MEMO 124 3/14/97 RE: Respondent IQ data - updates and recommendations The purpose of this memo is to describe the work done on the IQ scores of WLS main respondents, the problems we encountered, and our recommendations for which measures of respondents' IQ are best. Section 1 describes the gathering of IQ data, Section 2 describes how we interpret this data, and Section 3 describes the new measures, and our recommendations for the best ones to use. Supporting Figures can be found in MEMO124.PRE. SECTION 1 In 1996/97, we had access to the records of the Wisconsin State Testing Service, in order to find the test scores of the siblings of the WLS respond- ents. As long as we had the records, we went ahead and looked up the scores for each of the ORIGINAL respondents as well, for tests taken in both the Junior year (Spring, 1956), and Freshman year (Fall, 1953). We had obtained the original Henmon-Nelson (1954) manual which contained the "Table for Determining I.Q.'s in Grades 7-12", and wanted to use the raw scores we found in the State Testing Service records to determine the actual IQ scores for the original respondents. We looked up scores for all respondents who had not had their scores looked up in 1983 (see COR XXX). In total, we looked for the scores of 8,964 original respondents. Of these 8,964 respondents, we found: * 7,357 Junior-year scores (82.1%) * 5,503 Freshman-year scores (61.4%) * 34 errors on Junior-year scores (out of approx. 6753 checked - .5%) * 4 errors on Freshman-year scores (out of approx. 248 checked - 1.6%) Combining this new data with that found in the 1983 lookup, we now have: * 9,508 Junior-year raw scores and Wisconsin centile ranks (809 missing) * 7,001 Freshman-year raw scores and Wisconsin centile ranks (3,316 missing) * 215 cases where both Junior-year and Freshman-year scores are missing. These raw Henmon-Nelson scores allow us to determine nationally-normed IQ scores for the original respondents for both the Freshman and Junior years. These IQ scores are determined by dividing the Mental Age corresponding to the raw score by the respondent's real age at the time the test was taken: Mental Age (in months) IQ = -------------------------------------- Chronological Age (in months) In the testing manual, Chronological Age is truncated at 16 years. SECTION 2 The distributions of the Henmon-Nelson raw scores for Freshman and Junior years are displayed in Figures 1 and 3; the distributions of the Henmon-Nelson IQ scores for Freshmen and Juniors are displayed in Figures 2 and 4. Because these scores are (except for a few missing scores) for the same people, measured at different points in time, we would expect the distributions to look the same for both Freshman and Junior years. We might not expect the distrib- utions to look exactly normal, as this sample consists entirely of high school graduates. It is clear from Figures 2 and 4, however, that something has changed drastically between the Freshman and Junior years. While the Freshman- year scores looks fairly close to normally distributed, the Junior IQ scores appear to be quite skewed to the left, and the standard deviation of the junior scores is much smaller than that for the freshman scores. In Figures 1 and 3, we see that the distributions of the raw scores are much more similar between the Freshman and Junior years than are the IQ scores. To uncover the source of the dissimilarity in IQ score distributions between the Freshman and Junior years, we concluded that it must be the translation from raw score to IQ score that is causing the skew. Despite the common graduation date, WLS respondents are not the same age; the youngest and oldest in this cohort are separated by about 2.5 years (see Figure 5). We wondered whether this age gap might be causing the skew in the Junior- year IQ distribution. In Figures 6 and 7, we can see that intelligence (as measured by the Henmon- Nelson test) is not equally distributed among those who graduated high school in 1957. In particular, those who were the oldest in this cohort (born October 1938 or before) had both lower raw scores and lower IQ scores in their Freshman year than those respondents whose age was "average" for their grade (born September 1938 - November 1939), and compared to those who were "young" for their grade (those born December 1939 or later). The oldest of the WLS respondents had a mean raw score around ten points lower than their classmates, and a mean IQ score around 17 points lower than their classmates. The young respondents, on the other hand, tended to score about the same (raw score) as their average-aged classmates, but because of their younger age, tended to receive higher IQ scores than their average classmates (recall that IQ scores is computed by dividing the mental age that corresponds to a given raw score by the age of the test-taker. If two people have the same raw score, the younger one will have a higher IQ score because the denominator will be smaller.) The norms for the Henmon-Nelson test do not change uniformly for people over time. Those who are younger at the first administration of the test have to earn more additional raw score points to keep their same IQ level than those who are older. Also, those who had a higher IQ score during the first administration of the test had to earn more points to keep their same IQ level than those who had a lower IQ level. This is illustrated in Figures 8 and 9. Note that in the Junior year, all but a handful of respondents were aged 16 and older. In the Freshman year, the "average-aged" respondents would have fallen into the age category "14 years, 3 months", while the "older" respondents would have been "15 years, 0 months" and the "younger" respondents might have been in the "13 years, 9 months" category. In Figure 8, the distance between the solid "16 years and above" line is (horizontally) the farthest to the dotted "13 years, 9 months" line, and closest to the "15 years, 0 months" line. For example, an "average-aged" respondent with an IQ of 120 his or her Freshman year would have had to earn 15 additional raw score points (73-58) to keep that IQ score in the Junior year, compared to 9 (73-64) for an "older" respondent, and 19 (73-54) for a "younger" one. Also note in Figure 8 that the distance between any of the Freshman-age lines (13 years and 9 months, 14 years and 3 months, and 15 years) and the Junior-age line decreases as the IQ score decreases. That is, the lower the IQ score in the Freshman year, the fewer additional raw score points needed in the Junior year to achieve that same score. Looking only at the "average-aged" respond- ents, a person with a Freshman-year IQ of 120 needs to gain 15 raw score points (73-58) by the Junior year to keep that same IQ, while a Freshman respondent with an IQ of 80 needs only to gain 13 points to keep that IQ. Thus, if two respondents gained the same number of raw score points between Freshman and Junior years, the respondent with the lower IQ score would gain the most IQ points (or lose fewer points) than the higher-IQ person. Figure 9 illustrates the same point. The solid line in this figure is set at the mean difference in H-N raw scores between Freshman and Junior years for the WLS sample. Note that not only is the dotted line corresponding to the "young" respondents almost always above the mean as opposed to the dashed line for the "old" respondents, the lines for the higher IQs (above 102) are similarly above this mean line (except for the "old" respondents), compared to the lines for the lower IQ scores. Finally, turning to Figures 10 and 11, we can see what happened to the distrib- ution of Junior-year IQs in our sample. As shown in Figure 10, most respond- ents, regardless of their age, gained around 11.5 points between their Freshman and Junior years. True, the "young" respondents tended to gain a little more than average, and the "old" gained fewer raw score points, but their distribut- ions overlap to a remarkable degree. In Figure 11 we see, however, that these similar raw score gains did not translate into similar IQ gains. The "old" tended to gain IQ points--more than 7 on average, while the "young" tended to loose IQ points between their Freshman and Junior years--around 4 points. Those in the "average" age group stayed about the same, as their mean gain in IQ points between Freshman and Junior years was only .30. We think that this combination of events explains the skewed distribution of Junior-year IQ scores. Those respondents who were "older" than their classmates tended to be concentrated in the lower end of the IQ distribution. When they re-took the Henmon-Nelson test in their Junior year, they gained around the same raw score points as their younger classmates, but this gain in raw score translated into a much large gain in IQ score for them, because (1) they are older, so fewer points were needed to keep the same IQ, and (2) they had lower IQ scores to start with, so again fewer points were needed to stay at the same level. This brought the low end of the IQ distribution "up". At the same time, those respondents who were "younger" tended to loose points, because (1)they had to gain more points just to stay at the same level, and (2) they needed more points to keep their originally higher IQs. This moved the upper end of the IQ distribution "down" a bit. Finally, the "average-aged" respond- ents stayed about the same. Thus, the distribution of Junior-year IQs has a smaller standard deviation than the Freshman one, with fewer respondents in the left tail. SECTION 3 Despite our understanding of how the distribution of IQ scores changed in the WLS sample from the Freshman to the Junior years, we have no real basis for deciding which score is the "best" measure of a respondent's mental ability. In a perfect world, we would like to have the nationally-normed centile rank for each H-N raw score by age. But, we have either a centile rank by grade level (normed on either a Wisconsin sample, or a national one), or an IQ score based on age, but which is constructed from the outdated notion of a mental age. Because we don't have the information we need to construct the best indicator of IQ, we need some criterion for deciding which of the measures we do have is the best. We have decided to look at how well the different measures of IQ correlate with various other variables. We ran several sets of regressions (OLS and logistic): * [IQ measure] = DadSES + DadEduc + MomEduc + Farm + Non-Intact+ FamIncome * High School Rank = [IQ measure] * Attends College = [IQ measure] * Graduates College = [IQ measure] There are 16 possible measures of IQ: * JUNIQ = Nationally-normed measure of IQ, test taken Junior year, age cutoff 16 * JUNRS = Raw Henmon-Nelson score, Junior year * New_JIQ = Nationally-normed measure if IQ, test taken Junior year, no age cutoff (calculated by hand, IQ=mental age/actual age) * JUNCR = Wisconsin centile rank of Junior year raw score * J_NCR = National centile rank of Junior year raw score (grade 11) * FRESHIQ = Nationally-normed measure of IQ, test taken Freshman year, IQ from table * FRESHRS = Raw Henmon-Nelson score, Freshman year * New_FIQ = Nationally-normed measure if IQ, test taken Freshman year, no age cutoff (calculated by hand, IQ=mental age/actual age) * FRESHCR = Wisconsin centile rank of Freshman year raw score * F_NCR = National centile rank of Freshman year raw score (grade 8 because test taken in Fall, not Spring) * IQHNQ = Wisconsin centile rank of H-N score, collected from original questionnaires or from 1983 lookup of scores * IQHNSCRQ = IQ scores constructed from Wisconsin centile rank norms (see CORXXX) * WAIS = Total items correct on WAIS test, administered in 1992/93 follow- up survey * BM1 = Best measure constructed by taking JUNIQ first, FRESHIQ second, and IQHNSCRQ third * BM2 = Best measure constructed by taking FRESHIQ first, JUNIQ second, and IQHNSCRQ third * BM3 = Best measure constructed by taking the average of JUNIQ and FRESHIQ first, JUNIQ second, FRESHIQ third, and IQHNSCRQ fourth Results, [IQ measure] = Social Background IQ Measure Adj R-Squared N JUNIQ .0814 8217 JUNRS .0833 8217 NEW-JIQ .0804 8217 JUNCR .0832 8217 J_NCR .0802 8217 FRESHIQ .0887 6108 FRESHRS .0918 6108 NEW_FIQ .0894 6108 FRESHCR .0859 6108 F_NCR .0816 6108 IQHNQ .0835 8904 IQHNSCRQ .0858 8904 WAIS .0397 7828 BM1 .0833 8904 BM2 .0863 8904 BM3 .0902 8904 Results, HSRank = [IQ measure] IQ Measure Adj R-Squared N JUNIQ .3532 8878 JUNRS .3561 8878 NEW-JIQ .3477 8878 JUNCR .3498 8878 J_NCR .3494 8878 FRESHIQ .3664 6587 FRESHRS .3648 6587 NEW_FIQ .3679 6587 FRESHCR .3623 6587 F_NCR .3574 6587 IQHNQ .3443 9624 IQHNSCRQ .3509 9624 WAIS .1253 7882 BM1 .3486 9624 BM2 .3463 9624 BM3 .3709 9624 Results, Attends College = [IQ measure] IQ Measure Z-Score, Coeff. N JUNIQ 34.773 8864 JUNRS 35.261 8864 NEW-JIQ 34.284 8864 JUNCR 36.208 8864 J_NCR 35.424 8864 FRESHIQ 29.026 6578 FRESHRS 28.980 6578 NEW_FIQ 29.016 6578 FRESHCR 29.288 6578 F_NCR 28.581 6578 IQHNQ 37.114 9612 IQHNSCRQ 36.326 9612 WAIS 30.470 8423 BM1 35.522 9612 BM2 34.843 9612 BM3 36.130 9612 Results, Graduates College = [IQ measure] IQ Measure Z-Score, Coeff. N JUNIQ 34.643 8864 JUNRS 35.104 8864 NEW-JIQ 33.980 8864 JUNCR 35.349 8864 J_NCR 34.045 8864 FRESHIQ 28.087 6578 FRESHRS 28.283 6578 NEW_FIQ 28.108 6578 FRESHCR 27.654 6578 F_NCR 26.696 6578 IQHNQ 36.379 9612 IQHNSCRQ 36.430 9612 WAIS 29.810 8423 BM1 35.465 9612 BM2 34.282 9612 BM3 35.745 9612