the other statistic commonly used in metaanalyses." As Wollert and others have pointed out, the reason it is so difficult to predict recidivism is BECAUSE of the low base rate. You cannot get around this by using a statistic that is insensitive to base rates. The "d statistic" Hanson uses is inappropriate since one cannot control the base rate. Hanson's more recent conclusion is wrong; it is NOT possible to conduct risk assessments "of high predictive accuracy".
Specific comments on R. Karl Hanson's Declaration
5. "Dr. Wollert's testimony contains some ... statements that are demonstrably false. These false statements include both misrepresentations of facts as well as misrepresentations of statistics and research methods"
I know of no such statements in Dr. Wollert's work. I find Hanson's claim outrageous and slanderous. I do not believe, in view of Hanson's limited expertise, that he is qualified to make such a judgment.
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6. "Dr. Wollert's most serious error is that the method he proposed to mathematically adjust actuarial risk prediction ... is incorrect. ... Such adjustments only make sense when age is unrelated to Static99 scores. ... The adjustments made by Dr. Wollert in this case have the effect of underestimating recidivism rates."
This is absolutely false; there is no such assumption and Dr. Wollert produces almost exactly the same age adjusted estimates that Hanson produced in his 2006 paper. In Hanson's own paper he says that "evaluators using STATIC99 should consider advanced age in their overall estimate of risk."
________________________________________________________________
7. "The available research has demonstrated that age is related to Static99 scores. ... It indicates that the older offenders were different from the younger offenders even when they were younger."
This is absurd; it is impossible to say what older offenders were like "when they were younger" except to say that they were younger. The very small differences Hanson observes in Static99 scores may not even be statistically significant. The average score he reports for the 1824.9 group is biased because he adds 1 to their Static99 score for being under 25. When using his new tables, 1 should not be added for being under 25.
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8. "Dr. Wollert, based on data I present, uses age to estimate new (lower) recidivism rates for older sexual offenders. ... Dr. Wollert's method ... uses Bayes' theorem. ... This theorem is false when the variables used to adjust the recidivism base rates are correlated with scores on the assessment measure."
Hanson stated on page 2 of his declaration that Bayes theorem is true "by definition". Bayes theorem is true because it is simply a relation between probabilities. There is no assumption that "age is unrelated to Static99 scores". Were this so, there would be nothing to adjust. The adjustment depends on there being such a correlation. The point is to show just how Static99 scores are related to age. This is what BOTH Hanson and Wollert have done in their papers.
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9. "Dr. Wollert's method of adjusting the actuarial scores produce numbers without any substantive meaning, and artificially reduces the recidivism rate for older offenders. In Appendix A, attached, I demonstrate how Bayes' theorem can be used to produce a completely false recidivism rate"
In fact, Dr. Wollert's produces numbers that are very close to the numbers in Hanson's tables. He has offered independent evidence of the validity of Hanson's own ageadjusted tables. If Hanson's statement here is correct, he is criticizing his own work. Hanson has blundered in Appendix A, reinforcing the suggestion that he lacks statistical competence.
Hanson has stated that Bayes' theorem is true "by definition". This is obvious since it is simply a relationship between conditional and unconditional probabilities in a bivariate table. The theorem is also true for estimated probabilities when these estimated probabilities are obtained from a bivariate frequency tables such as found in Appendix Six of Hanson's original Static99 paper. Hanson has provided an example of it's validity in the first part of his Appendix A. Obviously the validity of his computations does not depend on the special nature of the bivariate table; the computations must be valid for ANY bivariate frequency table.
In Static99 Appendix six, the five year recidivism rate for a score of 6+ is .39. This is exactly what Prob(recid6+) means, the probability of being a recidivist, given that one obtains a score of 6+. The Bayes computation must yield this result for ANY bivariate table that includes this as an entry. Hanson's first computation used the whole table and obtained the correct value of .39. His second computation used a "subsample", dropping off the first four rows corresponding to Static99 scores of 0, 1, 2, and 3; this gave Hanson a new restricted frequency table to base his computations on. Any new computations for Bayes Theorem must be based on THIS table and use no other information. Hanson's computation for the second table gave an incorrect value of .49 instead of .39 and Hanson claimed that this "demonstrates how Bayes' theorem can produce meaningless numbers". What it actually shows is that Hanson has made a computational error and the only problem is to find the error.
Dr. Wollert discovered that Hanson made two errors; first, he added the sample sizes 190, 100, and 129 in column two of Hanson's Appendix Six and obtained 519 instead of 419. Secondly, he mistakenly used numbers from outside the restricted table.
Hanson wrote
Prob(recid6=) = (.256)(.254) / [(.256)(.254) + (.089)(.746)] = .49
Hanson did not say where the numbers .256 and .089 came from, but they could only have come from the equations
P(6+recid) = 50/195 = .256
and
P(6+nonrecid) = 79/891 = .089
in his first computation where 891+195 = 1086, the sample size of the full table, rather than the restricted table which MUST be used for the second computation. Curiously, Hanson seems to recognize that he has used the wrong numbers when he says Such distortions are only observed when the overall sensitivity and specificity are used. In other words the results are correct if the proper values of P(6+recid) and P(6+nonrecid) are used. He then goes on to say To use Bayes theorem, it is necessary to establish that the factors used to change the base rate are either unrelated to the relative recidivism risk of individuals, or are uncorrelated with the actuarial measure. Evidently he believes that either is sufficient but he has nowhere demonstrated that either is a requirement. All he has shown is that if you make a computational error and use the wrong values of P(6+recid) and P(6+nonrecid), you get incorrect results.
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10. "Dr. Wollert states that 'Wollert recently duplicated Hanson's results ... with an independent sample of 3,106 subjects. ... the correlation between Hanson's and Wollert's results is .97, which shows the results of these studies closely parallel one another.' Dr. Wollert is suggesting that he has either crossvalidated research presented in my 2006 article."
This is PRECISELY what Dr. Wollert has done. I find it incredible that Hanson does not realize that Dr. Wollert is supporting what Hanson himself has done.
________________________________________________________________
11. "I noted that 'although it is possible to compute numeric estimates of the combined effect of Static99 and advanced age, ... the stability of these estimates will be unknown until they have been replicated in independent samples.' ... more troubling is that he appears to be relying on my research to suggest that I agree with his analysis, when in fact I disagree with it."
Hanson does not seem to understand that the confidence intervals reported in HIS paper DO provide information on the stability of HIS estimates. The obvious conclusion of Dr. Wollert's paper is that he agrees with Hanson's results since, using independent data and another method of analysis, he arrives at almost identical results. Hanson may disagree with the method of analysis (although he is not competent to do so) but he CANNOT disagree with the results since they are virtually the same as his own.
________________________________________________________________
12. "The effect of age on sexual recidivism risk has not been resolved in the scientific community."
I believe that there is almost universal consensus (including Hanson's own statement below) that recidivism goes down with age. His colleague and coauthor recently said as much as noted above.
________________________________________________________________
13. "Even if advanced age has some relationship to reduced recidivism (a position I believe to be true), it is merely one factor among many that could influence recidivism risk beyond that measured by Static99."
Obviously, as Hanson himself has stated, it should be taken into account and the obvious way is to use Hanson's new tables which are based on three times the sample size of his old tables.
________________________________________________________________
14. "In summary, I believe that it is the role of evaluators to estimate recidivism rates based on the average recidivism rates for members of the class that the offender most closely resembles. ... For purposes of Static99, those estimates should be determined by reference to Appendix Six in the Static99 scoring manual."
This view is obviously incorrect for reasons I have stated above.
I have written Dr. Hanson four times, requesting data from his paper , Does STATIC99 Predict Recidivism Among Older Sexual Offenders?. He has declined twice, saying that I do not see how the requested information would advance our understanding. and You have not convinced me of the merits of your request.. After two days, I have not yet received a reply to my third request. I believe that my request is reasonable and well justified. The correspondence is attached.
Conclusions:
Hanson has unjustifiably criticized Dr. Wollert's work on statistical grounds when Hanson has substantially less statistical competence than Dr. Wollert. In particular, the paper that Hanson severely criticizes produces results that are consistent with Hanson's own published work, but from a Bayesian perspective. Hanson produces an example which he claims shows that "Bayes' theorem can produce meaningless results". Because of an addition error and a conceptual error, he obtains the wrong answer. When properly done, both of his examples support what Dr. Wollert has done. Hanson says "The estimate of the recidivism rates should be those observed in actual recidivism studies, and not those generated by arithmetic manipulations based on incorrect assumptions." Both Dr Wollert and I agree. Hanson further says "those estimates should be determined by reference to Appendix Six in the Static99 scoring manual." Dr. Wollert and I believe that these estimates should be based on Table 3 of Hanson's 2006 paper which is based on three times the sample size of the earlier tables and which takes age into account in a more proper manner than Hanson's original paper. A further point in favor of this is the fact that Dr. Wollert has replicated these estimates with an independent sample and a different valid methodology.
___________________________
Elliot M. Cramer
Chapel Hill, North Carolina
March 12, 2008
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