Stratosphere: Verbal Ability Index – Technical Report Introduction The goal of Stratosphere was to solve some of the issues its previous iteration had (The Verbal Ability Test, or VAT) and tur n the test int o a free, elite high range resource for testing V erbal A bility. The 1974 - 1994 SAT is considered to be an accurate measure of intellectual ability and is an accepete d by all reputable IQ societies. T ests in a given year were normalized on a sample population of approximately 1 million high scho ol seniors The VAT was a quick to administer and streamlined test put together from a sample of Analogies and Antonyms from the 1987 SAT Verbal , plus 4 items from the 1989 GRE . H owever, it had several flaws. The item difficulty curve was too sharp at the +3SD range, caused by an underestimation of the experimental 1989 GRE item s that were added . This distorted the normalization and rendered scores above IQ ~150 unreliable. In addition, it cut too many SAT V questions , decreasing reliability. Stratosphere construction Stratosphere was constructed using a complete SAT Verbal Test from 1980. All tests from this year included Reading Comprehension sections; however, to streamline the test taking time and maximize the g eneral factor loading, these items were removed. They were replaced, matched exactly in difficulty, by the same number of items from two SAT Vs from 1980 and 1982. These items were split between Antonyms, Sentence Completion and Analogies. The Stratosphe re ceiling was extended by selecting 17 items across a difficulty gradient, all of which were estimated to be harder than anything on the SAT V. The items were selected from 30 GREs between 1989 and 1992, normalized on a sample of 1,135,982 students applyi ng to graduate school. These items represented a sample of the hardest items ever normalized and released by the College Board. As such, the Stratosphere is a 102 item test containing 85 SAT V items, plus 17 additional items of increased difficulty to e xt end the ceiling. The goal for the distribution of the 17 items was a smooth curve extending above the SAT V that was also hard enough as to produce a guessing threshold at or below chance for the general population, as to not shift the standard norms of th e test. Preliminary normalization A number of resources were used to estimate the SAT V to IQ conversion. See some of the graphed data and links below for more information. Data from Charles Murray , Pumpkin P erson, Prometheus society and several other sources were used. These were averaged, and a preliminary distribution was formed. I then removed the skew towards the ceiling of the test and extrapolated the ceiling to 102 raw. http://web.archive.org/web/20030713190013/www.prometheussociety.org/mcreport/memb_comm_rept.html htt ps://pumpkinperson.com/2019/10/12/charles - murray - the - strangely - high - ceiling - of - the - old - sat/ Data collection: As of 3/15/2021, 234 attempts of Stratosphere were taken. Attempts were removed for any of the following reasons: 1. Blatant trolling or otherwise advising me not to use the data. 2. Incomplete test 3. More than one attempt (only the first attempt was counted). The final count of acceptable attempts was N = 157. Regressions Stratosphere vs Verbal Ability Test (VAT) At N=25, the VAT and Stratosphere correlated at r = 0.90 uncorrected. Professional Tests vs Stratosphere 30 Verbal Professional Test scores were reported and acceptable, with an average IQ of 138.5. Accepted tests include : WAIS VCI, Stanford Binet V, RIAS V and Jouve Tests: CCAT and IAW. Descriptive Statistics N Range Minimum Maximum Mean Std. Deviation Variance Protest 30 61.00 109.00 170.00 138.5333 15.08535 227.568 Stratosphere 30 63.00 105.00 168.00 138.9333 18.18285 330.616 Valid N (listwise) 30 All Professional tests correlated with Stratosphere at r = 0.77 uncorrected. Time vs Stratosphere Total test time was plotted in comparison to Stratosphere raw score. The correlation was r = 0.00 uncorrected. Note: This suggests that the Stratosphere could function as an untimed verbal battery. Stratosphere Predicted SAT V vs Actual SAT V To ensure the GRE items were not distorting SAT V scores, I plotted actual SAT V scores vs Stratosphere predicted SAT V score s. The correlation was r = 0.97 uncorrected. Note: There was a very minor distorti on below SAT V 500, where Stratosphere deflated scores by approximately 10 points. Scores showed approximately 10 point inflation in the range of SAT V 700 - 720, and 20 point inflation by SAT V 740 - 750. This was corrected in the final normalization. The SAT V showed strong ceiling effects at 760. Reliability At N=157, all measures of reliability were deemed very high. Reliability greatly exceeded that of the VAT. Reliability Statistics Cronbach's Alpha N of Items .950 102 Reliability Statistics Cronbach's Alpha Part 1 Value .897 N of Items 51 a Part 2 Value .915 N of Items 51 b Total N of Items 102 Correlation Between Forms .894 Spearman - Brown Coefficient Equal Length .944 Unequal Length .944 Guttman Split - Half Coefficient .944 Difficulty analysis – H ardest 20 Questions The 20 hardest questions are listed below, in order of the % of individuals correctly answering the question. SAT V items are items from the original 1980 C ollege B oard Verbal test. GRE items were taken from 1989 - 1992 GRE Verbal tests to extend the ceiling of Stratosphere. Note: Some questions were harder or easier than expected. Of the GRE items used to extend the c eiling, 4 were easier than expected and 2 were harder than expected. I suspect this is the source of the 1 - 2 raw point inflation of the test above the 700 range. Q 63 (SAT V Antonym) 51% Q 82 ( GRE Sentence completion ) 46% - > Easier than expected Q30 ( GRE SC) 44% - > Ea sier than expected Q 69 ( GRE Antonym) 42% - > Easier than expected Q 43 (SAT V Analogy) 39% - > Harder than expected Q 47 ( GRE Analogy) 38% - > Easier than expected Q 16 ( GRE Antonym ) 35 % Q 76 (SAT V SC ) 33% - > Harder than expected Q 17 ( GRE Antonym) 32% Q 46 ( GRE Analogy) 31% Q29 ( GRE SC) 29% Q 99 ( GRE Analogy) 24% Q 100 ( GRE Analogy) 21% Q 101 ( GRE Analogy) 21% Q 71 ( GRE Antonym) 19% Q 18 ( GRE Antonym) 15% Q 83 ( GRE SC) 11% Q 70 ( GRE Antonym) 11% Q 102 ( GRE Analogy) 4% - > Ha rder than expected Q 48 ( GRE Analogy) 4% - > Harder than expected Factor Analysis G - loadings (h^2, or communalities) were all above 0.646. 99/102 items were above 0.7. Normalization The updated version 2.0 normalization follows. Distortions in the high and low ranges were corrected based on the data. CALCULATING YOUR SCORE (no.correct /102) – 0.25 x (no. incorrect) = Score (round to nearest whole number) e.g 70 – 0.25x(32) = 62 = 131 IQ / 610 SAT V. Score IQ SAT Verbal 102 180+ 950 101 180+ 940 100 180 930 99 178 920 98 176 910 97 174 900 96 172 890 95 170 880 94 168 870 93 166 860 92 165 850 91 163 840 90 162 830 89 160 820 88 159 810 87 157 800 86 156 790 85 154 790 84 153 780 83 152 780 82 151 770 81 150 760 80 149 760 79 148 750 78 147 740 77 146 730 76 145 720 75 144 720 74 143 710 73 142 700 72 141 690 71 140 680 70 139 680 69 138 670 68 137 660 67 136 650 66 135 640 65 134 640 64 133 630 63 132 620 62 131 610 61 130 600 60 130 600 59 129 590 58 128 580 57 127 580 56 126 570 55 125 560 54 124 560 53 123 550 52 121 540 51 120 530 50 119 530 49 11 8 520 48 11 7 510 47 11 6 510 46 11 5 500 45 11 4 490 44 11 3 490 43 11 2 480 42 11 1 470 41 1 10 470 40 10 9 460 39 10 8 450 38 10 7 440 37 10 6 440 36 10 5 43 0 35 10 4 420 34 10 3 420 33 102 410 32 101 400 31 101 400 30 100 390 29 100 380 28 99 380 27 98 370 26 97 360 25 96 350 24 95 350 23 94 340 22 93 330 21 92 330 20 91 320 19 90 310 18 89 310 17 88 300 16 87 290 15 86 290 14 85 280 13 83 270 12 82 260 11 81 260 10 79 250 9 77 240 8 76 240 7 74 230 6 72 220 5 71 220 4 69 210 3 67 200 2 65 200 1 63 200 0 60 200 Conclusion The Stratosphere – Verbal Ability Index is a very reliable battery with excellent items that strongly correlates with professional measures of IQ up to the highest levels. It is considered an excellent tool in personal use as a measure of general i ntelligence and verbal ability.