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​​NAEP Technical DocumentationTransformation Coefficients Used for Variance Calculation, Science National Assessment: 2019

Transformation coefficients for sampling variance calculation, grade 4 science national assessment: 2019
ScaleIndexAB
Univariate11.0062863979-1.3297563933
Univariate21.0042501260-0.8987008789
Univariate31.0048141494-0.9394239321
Univariate41.0036136789-0.8460384460
Univariate51.0051641580-1.1565550921
Univariate61.0055577325-1.2190321488
Univariate71.0042802943-0.9147988663
Univariate81.0043770429-0.8343872707
Univariate91.0041579172-0.7490002702
Univariate101.0048077858-1.0843862072
Univariate111.0028759952-0.7924011876
Univariate121.0028477253-0.5769322247
Univariate131.0026315558-0.6746240370
Univariate141.0057192993-1.1886905820
Univariate151.0023262436-0.6858421690
Univariate161.0044723435-0.9892318781
Univariate171.0065871208-1.3518505889
Univariate181.0059396692-1.1712893609
Univariate191.0038041583-0.8696234386
Univariate201.0040322030-0.8443650273
Univariate211.0032154722-0.7586395642
Univariate221.0042434362-0.9271443132
Univariate231.0033983290-0.7353362837
Univariate241.0045962300-1.0037106686
Univariate251.0030243927-0.7448564360
Univariate261.0041401270-0.9618346760
Univariate271.0046830263-0.9970786438
Univariate281.0055244267-1.0401573581
Univariate291.0040788158-0.9034351240
Univariate301.0054216409-1.1613474870
Univariate311.0051025887-1.0085708780
Univariate321.0028722977-0.7934462329
Univariate331.0041875903-0.9625240988
Univariate341.0050587239-1.0900460353
Univariate351.0035229871-0.7215599761
Univariate36
1.0047655882-0.9644881645
Univariate371.0044549194-1.0163824942
Univariate381.0054344212-1.1345758443
Univariate391.0039729151-0.8723364602
Univariate401.0053247831-1.1729860069
Univariate411.0041428629-0.8935769054
Univariate421.0051368785-1.0880352013
Univariate431.0048287418-1.0766238664
Univariate441.0038360408-0.8798611310
Univariate451.0048791795-1.1842770910
Univariate461.0046006959-0.9468112708
Univariate471.0032172010-0.7773262717
Univariate481.0035397487-0.8512800145
Univariate491.0010009340-0.3837291619
Univariate501.0032122418-0.7665615303
Univariate511.0045626008-1.0016866328
Univariate521.0034544733-0.7699160079
Univariate531.0037869051-0.9838287358
Univariate541.0047382589-0.9292894466
Univariate551.0033340296-0.9081206876
Univariate561.0040853627-0.9571718681
Univariate571.0022937473-0.6403607093
Univariate581.0044811822-0.9883198235
Univariate591.0059301333-1.2321057539
Univariate601.0056089410-1.2642667464
Univariate611.0042590788-0.8882223619
Univariate621.0013807798-0.5152847625
Physical science11.0064075564-0.7098111190
Physical science21.0044135135-0.3491101888
Physical science31.0032709969-0.1344592379
Physical science41.0022164682-0.0194436318
Physical science51.0033949936-0.2338143870
Physical science61.0034275788-0.2183613499
Physical science71.0036352217-0.2480750654
Physical science81.0035997025-0.1285553150
Physical science91.00242665750.0376029081
Physical science101.0027677742-0.1006487783
Physical science111.0044102505-0.4097494373
Physical science121.0025197507-0.0014237776
Physical science131.00134026130.0883268949
Physical science141.0026498347-0.0661745469
Physical science151.00117848730.1057292024
Physical science161.0033138201-0.1883852359
Physical science171.0052326825-0.5239280550
Physical science181.0051875077-0.3852965359
Physical science191.0036285790-0.2281704043
Physical science201.0024657352-0.0577399612
Physical science211.0028773717-0.1162353844
Physical science221.0037876024-0.2891095349
Physical science231.0039573801-0.1981057246
Physical science241.0028210944-0.0792568817
Physical science251.0031148878-0.1450588165
Physical science261.0021997909-0.0817829276
Physical science271.0034491185-0.1566321793
Physical science281.0048790875-0.2902223349
Physical science291.0021662484-0.0423542955
Physical science301.0047880067-0.4538140858
Physical science311.0040731281-0.2045041064
Physical science321.0029051182-0.1878625795
Physical science331.0029158230-0.1123927898
Physical science341.0027737475-0.1028852094
Physical science351.0034348292-0.1613383336
Physical science361.0035015417-0.2212825041
Physical science371.0024449190-0.0793215235
Physical science381.0032096996-0.2129366075
Physical science391.0031915789-0.1272565189
Physical science401.0020187969-0.0554033443
Physical science411.0025737929-0.0745330591
Physical science421.0038084633-0.2393877065
Physical science431.0037238198-0.3197167051
Physical science44
1.00204594810.0042961592
Physical science451.0052185212-0.6327736649
Physical science461.0042536184-0.2933691892
Physical science471.0029727733-0.0997883973
Physical science481.00253468190.0125275720
Physical science491.00061959890.2631395233
Physical science501.0040297233-0.2663215906
Physical science511.0046565032-0.3395786749
Physical science521.00215527700.0434916640
Physical science531.00116618250.1202892966
Physical science541.0045557737-0.2031521952
Physical science551.0047944765-0.4902240938
Physical science561.0039153931-0.3068340152
Physical science571.00186970000.0210680991
Physical science581.0046947892-0.3969800817
Physical science591.0038017384-0.2853275379
Physical science601.0055939279-0.5800085946
Physical science611.00194497790.0695661441
Physical science621.00161269130.0690508113
Earth and space sciences10.99826306890.2924628283
Earth and space sciences20.99701819470.6310881236
Earth and space sciences30.99611586020.7732443772
Earth and space sciences40.99638059820.6305159065
Earth and space sciences50.99620948830.6186289963
Earth and space sciences60.99684339400.5326431548
Earth and space sciences70.99605956880.6326328799
Earth and space sciences80.99634587090.7686822834
Earth and space sciences90.99734078550.6821516979
Earth and space sciences100.99718834730.5348365046
Earth and space sciences110.99779553580.3471517054
Earth and space sciences120.99618232630.8097038379
Earth and space sciences130.99694053400.5403073074
Earth and space sciences140.99618602120.6536761523
Earth and space sciences150.99570082380.7238269838
Earth and space sciences160.99670277380.6017090366
Earth and space sciences170.99985040510.0985934881
Earth and space sciences180.99906555500.2745613639
Earth and space sciences190.99748952770.3954554291
Earth and space sciences200.99700308340.5655543091
Earth and space sciences210.99647688240.6579400692
Earth and space sciences220.99754446150.4278605326
Earth and space sciences230.99745062510.5356754038
Earth and space sciences240.99632524410.6725425946
Earth and space sciences250.99620096790.6139740090
Earth and space sciences260.99600514760.6407647104
Earth and space sciences270.99729097470.4610206417
Earth and space sciences280.99870077330.3975434287
Earth and space sciences290.99590824260.7838271914
Earth and space sciences300.99902759370.2198363054
Earth and space sciences310.99866090340.3493104658
Earth and space sciences320.99730903400.4480258630
Earth and space sciences330.99603420820.6956456447
Earth and space sciences340.99622670040.6013288424
Earth and space sciences350.99591484340.8119946941
Earth and space sciences360.99720279540.5905184579
Earth and space sciences370.99574618710.7210340883
Earth and space sciences380.99706188190.5126721664
Earth and space sciences390.99773733710.4445416573
Earth and space sciences400.99620030920.5148183214
Earth and space sciences410.99682279930.5759498987
Earth and space sciences420.99787988590.4208620696
Earth and space sciences430.99735911250.4697568041
Earth and space sciences440.99519452740.7805330445
Earth and space sciences450.99766712590.2969017733
Earth and space sciences460.99676147680.5781546265
Earth and space sciences470.99656190060.6804680134
Earth and space sciences480.99602913290.7112911562
Earth and space sciences490.99525292660.8426968501
Earth and space sciences500.99645735280.5511477909
Earth and space sciences510.99948207360.2076293609
Earth and space sciences520.99567861080.8178221469
Earth and space sciences530.99525059720.7345313241
Earth and space sciences540.99778683450.5212014059
Earth and space sciences550.99566789270.6153400548
Earth and space sciences560.99760589420.3963293963
Earth and space sciences570.99462432420.9108458349
Earth and space sciences580.99843880240.3665813637
Earth and space sciences590.99755021100.3730671335
Earth and space sciences600.99921223500.1169638970
Earth and space sciences610.99632995110.7677828327
Earth and space sciences620.99319019181.0910990843
Life science11.0062817685-0.9806969278
Life science21.0053550603-0.7664495623
Life science31.0046420250-0.6386871409
Life science41.0057755343-0.8250747415
Life science51.0047505837-0.8182172792
Life science61.0058748241-0.8906379548
Life science71.0057451574-0.8611125400
Life science81.0050505493-0.6654238659
Life science91.0046476914-0.5675158021
Life science101.0049248910-0.6464156044
Life science111.0055792080-0.8723169249
Life science121.0039449379-0.5570467591
Life science131.0043225937-0.6606586871
Life science141.0045706889-0.7172133185
Life science151.0036409076-0.6026868722
Life science161.0058134472-0.8315129149
Life science171.0071182634-1.0333518909
Life science181.0074081828-0.9449803925
Life science191.0065546157-0.9901700838
Life science201.0053897968-0.7253521302
Life science211.0046193838-0.6508695671
Life science221.0065123697-0.9103712306
Life science231.0060865506-0.7817276716
Life science241.0043097973-0.6293943751
Life science251.0053223022-0.7896111576
Life science261.0052036074-0.7867368040
Life science271.0059622527-0.9156113009
Life science281.0064354113-0.8787505908
Life science291.0048731559-0.7074143692
Life science301.0070411137-1.1638684081
Life science311.0056204399-0.7394885764
Life science321.0052564858-0.8385099848
Life science331.0059597890-0.8562471072
Life science341.0048981897-0.7636159612
Life science351.0046185646-0.5726119517
Life science361.0053953604-0.7675257261
Life science371.0053720529-0.8130452087
Life science381.0059985212-0.7963766379
Life science391.0061880321-0.8421072593
Life science401.0053215333-0.8056048367
Life science411.0048393497-0.7073523328
Life science42
1.0065280181-0.9448520601
Life science431.0055131963-0.8629837463
Life science441.0047549525-0.6872494509
Life science451.0073597893-1.1470730858
Life science461.0060055312-0.8518712116
Life science471.0055063209-0.8030362187
Life science481.0046075268-0.6868606521
Life science491.0031872447-0.4852279061
Life science501.0055614022-0.8032510198
Life science511.0064553472-0.8789144400
Life science521.0041348585-0.5474738329
Life science531.0035299779-0.6266589908
Life science541.0060654596-0.8181231910
Life science551.0040357530-0.7141521609
Life science561.0059006353-0.8783406120
Life science571.0045573008-0.6656721689
Life science581.0067344503-1.0121916097
Life science591.0063682455-0.9152193429
Life science601.0075335083-1.1967752971
Life science611.0053132282-0.7149492423
Life science621.0023063103-0.3341597441
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Science Assessment.

Transformation coefficients for measurement variance calculation, grade 4 science national assessment: 2019
ReplicateScaleDBA plausible valueBridge PBA plausible valueAB
1Univariate111.0043058396-0.9617315211
1 Univariate221.0040780916-0.2026830994
1 Univariate331.0104901645-1.6178537199
1 Univariate441.0055433182-0.9383813972
1 Univariate551.0027915125-0.7469119730
1 Univariate660.99301664341.1208776520
1 Univariate770.99762612080.4505507802
1 Univariate881.0043350090-0.7171141023
1 Univariate990.99939730060.2812115183
1 Univariate10100.99223221221.1520874100
1 Univariate11111.0006786473-0.2067151397
1 Univariate12120.99783898170.4614993224
1 Univariate13130.99133230491.3631708084
1 Univariate14141.0014107347-0.6718253761
1 Univariate15151.0067101532-1.0436690319
1 Univariate16160.99880689380.1953855045
1 Univariate17170.99530666200.4125809062
1 Univariate18180.99158669731.4093938685
1 Univariate19191.0085359424-0.9989636325
1 Univariate20200.99415015611.2355497302
1 Physical science111.0033009103-0.1875040133
1 Physical science221.0102503491-1.8509020247
1 Physical science330.98922791011.7874482046
1 Physical science441.0019598081-0.6934580178
1 Physical science550.99084859971.8610263240
1 Physical science660.99605935021.1692692631
1 Physical science771.0159286888-2.2210424706
1 Physical science880.98951484291.7345505843
1 Physical science990.98621048152.0266165041
1 Physical science10101.0085706910-1.3185681419
1 Physical science11110.98818352171.3038359693
1 Physical science12121.0013206979-0.4765483607
1 Physical science13130.99740843390.3551955424
1 Physical science14140.98957342191.9929492856
1 Physical science15151.0090718496-1.4166351125
1 Physical science16161.0004762522-0.7353896025
1 Physical science17171.0101522140-0.9209658109
1 Physical science18181.0072122582-1.6575762143
1 Physical science19191.0120856621-1.6913410735
1 Physical science20200.99263898830.9355542723
1 Earth and space sciences110.99702210360.5341098757
1 Earth and space sciences220.99393303020.0888158142
1 Earth and space sciences330.98746365082.1196360940
1 Earth and space sciences440.9997653360-0.4694377920
1 Earth and space sciences550.97458504863.9451832335
1 Earth and space sciences660.99030690191.2256774593
1 Earth and space sciences771.0097242828-1.0144183175
1 Earth and space sciences881.0132591983-2.1028570380
1 Earth and space sciences990.99722298650.1654375368
1 Earth and space sciences10101.00062846270.1855993939
1 Earth and space sciences11111.0052925953-1.1939631059
1 Earth and space sciences12121.0151144168-2.2742601958
1 Earth and space sciences13131.0023603084-0.4514307926
1 Earth and space sciences14140.99171131251.6750654647
1 Earth and space sciences15151.0098792581-1.4520436884
1 Earth and space sciences16160.99985112080.8786552526
1 Earth and space sciences17171.00138609810.2562769664
1 Earth and space sciences18180.99394753960.5508375099
1 Earth and space sciences19190.99397887881.0252816245
1Earth and space sciences
20201.0228881448-3.7463069120
1 Life science111.0057897083-0.8533513689
1 Life science221.0077464187-0.8404103449
1 Life science330.99881188450.8302712346
1 Life science440.98126685442.7714540619
1 Life science551.0112184618-1.9481144864
1 Life science660.99513567650.5156685892
1 Life science771.0108128652-1.4041162537
1 Life science880.9987415093-0.4840012255
1 Life science991.0056481814-1.2368268122
1 Life science10101.0084840955-1.3439307122
1 Life science11110.99355724381.3355933112
1 Life science12121.0079331403-1.4454877379
1 Life science13131.0086579939-1.0799841563
1 Life science14140.99309301980.6174615454
1 Life science15150.98128102503.0286163992
1 Life science16160.99821672200.4894261694
1 Life science17170.99327755391.2304299990
1 Life science18180.99774008720.2684549050
1 Life science19191.0015599720-0.3602787116
1 Life science20201.0010306073-0.1044358352
2 Univariate1140.99400618100.5472478116
2 Univariate2110.99941719370.2153640895
2 Univariate3180.99750770190.7060961807
2 Univariate4151.0080042962-1.1816440567
2 Univariate5200.99218122821.4066112310
2 Univariate6170.99729888690.2660380327
2 Univariate731.0052081973-1.0257285654
2 Univariate8161.0030095609-0.6500231826
2 Univariate9121.0020439235-0.2368153627
2 Univariate1060.98883480961.6879254382
2 Univariate11191.0057848610-1.0277481119
2 Univariate1220.99902882530.6345732759
2 Univariate1311.0053344062-1.0732567730
2 Univariate14130.99769514410.2585927665
2 Univariate1551.0071254449-1.3946408684
2 Univariate1670.99534350760.9137097316
2 Univariate1740.9982588380-0.0027657861
2 Univariate1890.99905209220.1858896318
2 Univariate1981.0069031671-0.6531596513
2 Univariate20100.99808016790.4062544000
2 Physical science1140.98871161702.0944994914
2 Physical science2110.99521603870.0938638977
2 Physical science3181.0070498412-1.6380666727
2 Physical science4151.0091824557-1.5424334446
2 Physical science5200.98929897211.6543616811
2 Physical science6171.0087440635-0.4160774166
2 Physical science730.98512616562.2460423136
2 Physical science8160.98852373621.4340854953
2 Physical science9120.9988496092-0.4654611034
2 Physical science1060.98878739262.0437087166
2 Physical science11191.0001774464-0.0740519095
2 Physical science1221.0090871836-0.9937221836
2 Physical science1311.00061485400.1067897135
2 Physical science14131.0009576020-0.0408735875
2 Physical science1551.00075476730.1811722639
2 Physical science1671.0199953038-3.0799918318
2 Physical science1741.0073257888-1.3162686256
2 Physical science1890.99076987561.5812961228
2 Physical science1981.0055699284-0.8775595409
2 Physical science20101.0052419840-0.9932380555
2 Earth and space sciences1140.98729968512.3810805985
2 Earth and space sciences2110.9987214577-0.3611047512
2 Earth and space sciences3180.99297954770.7416603921
2 Earth and space sciences4150.9995565997-0.0132112510
2 Earth and space sciences5201.0088179680-1.4562768074
2 Earth and space sciences6170.99543137111.2283083910
2 Earth and space sciences730.99580732711.0567231843
2 Earth and space sciences8160.99369710691.2988290805
2 Earth and space sciences9121.0094560106-1.2931006967
2 Earth and space sciences1060.99053381441.1390951949
2 Earth and space sciences11190.99210578311.0856433228
2 Earth and space sciences1221.0147539791-2.9082185749
2 Earth and space sciences1311.0027930310-0.5512043549
2 Earth and space sciences14131.0010450197-0.0792448431
2 Earth and space sciences1550.99067318751.4516741715
2 Earth and space sciences1671.0060705254-0.3896546378
2 Earth and space sciences1741.0063346588-1.4148820446
2 Earth and space sciences1890.99330550570.7479723404
2 Earth and space sciences1981.0128517334-1.7245899828
2Earth and space sciences20101.0075949082-0.9108178612
2 Life science1141.0002946181-0.1173117847
2 Life science2110.99569368561.1682167817
2 Life science3180.99633905780.2033290495
2 Life science4150.97515086604.4165837684
2 Life science5201.0076754664-0.9205191458
2 Life science6170.99495110940.7456356950
2 Life science730.99904184470.9323649273
2 Life science8161.0021871609-0.5448360491
2 Life science9121.0096704813-1.5757327287
2 Life science1060.99502219390.5987032635
2 Life science11191.0028896170-0.3267516896
2 Life science1221.0095468564-1.6934526744
2 Life science1311.0146693894-2.3660180635
2 Life science14130.99263266041.1581534819
2 Life science1551.0068228590-1.1133951894
2 Life science1671.0051661434-0.3467610037
2 Life science1740.98816254641.5467361486
2 Life science1891.0029725147-0.3040368729
2 Life science1980.9972341852-0.3565903410
2Life science
20101.0038905994-1.1276163095
3 Univariate160.98980317141.4512476569
3 Univariate241.0027263984-0.5421851914
3 Univariate331.0104901645-1.6178537199
3 Univariate491.0030433136-0.2515798307
3 Univariate5110.99663078760.6014088707
3 Univariate6100.99642841370.5830913816
3 Univariate721.0036072040-0.2803966177
3 Univariate8171.0012008104-0.5825743653
3 Univariate9191.0036772930-0.4653457452
3 Univariate10130.98934919851.7099436587
3 Univariate1170.99935398600.1062806618
3 Univariate1280.99784740640.5779149130
3 Univariate13151.0004837919-0.1684697536
3 Univariate14180.99446274760.8748482417
3 Univariate15200.99646930430.7657357919
3 Univariate16121.00011834430.0129999639
3 Univariate1751.0011148011-0.5943804558
3 Univariate18161.0003842793-0.1495512341
3 Univariate19141.0036949408-0.5693309570
3 Univariate2011.0092366129-1.4757557799
3 Physical science160.99113393931.6898340940
3 Physical science241.0002834992-0.6732027054
3 Physical science330.98922791011.7874482046
3 Physical science490.99144863351.1558072052
3 Physical science5110.98690782811.8711494630
3 Physical science6101.0159881433-2.2105030619
3 Physical science721.0068951206-0.9487590354
3 Physical science8170.99176885171.9509725750
3 Physical science9191.0036525853-0.4328967098
3 Physical science10130.99771814210.4189156910
3 Physical science1171.0121112184-1.8920091066
3 Physical science1280.99965812890.3617142015
3 Physical science13151.0054636768-0.8374000178
3 Physical science14181.0077615122-1.7847486572
3 Physical science15200.9991896471-0.0228651884
3 Physical science16121.0031449406-1.2766907567
3 Physical science1751.0062245764-0.5657189483
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NOTE: DBA = Digitally based assessment. PBA = Paper-based assessment.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Science Assessment.

Transformation coefficients for sampling variance calculation, grade 8 science national assessment: 2019
ScaleIndexAB
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Life science551.0030628810-0.9861476509
Life science561.0031445122-0.9134387559
Life science571.0023836991-0.8539321402
Life science581.0011328203-0.7310452737
Life science591.0007535449-0.6139025470
Life science601.0044361246-1.1945262831
Life science611.0039883864-1.1445035031
Life science621.0011649608-0.6666740150
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Science Assessment.

Transformation coefficients for measurement variance calculation, grade 8 science national assessment: 2019
ReplicateScaleDBA plausible valueBridge PBA plausible valueAB
1Univariate111.0060085763-0.9206264964
1Univariate221.0074136929-1.2795708372
1Univariate330.99587734490.7723302719
1Univariate440.99713505920.4378233188
1Univariate550.99875071740.0636380124
1Univariate661.0034191623-0.3645315847
1Univariate770.99707555990.8013652645
1Univariate881.0093767184-1.4878011390
1Univariate990.99568615160.8924083671
1Univariate10100.99622978120.6533116461
1Univariate11111.0030751184-0.8067021901
1Univariate12120.99342723890.9627214795
1Univariate13131.0053336502-0.9622795173
1Univariate14141.0092117394-1.1622581330
1Univariate15150.99768162580.2704752206
1Univariate16161.0041817113-0.9855898708
1Univariate17170.99594267340.6465560953
1Univariate18180.99048122331.5430572844
1Univariate19190.9998084288-0.1203085772
1Univariate20200.99409003461.0155841038
1Physical science110.99731883540.1980089202
1Physical science221.0063388672-1.7946916020
1Physical science330.99026556002.2042192743
1Physical science441.0108717798-1.8819300854
1Physical science551.0024639776-0.2897111215
1Physical science660.98783486222.0111330031
1Physical science771.0113626016-1.9673896894
1Physical science880.98796972202.5318398492
1Physical science990.98894510921.3591203438
1Physical science10100.99527870020.5064005766
1Physical science11111.0133699255-1.9852369487
1Physical science12121.0003080612-0.2544862400
1Physical science13131.0041038982-0.6737282392
1Physical science14141.0100236109-1.3546963482
1Physical science15150.99117707012.3306527538
1Physical science16161.0004937960-0.2555276141
1Physical science17170.99966017980.0777385503
1Physical science18181.0042264479-0.8942030970
1Physical science19190.98980552241.3544570955
1Physical science20201.0086824209-1.3067715321
1Earth and space sciences111.0020446528-0.2560597519
1Earth and space sciences220.99768180050.2331757577
1Earth and space sciences330.99095980351.6949749056
1Earth and space sciences441.0009782952-0.5528978111
1Earth and space sciences551.0052996219-0.7617412260
1Earth and space sciences661.0040817782-0.4822912136
1Earth and space sciences770.99007884911.5570286359
1Earth and space sciences880.99138937711.1180259519
1Earth and space sciences990.99596492250.4333511789
1Earth and space sciences10100.99266083901.5348849958
1Earth and space sciences11110.9972708226-0.1378455419
1Earth and space sciences12121.0048451817-0.6536527804
1Earth and space sciences13131.0021626830-0.3525443454
1Earth and space sciences14141.0071776748-1.0613951032
1Earth and space sciences15150.99791489880.2205562114
1Earth and space sciences16160.99441046531.2222263595
1Earth and space sciences17170.99900431940.2705569130
1Earth and space sciences18181.0117107333-1.8042580195
1Earth and space sciences19191.00004347790.0337740360
1Earth and space sciences20201.0143253669-2.2520133208
1Life science111.0028256954-0.9632942596
1Life science220.99755752300.4880141865
1Life science330.99894399410.6633190982
1Life science441.0041621416-0.7758625558
1Life science550.99304480351.5231375214
1Life science660.99246406241.4437123573
1Life science770.99031170391.5890782005
1Life science880.99328280271.4987218336
1Life science990.98489193262.9141508710
1Life science10101.0103739638-2.0157676691
1Life science11111.0074790894-1.2500610501
1Life science12121.0005153752-0.5724518165
1Life science13130.99753603510.3811159554
1Life science14141.0055219468-1.5347721311
1Life science15150.99824360470.3451086597
1Life science16161.0124667494-1.7788086795
1Life science17170.99409231911.1012388516
1Life science18181.0095066708-1.5509612877
1Life science19190.99757510620.1486021324
1Life science20201.0093461617-1.6835357912
2Univariate1141.0135713303-1.8579187607
2Univariate2111.0048084791-0.9556138486
2Univariate3180.99805806120.3248481157
2Univariate4150.99189517831.2609887056
2Univariate5200.99775945310.2021344117
2Univariate6170.99324568701.3447496801
2Univariate730.99903244940.1141633033
2Univariate8161.0102550768-1.8912614498
2Univariate9120.98851487721.9589060775
2Univariate1061.0079780596-1.3281945550
2Univariate11191.0028573646-0.4799064219
2Univariate1221.0008811870-0.4441420914
2Univariate1311.0055331720-0.9326035088
2Univariate14131.0014827569-0.2599719254
2Univariate1551.0072663017-1.1496721761
2Univariate1670.99339196591.5301172271
2Univariate1741.0012515680-0.4426592761
2Univariate1890.99489945141.0185465079
2Univariate1981.0037092355-0.8871661933
2Univariate20100.98405217482.7992447798
2Physical science1141.0045877614-0.7409046685
2Physical science2111.0092636072-1.3762936925
2Physical science3180.99406066641.0429517381
2Physical science4151.00062183220.4049766287
2Physical science5201.0047337570-0.5818788114
2Physical science6170.99388958141.0494536170
2Physical science731.0046530124-0.5865117010
2Physical science8160.99389815870.8672902441
2Physical science9120.98919144191.4388659368
2Physical science1060.98703200521.9328276650
2Physical science11190.99548053900.3868742050
2Physical science1221.0071537978-1.9689587963
2Physical science1310.99589166390.3558907010
2Physical science14131.0109838557-1.4472871517
2Physical science1550.99828983490.7667880162
2Physical science1671.0110887466-1.8794748763
2Physical science1741.0079127338-1.4629329392
2Physical science1890.99592088080.6850284841
2Physical science1980.99224250561.7108072382
2Physical science20101.0034184362-0.6457235211
2Earth and space sciences1140.99292763281.1741804640
2Earth and space sciences2110.99011313151.1466825428
2Earth and space sciences3181.0063194141-0.9212681303
2Earth and space sciences4151.0013562156-0.4664778026
2Earth and space sciences5201.0093714862-1.3726178115
2Earth and space sciences6170.99280474471.2573503492
2Earth and space sciences730.98799991361.9623811396
2Earth and space sciences8160.9994771881-0.0685053898
2Earth and space sciences9121.0091466785-1.5420461538
2Earth and space sciences1061.0031299690-0.4450603428
2Earth and space sciences11191.0002678380-0.0834216480
2Earth and space sciences1221.0050858317-0.8567919207
2Earth and space sciences1311.0067942775-0.9827917610
2Earth and space sciences14131.0117496365-1.8748792427
2Earth and space sciences1551.0058392410-0.9846262369
2Earth and space sciences1670.99290814721.5492238750
2Earth and space sciences1741.0022134787-0.6305406101
2Earth and space sciences1890.99492568610.7042924315
2Earth and space sciences1980.98817857841.7929798325
2Earth and space sciences20100.99949084480.6270188921
2Life science1140.9966509340-0.0025892376
2Life science2110.99904230520.1967379591
2Life science3181.0096525348-1.4633300898
2Life science4151.0010653151-0.4927274659
2Life science5200.99039308641.1610793998
2Life science6170.98526585902.5391586064
2Life science730.99383484621.3311864651
2Life science8161.0087646806-0.8648110257
2Life science9121.0040967131-0.9455477185
2Life science1061.0012245117-0.0031233796
2Life science11190.9997563298-0.0730035064
2Life science1221.0005251994-0.1598400630
2Life science1311.0031170688-0.7081655689
2Life science14131.0061225947-1.4056914200
2Life science1550.99275141821.5021735015
2Life science1670.99506811140.5252453839
2Life science1741.0085459982-1.1405232030
2Life science1890.98576293942.9203962336
2Life science1980.99592108790.7058194276
2Life science20101.0227791484-3.6712279904
3Univariate161.0072386708-1.0647310627
3Univariate241.0032692266-0.6145896287
3Univariate330.99587734490.7723302719
3Univariate491.00100705700.1102739038
3Univariate5110.99599872050.3111069585
3Univariate6100.99172401921.6057428433
3Univariate721.0059344890-1.2009729500
3Univariate8170.99880746230.3863076614
3Univariate9190.99314080091.2051480610
3Univariate10131.0065472994-1.2133944041
3Univariate1170.99681918670.8714424959
3Univariate1281.0019701990-0.5612894842
3Univariate13150.99660272140.3783558874
3Univariate14180.99745598660.4515166530
3Univariate15201.0062665857-1.0099715613
3Univariate16120.99475426160.9412783743
3Univariate1751.0055584802-1.0339128951
3Univariate18160.99709475910.1680985299
3Univariate19141.0096806756-1.5234552781
3Univariate2010.99444089570.9848196960
3Physical science160.99133378371.4437047342
3Physical science241.0089855360-1.8805618971
3Physical science330.99026556002.2042192743
3Physical science491.0011178137-0.1621255547
3Physical science5111.0057942405-0.4917330864
3Physical science6100.99608826510.5853601592
3Physical science721.0072578894-1.8060962090
3Physical science8170.99476547810.8630552318
3Physical science9190.98122251812.4930897738
3Physical science10131.0011794013-0.3367782691
3Physical science1171.0145509382-2.5655915446
3Physical science1280.99469258261.1683972022
3Physical science13150.99402249471.3773307749
3Physical science14181.0096801347-1.5400342477
3Physical science15201.00055016320.4770124521
3Physical science16121.0001405557-0.0057677870
3Physical science1751.0048523122-0.7549820075
3Physical science18160.99652078870.5151184318
3Physical science19141.0062573944-1.1862590172
3Physical science2011.0011121126-0.4593911106
3Earth and space sciences160.99838447610.3641238477
3Earth and space sciences240.98952045311.3562562753
3Earth and space sciences330.99095980351.6949749056
3Earth and space sciences490.99581275900.4863108410
3Earth and space sciences5110.99760027170.1447490152
3Earth and space sciences6100.99360271471.4980426836
3Earth and space sciences720.9999660463-0.3201164337
3Earth and space sciences8170.99648690850.4093197660
3Earth and space sciences9191.0047412996-0.7644980598
3Earth and space sciences10131.0021758876-0.4375701214
3Earth and space sciences1170.99495828210.8233007003
3Earth and space sciences1280.98858875631.8781996532
3Earth and space sciences13150.99541241270.5675852062
3Earth and space sciences14181.0162315754-2.5093085423
3Earth and space sciences15201.0099132909-1.5964055955
3Earth and space sciences16121.0025834901-0.1249866049
3Earth and space sciences1751.0105533469-1.7554048186
3Earth and space sciences18160.99987574380.0890078972
3Earth and space sciences19140.99905130330.1617964349
3Earth and space sciences2011.0137348853-1.9890148650
3Life science160.99404228061.0734883294
3Life science241.00046208430.1845678648
3Life science330.99894399410.6633190982
3Life science490.98208692252.9762510692
3Life science5111.00020618990.0980210372
3Life science6101.0015334592-0.5557103679
3Life science720.99999894750.2326768053
3Life science8170.98965365401.9896837514
3Life science9190.99789273830.3480694444
3Life science10131.0044516637-0.9526751274
3Life science1170.99623656770.4112879745
3Life science1280.99268488461.2751318979
3Life science13150.99838312320.4802559276
3Life science14181.0116813885-2.3129115268
3Life science15200.99010048461.1401713600
3Life science16121.0047920161-1.2541674992
3Life science1750.99990389580.3074111079
3Life science18161.0126609091-1.4614158440
3Life science19141.0021548236-0.9842007793
3Life science2011.0224728587-3.7043835356
4Univariate121.0064817744-1.1017886491
4Univariate2141.0145098131-2.0369532286
4Univariate370.99392663551.4582430257
4Univariate491.00100705700.1102739038
4Univariate5200.99775945310.2021344117
4Univariate6131.0019948732-0.2510992916
4Univariate7161.0079053147-1.7222571865
4Univariate881.0093767184-1.4878011390
4Univariate940.99183473571.2169324059
4Univariate10111.0046158931-1.0408761078
4Univariate11191.0028573646-0.4799064219
4Univariate1211.0004106221-0.2632891317
4Univariate13181.0012913962-0.2479670946
4Univariate14100.99121715231.5969611576
4Univariate1561.0078525886-1.1857031869
4Univariate16120.99475426160.9412783743
4Univariate17150.99599005510.3851329903
4Univariate1830.98831706211.9878777030
4Univariate1951.0027886437-0.6965899729
4Univariate20170.98556207112.5400828855
4Physical science121.0030060228-0.9751004759
4Physical science2141.0079258617-1.5617882882
4Physical science370.99687906250.8419792219
4Physical science491.0011178137-0.1621255547
4Physical science5201.0047337570-0.5818788114
4Physical science6131.0019937659-0.2573505594
4Physical science7161.0007647813-0.3425211895
4Physical science880.98796972202.5318398492
4Physical science940.9985804757-0.3458625738
4Physical science10111.0015559982-0.0580002905
4Physical science11190.99548053900.3868742050
4Physical science1211.0014430918-0.7902140816
4Physical science13181.0028090493-0.7674728834
4Physical science14101.0050253696-0.5975632442
4Physical science1560.98708150952.5500218803
4Physical science16121.0001405557-0.0057677870
4Physical science17150.99769279010.8197252650
4Physical science1831.00039253080.2744600729
4Physical science1951.0042567071-0.7965602524
4Physical science20171.0012035724-0.1789126698
4Earth and space sciences120.99851070600.0746426552
4Earth and space sciences2140.99210336201.3318271444
4Earth and space sciences3
70.99304496711.2890597294
4Earth and space sciences490.99581275900.4863108410
4Earth and space sciences5201.0093714862-1.3726178115
4Earth and space sciences6131.0031267916-0.4747655818
4Earth and space sciences7160.99157688641.2300429294
4Earth and space sciences880.99138937711.1180259519
4Earth and space sciences941.0011312480-0.6061321886
4Earth and space sciences10110.99564583650.1862050681
4Earth and space sciences11191.0002678380-0.0834216480
4Earth and space sciences1211.0086430493-1.1907908776
4Earth and space sciences13181.0066021527-0.9802298701
4Earth and space sciences14101.00214369100.1112222476
4Earth and space sciences1561.0056386068-0.7096685672
4Earth and space sciences16121.0025834901-0.1249866049
4Earth and space sciences17151.0025918654-0.5441499157
4Earth and space sciences1830.99626883410.8254622292
4Earth and space sciences1951.0047422159-0.9287704795
4Earth and space sciences20170.99868814600.3870260835
4Life science120.99827410910.2495612087
4Life science2140.99593551300.2354760202
4Life science370.99540273980.9235784220
4Life science490.98208692252.9762510692
4Life science5200.99039308641.1610793998
4Life science6130.99566297770.4988240578
4Life science7161.0076271768-0.6963748828
4Life science880.99328280271.4987218336
4Life science941.0070302024-0.8393586339
4Life science10111.0069835008-1.1248742575
4Life science11190.9997563298-0.0730035064
4Life science1211.0050870494-1.3745621781
4Life science13181.0030473884-0.5162321003
4Life science14101.0120547467-2.4714549697
4Life science1560.99419214961.1917836718
4Life science16121.0047920161-1.2541674992
4Life science17151.0054356518-0.8562635032
4Life science1830.99879967710.5766173312
4Life science1950.99808329490.4064261108
4Life science20171.0061664609-0.5257546207
5Univariate1191.0036610423-0.4515018120
5Univariate2100.99642075960.7378621718
5Univariate3131.0020872621-0.3871518288
5Univariate481.0023436033-0.3397169848
5Univariate5170.98920001091.7336115043
5Univariate6120.99519790221.0044352407
5Univariate711.0054615483-1.0197641658
5Univariate8111.0056722033-1.0454568192
5Univariate950.99610114110.6328175679
5Univariate1061.0079780596-1.3281945550
5Univariate11181.0009626358-0.2643915506
5Univariate1291.0006341506-0.1110031461
5Univariate13150.99660272140.3783558874
5Univariate1421.0021526772-0.4109939097
5Univariate1531.00018522700.0926152549
5Univariate1670.99339196591.5301172271
5Univariate17141.0124695487-1.8630965755
5Univariate18200.99432625950.8968145229
5Univariate19161.0045826620-1.2901038323
5Univariate2040.99081563171.4609610008
5Physical science1190.98816318721.7925300937
5Physical science2101.0029380014-0.8036303611
5Physical science3130.99534421921.1390340420
5Physical science480.99574575421.3391605247
5Physical science5170.99728418580.5406053535
5Physical science6120.99267242301.3028237565
5Physical science711.0015465933-0.6282749484
5Physical science8111.0032540401-0.1665316693
5Physical science950.99554839060.3586964907
5Physical science1060.98703200521.9328276650
5Physical science11181.0116825799-2.3549850773
5Physical science1291.0000589602-0.3338101471
5Physical science13150.99402249471.3773307749
5Physical science1421.0084333134-1.5879257313
5Physical science1530.99612092631.3587834775
5Physical science1671.0110887466-1.8794748763
5Physical science17141.0068541862-1.1445979398
5Physical science18201.0048407613-0.6121323803
5Physical science19160.99819658170.0413309235
5Physical science2041.0094688677-1.7217029074
5Earth and space sciences1190.99391372581.0471634806
5Earth and space sciences2100.98714472132.4924829096
5Earth and space sciences3131.0018811914-0.2938426478
5Earth and space sciences480.99266898021.0569712117
5Earth and space sciences5170.99381063621.2528645013
5Earth and space sciences6121.0039682884-0.5687606123
5Earth and space sciences711.0035051439-0.6522159793
5Earth and space sciences8111.0002867493-0.7020123562
5Earth and space sciences951.0094621106-1.7307932837
5Earth and space sciences1061.0031299690-0.4450603428
5Earth and space sciences11181.0082583052-1.3932531550
5Earth and space sciences1290.99171961311.3101401098
5Earth and space sciences13150.99541241270.5675852062
5Earth and space sciences1421.0128408737-2.1735031956
5Earth and space sciences1530.99373021871.2913393531
5Earth and space sciences1670.99290814721.5492238750
5Earth and space sciences17141.0048295198-0.6601558040
5Earth and space sciences18201.0124932481-2.0698696107
5Earth and space sciences19160.99624019540.6119548030
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5Life science1190.99209636871.1257278370
5Life science2101.0024060306-0.6897056503
5Life science3131.0041048888-0.5607781009
5Life science480.99340086860.9677716267
5Life science5170.98727309272.3098992987
5Life science6120.99667938570.2087419270
5Life science711.0045583981-0.9802556467
5Life science8111.0026179362-0.2263892753
5Life science950.99840108880.6059950363
5Life science1061.0012245117-0.0031233796
5Life science11181.0104982994-1.9829542862
5Life science1290.98137909293.2801107822
5Life science13150.99838312320.4802559276
5Life science1421.0071595696-1.2851170431
5Life science1530.99227021921.4660334500
5Life science1670.99506811140.5252453839
5Life science17141.0039828513-1.0836196988
5Life science18200.99661566490.2527000713
5Life science19161.0114440877-1.6700720654
5Life science2041.0207956929-2.7911724678
NOTE: DBA = Digitally based assessment. PBA = Paper-based assessment.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Science Assessment.

Transformation coefficients for sampling variance calculation, grade 12 science national assessment: 2019
ScaleIndexAB
Univariate11.0098725205-1.5971968561
Univariate21.0113671808-1.9102784040
Univariate31.0113706995-2.0892095956
Univariate41.0116919065-1.9691687739
Univariate51.0115694574-1.9683752370
Univariate61.0082036187-1.3541772422
Univariate71.0123447142-1.9546254381
Univariate81.0138129191-2.2542802305
Univariate91.0123849412-1.9892249580
Univariate101.0122548536-2.1997906017
Univariate111.0132470492-2.1721703095
Univariate121.0123680075-2.0536349532
Univariate131.0098632015-1.7618672865
Univariate141.0126811642-2.1881144090
Univariate151.0106903677-1.7351441598
Univariate161.0108784332-1.7795890203
Univariate171.0090392924-1.5776696875
Univariate181.0108160587-1.8369964012
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Univariate341.0124370362-2.1018989991
Univariate351.0126229367-2.2138487376
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Univariate371.0118014107-1.9997782164
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Univariate431.0112962411-1.9141784999
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Univariate451.0110671594-1.8633693820
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Univariate591.0124764017-2.0345563303
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Physical science30.99342012550.7174881467
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Earth and space sciences191.0012390430-0.2963475414
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Earth and space sciences211.0042778232-0.7479124470
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Life science30.99654922570.5487348702
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Life science100.99691311740.5661615955
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Life science120.99876715600.3250554750
Life science130.99547745500.6982726536
Life science140.99847593130.3073128090
Life science150.99582195700.8579090765
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Life science360.99583938150.6839251294
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Life science420.99390424311.0440353033
Life science430.99692234340.5892319963
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Life science450.99707545720.5819818587
Life science460.99470610360.9527343494
Life science470.99733025550.6428981591
Life science480.99598923240.9194981434
Life science490.99532209430.8768470232
Life science500.99686014960.5790813941
Life science510.99795336230.4057316516
Life science520.99756011180.4568526849
Life science530.99611988940.7216791017
Life science540.99854214760.2990233160
Life science550.99653716480.7241653716
Life science560.99615948350.6434562548
Life science570.99708174620.6279295267
Life science580.99744854760.4911085444
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Life science600.99740255950.5530325987
Life science610.99813078800.4290256071
Life science620.99714834170.5549446442
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Science Assessment.

Transformation coefficients for measurement variance calculation, grade 12 science national assessment: 2019
ReplicateScaleDBA plausible valueBridge PBA plausible valueAB
1Univariate111.0115852669-1.9306117444
1Univariate220.99600494250.8097967659
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1Univariate20200.99609362500.5513860221
1Physical science110.99375315600.8006583685
1Physical science220.99905760240.1372816447
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1Life science19191.0019456235-0.4997848354
1Life science20200.98701955741.9409857263
2Univariate1141.0030318643-0.4304131037
2Univariate2110.99820150050.4198680113
2Univariate3180.99892596940.2449292239
2Univariate4150.99256283451.0767231901
2Univariate5200.99267577571.0747351344
2Univariate6170.99131708231.2743823431
2Univariate731.0033653434-0.4653074285
2Univariate8160.99881409350.3142973693
2Univariate9120.99981373990.1672388814
2Univariate1061.0143362242-2.1075534556
2Univariate11191.0040134418-0.4847164350
2Univariate1221.00121326290.0066275572
2Univariate1311.0182743024-3.0042270287
2Univariate14130.99762864750.2239146168
2Univariate1550.99586271710.4751026467
2Univariate1670.99150749351.2748718654
2Univariate1740.99906184840.0739796910
2Univariate1890.99627366540.3995496583
2Univariate1980.9998041622-0.0816897504
2Univariate20101.0033337132-0.4546163625
2Physical science1140.99473436140.5880887712
2Physical science2110.99492057470.3400383026
2Physical science3180.99970807360.2177264201
2Physical science4151.0108164194-1.6504842429
2Physical science5201.0058767141-0.7309999928
2Physical science6171.0037976874-0.5983513561
2Physical science730.99824340040.2772918916
2Physical science8160.99488408920.5601441453
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3Univariate161.0093001888-1.3081435504
3Univariate241.00006087570.0398132645
3Univariate331.0022464108-0.2712585079
3Univariate490.99490601190.6663481678
3Univariate5110.99802913260.5237420568
3Univariate6101.0039063385-0.7632332122
3Univariate720.99913381420.4300672116
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NOTE: DBA = Digitally based assessment. PBA = Paper-based assessment.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Science Assessment.

Last updated 09 January 2024 (ML)