## STATISTICAL REPORT

LAIT NORMING #2, 7/15/79
Permission to republish granted to Darryl Miyaguchi

 Introduction by Kevin Langdon (August 22, 2000):     The second norming of the LAIT was done with what I now regard as very crude statistical methods.  Working with data far from the general-population mean, there were many outlying points, both super-high scores and scores from outside the main, self-selected population taking the test.  I made some assumptions that enabled me to do a reasonably accurate fit of scores on the LAIT to self-reported scores on various tests previously taken.  Later, I realized that the effect of outliers became negligible if I simply equated the means and average deviations (rather than standard deviations) of the two distributions.  I have made a number of other refinements to my norming methods as well.  A new norming study on the LAIT will be released shortly.

This report provides an overview of the norming of the Langdon Adult Intelligence Test completed in July 1979, including 553 testees.  Only a handful of the earliest responses to the test's appearance in the April 1979 issue of Omni are included.  A further norming will be completed after the bulk of the Omni response has been analyzed.

The norming sample included 207 persons tested on Form A and 346 tested on Form B.  Form A was an early version of the test, now out of print, differing from Form B only in a few items.  Thus, one form cannot be used to obtain an independent measure of intelligence for an individual tested using the other.

Raw scores of all testees were computed using the appropriate formula for form A or Form B.  Additionally, a score for items unchanged between the two forms, and scores for each of two matched sets of items containing one half of the items on each part of the test, were computed for each testee.

Correlations between halves of a test (split-test correlations) are generally lower than those which would be obtained if the tests were full length because any chance variation is a larger percentage of the half test.  To compensate for this effect, it is usual to apply the formula where r1 is the uncorrected correlation coefficient and r2 is the corrected correlation.  For Form A of the LAIT r1 = .822 and r2 = .902 and for Form B r1 = .815 and r2 = .898.

Scores on other tests reported by testees were entered into the computer with other data from the answer sheets and paired with LAIT scores.  A table of LAIT-previous score pairs for LAIT total score and each subscore was constructed for each test which was used in the norming (see Table 1) and arranged in LAIT score order (lowest to highest).

 MEANS AND STANDARD DEVIATIONS OF TESTS USED IN NORMING THE LAIT Test Test     Code Mean Standard     Deviation Stanford-Binet S 100 15.80 Terman Concept Mastery T 67 29.00 Army General Classification Test A 100 20.00 California Test of Mental Maturity C 100 16.00 Miller Analogies M 10 28.00 Wechsler Adult Intelligence Scale W 100 15.00 Scholastic Aptitude Test (Total) X 765 255.00 Graduate Record Exam (Total) G 715 255.00 Cattell Verbal V 100 23.65 Harding Skyscraper H 100 16.00 W87 8 100 16.00 Bloom Analogies Test B 0 7.75 Cattell Culture Fair F 100 16.00 Eysenck E 100 15.00 RAM R 23 3.00 ACT 7 23 3.00 Table 1

 CORRELATIONS BETWEEN LAIT AND VARIOUS STANDARD I.Q. TESTS Test     Code Total     Number Part Limit     Number Limit     LAIT     Score Limit     Correlation Total     Correlation S 44 0 Verbal 32 594 .330 .136 1 Spatial 36 568 .327 .085 2 Inductive 44 850 .225 .225 3 Total 32 563 .429 .204 T 10 0 7 665 .295 .169 1 7 505 .617 .240 2 8 551 .747 .177 3 7 599 .522 .273 A 46 0 27 564 .282 .167 1 45 787 .146 .139 2 44 766 .138 .107 3 46 837 .136 .136 C 139 0 87 544 .365 -.242 1 75 368 .328 -.202 2 44 263 .342 .165 3 71 422 .305 -.198 M 37 0 37 818 .338 .338 1 36 703 .362 .339 2 10 258 .715 .272 3 36 710 .441 .410 W 22 0 22 746 .285 .285 1 15 370 .350 .282 2 22 783 .271 .271 3 22 814 .285 .285 X 54 0 54 1000 .141 .141 1 54 881 .119 .119 2 54 913 .140 .140 3 54 865 .111 .111 G 55 0 55 1000 .534 .534 1 54 829 .484 .470 2 54 775 .457 .447 3 55 860 .532 .532 V 160 0 160 974 .411 .236 1 158 838 .412 .229 2 158 850 .276 .198 3 159 670 .323 .245 H 18 0 12 597 .571 .096 1 9 289 .285 -.150 2 7 349 .573 .019 3 10 405 .275 -.082 R 4 0 4 974 .561 .561 1 4 838 .204 .204 2 4 757 .586 .586 3 4 846 .529 .529 7 4 0 4 949 .617 .617 1 4 872 .607 .607 2 4 913 .642 .642 3 4 907 .617 .617 Table 2

Correlations between the LAIT and previous score distributions for LAIT-previous score pairs from the lowest LAIT score through each LAIT score were calculated and printed out and a cutoff point was determined to maximize r2N, where r is the correlation coefficient and N is the number of score pairs included.  Table 2 shows the total number of previous scores reported, the total falling below the cutoff, the overall correlations, and the correlations for the truncated distributions for each test used.  Scores on each test were weighted by this correlation figure, representing the relationship between the LAIT and the test concerned without the effects of the generally lower effective ceiling of most other tests, in calculating the overall means, standard deviations, and correlations for LAIT and previous score distributions for all tests included in the norming.

A scatter diagram of LAIT scores against all reported scores on other tests was produced for LAIT total scores and subscores.  Outlying points were identified and were not used in calculating distribution means and standard deviations and correlations between LAIT and previous scores.  Table 3 summarizes the values obtained.

 LAIT AND PREVIOUS SCORE MEANS, STANDARD DEVIATIONS, AND CORRELATIONS VERBAL SPATIAL INDUCTIVE TOTAL Number of Score Pairs 563 566 564 575 LAIT Mean 442.014 408.889 364.927 466.990 LAIT Standard Deviation 238.188 233.495 221.871 222.501 Previous Mean   (Z-score form) 2.63167 2.62932 2.62215 2.64632 Previous Standard   Deviation .517525. .527115 .511561 .533550 Correlation 258021 .479881 .179265 .463281 Table 3

A correction for the very tight distribution of previous scores reported due to the bulk of the norming population having been preselected by these scores was applied to the previous score standard deviations by the formula , where is the uncorrected standard deviation, is the corrected standard deviation, and r is the correlation between LAIT and previous score distributions.

 MEAN LAIT SCORES OF SELECTED GROUPS Group Number Verbal Spatial Inductive Total All Testees 553 476.262 393.278 414.326 445.333 Men 455 495.323 410.222 432.530 462.455 Women 98 387.765 314.612 329.806 365.837 Mensa Members 442 487.113 397.887 418.570 453.219 Intertel Members 75 462.920 361.907 375.253 418.653 ISPE Members 61 519.049 417.590 434.492 475.754 MM Members 11 622.000 490.364 531.182 553.091 Four Sigma Members 43 840.023 782.861 757.233 802.093 Age Under 20 24 424.348 421.261 423.217 438.087 Age 20-24 52 412.865 385.788 384.846 413.615 Age 25-29 118 514.492 433.712 457.898 485.025 Age 30-34 102 500.794 424.461 436.441 470.657 Age 35-39 61 482.443 413.246 421.869 452.934 Age 40-44 53 464.792 361.698 397.755 424.283 Age 45-49 51 472.588 370.490 395.608 432.333 Age 50-54 37 503.595 383.514 422.811 457.757 Age 55-59 26 491.731 331.885 394.538 425.462 Age 60-64 19 371.526 245.947 279.947 315.368 Age 65+ 10 351.400 245.300 254.300 315.800 Table 4

At this point, the LAIT and previous total score means and standard deviations were equated and I.Q.'s were calculated.  Total and part score means and standard deviations for the entire score distributions were equated to yield subscore I.Q.'s.  General population percentiles were looked up in an internal table and tested population percentiles were calculated directly.

 MUTUAL CORRELATIONS OF LAIT TOTAL SCORES AND SUBSCORES SPATIAL INDUCTIVE TOTAL Verbal .815947 .941721 .946253 Spatial .939251 .939024 Inductive .963145 Table 5

 MINIMUM AND MAXIMUM IQ SCORES ON FORMS A AND B OF THE LAIT Form A Form B Subscore Min Max Min Max Verbal 112 169 114 171 Spatial 118 175 120 178 Inductive 116 176 118 178 Total 114 174 116 176 Table 6

 LAIT SCORE DISTRIBUTIONS FOR TESTED POPULATION VERBAL Tested Group   Percentile LAIT   Scaled Score General Population     Percentile IQ 10 138 89 120 20 239 94 126 30 341 97 132 40 402 98 136 50 493 99 141 60 559 99.7 145 70 628 99.8 149 80 706 99.96 154 90 777 99.98 158 95 848 99.99 162 98 899 99.997 165 99 949 99.999 168 SPATIAL Tested Group   Percentile LAIT   Scaled Score General Population     Percentile IQ 10 104 93 124 20 186 96 129 30 232 97 131 40 304 98 136 50 368 99 140 60 445 99.7 144 70 539 99.9 150 80 616 99.96 154 90 703 99.98 159 95 764 99.996 163 98 838 99.998 167 99 872 99.999 169 INDUCTIVE Tested Group   Percentile LAIT   Scaled Score General Population     Percentile IQ 10 133 93 124 20 203 95 128 30 298 98 134 40 352 98 137 50 402 99 141 60 476 99.7 145 70 541 99.8 149 80 616 99.96 154 90 705 99.98 159 95 757 99.996 163 98 827 99.998 167 99 870 99.9995 170 TOTAL Tested Group   Percentile LAIT   Scaled Score General Population     Percentile IQ 10 161 92 123 20 253 96 129 30 324 98 133 40 385 98 137 50 441 99 141 60 501 99.7 144 70 581 99.8 149 80 651 99.96 154 90 720 99.98 158 95 790 99.99 162 98 857 99.998 167 99 870 99.998 167 Table 7

 IQ DISTRIBUTIONS FOR TESTED POPULATIONS IQ RANGE VERBAL SPATIAL INDUCTIVE TOTAL 110 - 114 22 0 0 6 115 - 119 25 18 31 25 120 - 124 48 53 45 36 125 - 129 56 64 55 56 130 - 134 46 78 53 58 135 - 139 69 65 83 79 140 - 144 65 68 60 72 145 - 149 61 44 66 58 150 - 154 63 61 62 62 155 - 159 56 53 50 54 160 - 164 25 27 32 30 165 - 169 16 18 11 15 170 - 174 1 4 4 2 175 - 179 0 0 1 0 Table 8