COR652 Construction of "new" IQ variables 2/2/98 I. New WLS IQ variables. In 1996/97, we looked up both freshman and junior test scores for 8964 respondents who did not have their scores looked up in 1983. During the search, we found: - 7357 junior scores (82.1%) - 5503 freshman scores (61.4%) - 34 errors on junior scores (out of approx. 6753 checked - .5%) - 4 errors on freshman scores (out of approx. 248 checked - 1.6%) Combined with junior and freshman scores found in the 1983 lookup, we have: - 9508 junior scores (809 missing) - 7001 freshman scores (3316 missing) - 215 cases where _both_ junior and freshman scores are missing. For all of these 215 cases, we have IQHNQ (centile rank from questionnaire or 1964 mailing to schools). In 1996/97, test scores were also located for the bulk of the WLS siblings. See COR621 and COR622 for details. II. Types of IQ data We had a number of ways we could express the mental ability of our respondents, both Graduates and Siblings. First, we have the Henmon-Nelson Raw Score (HNRS), which can be used as-is as long as the test-takers all took the test at the same age. Second, we can compare the HNRS among either Wisconsin test-takers using centile ranks (WICR), or among National test-takers using Centile Ranks (HNCR). The WICR values which correspond to each HNRS can be found in the State Testing Service records. The most commonly-used WICR values are the Freshman Wisconsin Centile Ranks and the Junior Wisconsin Centile Ranks, which are noted in COR332, Addendum II, dated 4/16/82. The HNCR values which correspond to each HNRS can be found in the Henmon-Nelson Testing Manual (revised 1954), Page 7. Finally, we have constructed IQ scores which correspond to a Centile Rank. This is based on the Normal Distribution--these values were calculated in COR336, Attachment VII. We computed this constructed IQ score for only the Wisconsin Centile Ranks (WICR), and thus this variable is labelled WIIQ. Also included in the Henmon-Nelson testing manual are "National IQ Scores". These scores are based on the outdated concept of "mental age", and per MEMO124 are discarded from further consideration. I have included the tables used to produce these "IQ" scores in COR652.EXE; however, these variables are NOT included in the final release of this new IQ data. III. The Problem: Expressing test scores from different ages in the metric of Junior-year, Wisconsin Henmon-Nelson scores. In Memo124, I have outlined the problem of comparing scores on the Henmon-Nelson test when the test was taken at different ages. In the WLS Graduate sample, we have the scores of XXXX Graduates who took the test in both their Freshman and Junior years of high school. Using the distributions of both sets of scores from these Graduates, we devised a way to express test scores taken at any grade level in the metric of the Junior-year Wisconsin Henmon-Nelson test score distribution. The first problem in converting test scores into the Junior-year metric is figuring out what age the test-taker was, and in which grade the test was taken. The difficulty of this task comes from two sources: (1)The season the test was taken is missing from the books in several cases; (2)we are missing date-of-birth data for several siblings. "Guesses" were made for season of test in many cases--flag variable STSEAFLG indicates whether a "best guess" was used. Season of test is important because Freshman tests were generally given in the Fall of 9th grade, while Junior tests were generally given in the Spring of 11th grade. In the Henmon-Nelson manual, distributions are always given as if the test was given in the SPRING of the grade-year. Thus, our "Freshman" test scores are really treated as 8th grade scores in the Henmon-Nelson manual, because we would rather compare 9th graders at the beginning of their school year to 8th graders at the end of their school year, rather than comparing the 9th graders at the beginning of their school year to national 9th graders at the end of their school year. The variable SGRADE contains these *Constructed* grades in which tests were taken; that is, if a Graduate or Sibling took the test in the fall of 9th grade, then SGRADE=8 (the Graduate's or Sibling's score is considered to be at grade 8). SGRADE is available to the public. The variables it is based upon--STGRADE, STSEASN, STSEAFLG--are not available to the public. Following is the distribution. stseasn - 1 = fall , 2=spring Cumulative Cumulative SGRADE STGRADE STSEASN Frequency Percent Frequency Percent --------------------------------------------------------------------- 7 7 1 2 0.02 2 0.02 7 7 2 1 0.01 3 0.03 7 8 1 2 0.02 5 0.05 8 8 2 9 0.09 14 0.14 8 9 1 745 7.22 759 7.36 8 9 9 1 0.01 760 7.37 9 9 2 93 0.90 853 8.27 9 10 1 171 1.66 1024 9.93 10 10 2 331 3.21 1355 13.13 10 11 1 495 4.80 1850 17.93 11 9 * 1 2 0.02 1852 17.95 11 11 2 4414 42.78 6266 60.73 11 11 9 5 0.05 6271 60.78 11 12 1 132 1.28 6403 62.06 11 99 9 1 0.01 6404 62.07 12 12 2 212 2.05 6616 64.13 12 12 9 3 0.03 6619 64.16 98 98 8 746 7.23 7365 71.39 99 99 9 2952 28.61 10317 100.00 * correction was made to sgrade and not to stgrade. The age at which the test was taken was important for two reasons. First, as outlined in MEMO124, we used age to construct the "IQ" score as published in the Henmon-Nelson manual. We found that these "IQ" scores were based on the outmoded notion of "mental age", and as such were not at all useful as IQ scores. We have not included them in the new IQ data. However, the ages used to collect these IQ scores were useful in determining whether the Sibling respondent we located in the Testing Service Books was indeed the Sibling Respondent we were looking for. If the Sibling Respondent was younger than 11 or older than 21, we assumed that we had the wrong sibling, and did not include this data. SAGEMO_F, SAGEMO_J and SAGEMO_S are the three constructed variables of the age of Graduate/Sibling at the time the test was given. They are not available on the public version of the data. Once the grade in which the test was taken has been determined (SGRADE), a conversion could be made from the Henmon-Nelson score from any grade level to the metric of Wisconsin Juniors in 1957. In this way (for example), a score from a sibling who took the test as a 10th grader in 1938 could be compared to his or her WLS Graduate sibling who took the test as a Junior in 1956. Most WLS Graduates and Siblings took Henmon-Nelson tests. The conversions below are based on raw scores, and other scales (National Centile Rank, Wisconsin Centile Rank, Constructed Wisconsin IQ Score) are then calculated from the transformed raw score. A few WLS Siblings took other tests (for example, IOWA tests). For these people, the Wisconsin Centile ranks were averaged for all of the tests we found; this Wisconsin Centile Rank was used to find the corresponding Henmon-Nelson score (using the National Centile Ranks, found in the Henmon- Nelson manual). To accomplish these mappings, the following files contain code which will convert a (1)centile rank (CR) to iq score (IQ), (2)a raw score (RS) to a centile rank (CR), (3)a raw score (RS) to a mental age (MA) score, or (4)a centile rank (CR) to a raw score (RS): CONVERT1.SAS Convert CR to normally-distributed IQ CONVERT2.SAS Convert RS to Wisc Junior 1952 CR CONVERT3.SAS Convert Wisc Junior 1952 CR to RS CNVERT3a.SAS Convert Wisc Freshman 1952 CR to RS CNVERT4a.SAS Convert RS to National Grade 7 CR CONVERT4.SAS Convert RS to National Grade 8 CR CONVERT5.SAS Convert RS to National Grade 9 CR CONVERT6.SAS Convert RS to National Grade 10 CR CONVERT7.SAS Convert RS to National Grade 11 CR CONVERT8.SAS Convert RS to National Grade 12 CR CONVERT9.SAS Convert National Grade 12 CR to RS CNVERT10.SAS Convert RS to National MA HN_NORM_54.TXT Convert RS to National IQ (age-appropriate, with age 16 cutoff) These ascii files (and more) are included in COR652.EXE. ******************************************************** ***7th Grade test score (Henmon-Nelson scores only) * ***Sibling data only * ******************************************************** * We did not have a sample of respondents for whom * * we had both 7th grade scores and 11th grade scores. * * Thus, we found the National test score distribution * * which most matched the Wisconsin 11th grade HN * * distribution. This turned out to be the National * * 12th grade distribution, adjusted for mean and st. * * deviation differences. So, to get the predicted * * junior year score, we find a Senior year score based* * on the National norms in the Henmon-Nelson manual, * * and adjust mean/st. dev. * ******************************************************** 1. Start with Henmon-Nelson Raw Score 2. Get the predicted national 7th grade centile rank from the 7th grade raw score (CONVERT4a); this centile rank is the National Centile Rank (HNCR) 3. Use HNCR national centile rank to convert to 12th grade raw score (CONVERT9) 4. Subtract 6. 5. Multiply by 1.100 6. Subtract 5.818 7. Round to nearest 100th 8. Use resulting Raw Score to produce WICR (CONVERT2); use WICR to produce WIIQ (CONVERT1) **************************************************************************** * 8th Grade test score (Henmon-Nelson scores and other test scores) * * Sibling data and Graduate data * **************************************************************************** * Because we had a large sample of WLS Graduates for whom we had both * * Freshman scores (8th grade spring or 9th grade fall) and Junior scores * * (11th grade spring and 12th grade fall), we could simply adjust the * * the two known distributions to have the same mean and standard * * deviations to produce the best transformation. These values are used * * for all Freshman (8th grade spring or 9th grade fall) scores. * * **************************************************************************** 1. Start with Henmon-Nelson Raw Score. If score is an IOWA (or other) Wisconsin Centile Rank average, then get the Henmon-Nelson Raw Score which would correspond to that centile rank for Freshman Year (CONVERT3a) 2. Use freshman transformation to get Junior predicted HNRS: Jun_pred=(Fresh)(SD_Jun/SD_Fr)+Mean_Jun-((Mean_Fr*SD_Jun)/SD_Fr) to get Junior-year predictions from freshman year scores, where Mean_Jun=56.279 Mean_Fr=44.745 SD_Jun=11.567 SD_Fr=12.135 Fresh=starting Henmon-Nelson Raw score from Freshman Year (8th grade) 3. Round to nearest 100th 4. If score is greater than 90, then score equals 90 5. Use resulting Raw Score to produce WICR (CONVERT2) and HNCR (CONVERT7); use WICR to produce WIIQ (CONVERT1) ******************************************************** ***9th Grade test score (Henmon-Nelson & other scores) * ***Sibling data only * ******************************************************** * We did not have a sample of respondents for whom * * we had both 9th grade scores and 11th grade scores. * * Thus, we found the National test score distribution * * which most matched the Wisconsin 11th grade HN * * distribution. This turned out to be the National * * 12th grade distribution, adjusted for mean and st. * * deviation differences. So, to get the predicted * * junior year score, we find a Senior year score based* * on the National norms in the Henmon-Nelson manual, * * and adjust mean/st. dev. * ******************************************************** 1. Start with Henmon-Nelson Raw Score 2. Get the predicted national 9th grade centile rank from the 9th grade raw score (CONVERT5); this centile rank is the National Centile Rank (HNCR) 2a.If only a WICR is available (if test score is not Henmon-Nelson), then set National Centile Rank equal to Wisconsin Centile Rank (HNCR=WICR). We do not have a mapping of 9th grade Wisconsin Centile Ranks to Henmon-Nelson scores, so this assumption is necessary. 3. Use HNCR national centile rank to convert to 12th grade raw score (CONVERT9) 4. Subtract 6. 5. Multiply by 1.10 6. Subtract 5.818 7. Round to nearest 100th 8. Use resulting Raw Score to produce WICR (CONVERT2); use WICR to produce WIIQ (CONVERT1) ******************************************************** ***10th Grade test score (Henmon-Nelson & other scores)* ***Sibling data only * ******************************************************** * We did not have a sample of respondents for whom * * we had both 10th grade scores and 11th grade scores.* * Thus, we found the National test score distribution * * which most matched the Wisconsin 11th grade HN * * distribution. This turned out to be the National * * 12th grade distribution, adjusted for mean and st. * * deviation differences. So, to get the predicted * * junior year score, we find a Senior year score based* * on the National norms in the Henmon-Nelson manual, * * and adjust mean/st. dev. * ******************************************************** 1. Start with Henmon-Nelson Raw Score 2. Get the predicted national 10th grade centile rank from the 10th grade raw score (CONVERT6); this centile rank is the National Centile Rank (HNCR) 2a.If only a WICR is available (if test score is not Henmon-Nelson), then set National Centile Rank equal to Wisconsin Centile Rank (HNCR=WICR). We do not have a mapping of 10th grade Wisconsin Centile Ranks to Henmon-Nelson scores, so this assumption is necessary. 3. Use HNCR national centile rank to convert to 12th grade raw score (CONVERT9) 4. Subtract 6. 5. Multiply by 1.10 6. Subtract 5.818 7. Round to nearest 100th 8. Use resulting Raw Score to produce WICR (CONVERT2); use WICR to produce WIIQ (CONVERT1) ******************************************************** ***11th Grade test score (Henmon-Nelson & other scores)* ***Graduate and Sibling data * ******************************************************** * 11th Grade is the metric in which we would like all * * our test scores. Most respondents, Graduates and * * Siblings, have 11th grade (spring) scores. If the * * score is a Henmon-Nelson score, leave it as-is. If * * the score is from another test, then use the WICR * * to find the corresponding HNRS, and use this as the * * basis for all other measures of IQ. * ******************************************************** 1. Start with Henmon-Nelson Raw Score 1a.If only a WICR is available (if test score is not Henmon-Nelson), then find the Henmon-Nelson test score which corresponds to the WICR (CONVERT3). 2. Use resulting Raw Score to produce WICR (CONVERT2) and HNCR (CONVERT7); use WICR to produce WIIQ (CONVERT1) ******************************************************** ***12th Grade test score (Henmon-Nelson & other scores)* ***Sibling data only * ******************************************************** * We did not have a sample of respondents for whom * * we had both 12th grade scores and 11th grade scores.* * Thus, we found the National test score distribution * * which most matched the Wisconsin 11th grade HN * * distribution. This turned out to be the National * * 12th grade distribution, adjusted for mean and st. * * deviation differences. So, to get the predicted * * junior year score, we use the ACTUAL senior-year * * score (or the best-estimate based on the WICR from * * another test), and adjust mean/st. dev. * ******************************************************** 1. Start with Henmon-Nelson Raw Score 1a.If only a WICR is available (if test score is not Henmon-Nelson), then set National Centile Rank equal to Wisconsin Centile Rank (HNCR=WICR). We do not have a mapping of 12th grade Wisconsin Centile Ranks to Henmon-Nelson scores, so this assumption is necessary. 1b.If only a WICR is available (if test score is not Henmon-Nelson), then use the National Centile Rank (HNCR) to find the Henmon-Nelson Raw score which corresponds (HNRS) (CONVERT9). 2. Subtract 6. 3. Multiply by 1.10 4. Subtract 5.818 5. Round to nearest 100th 6. Use resulting Raw Score to produce WICR (CONVERT2) and HNCR (CONVERT7); use WICR to produce WIIQ (CONVERT1)