358:
2485:
2249:
1007:
2241:
195:
notation, and three years later, Werts gave the modern, coordinatized formula for the same. Both of the latter two papers named the new quantity simply "reliability". The modern name originates with Jöreskog's name for the model whence he derived
834:
676:
2480:{\displaystyle {\hat {\rho }}_{C}={\frac {\left(\sum _{i=1}^{k}{\hat {\lambda }}_{i}\right)^{2}}{\left(\sum _{i=1}^{k}{\hat {\lambda }}_{i}\right)^{2}+\sum _{i=1}^{k}{\hat {\sigma }}_{e_{i}}^{2}}}={\frac {106.22}{106.22+18.01}}=.8550}
800:
2103:
190:
two values. Seemingly unaware of McDonald's work, Jöreskog first analyzed a quantity equivalent to congeneric reliability in a paper the following year. Jöreskog defined congeneric reliability (now labeled ρ) with
1589:
2769:
McDonald, R. P. (1970). Theoretical canonical foundations of principal factor analysis, canonical factor analysis, and alpha factor analysis. British
Journal of Mathematical and Statistical Psychology, 23, 1-21.
2854:
Lucke, J. F. (2005). “Rassling the Hog”: The
Influence of Correlated Item Error on Internal Consistency, Classical Reliability, and Congeneric Reliability. Applied Psychological Measurement, 29(2), 106–125.
495:
2615:
2671:
should have a value of at least around 0.6. Often, higher values are desirable. However, such values should not be misunderstood as strict cutoff boundaries between "good" and "bad". Moreover,
2867:
Werts, C. E., Rock, D. R., Linn, R. L., & Jöreskog, K. G. (1978). A general method of estimating the reliability of a composite. Educational and
Psychological Measurement, 38(4), 933–938.
2842:
Graham, J. M. (2006). Congeneric and (Essentially) Tau-Equivalent
Estimates of Score Reliability What They Are and How to Use Them. Educational and Psychological Measurement, 66(6), 930–944.
1689:
1640:
586:
2784:
Cho, E. and Chun, S. (2018), Fixing a broken clock: A historical review of the originators of reliability coefficients including
Cronbach’s alpha. Survey Research, 19(2), 23–54.
698:
2072:
323:
282:
253:
2696:
2669:
2642:
2530:
221:
152:
121:
94:
55:
2550:
2000:
1485:
347:
184:
2093:
2042:
2021:
1935:
1863:
1791:
1719:
1462:
1378:
1348:
1285:
1255:
1213:
1183:
1162:
1132:
1104:
1076:
1048:
57:("rho C") a single-administration test score reliability (i.e., the reliability of persons over items holding occasion fixed) coefficient, commonly referred to as
1956:
1905:
1884:
1833:
1812:
1761:
1740:
1441:
1420:
1399:
1327:
1306:
1234:
1977:
1002:{\displaystyle \rho _{C}={\frac {\left(\sum _{i=1}^{k}\lambda _{i}\right)^{2}}{\left(\sum _{i=1}^{k}\lambda _{i}\right)^{2}+\sum _{i=1}^{k}\sigma _{E_{i}}^{2}}}}
386:
of numerical scores corresponding to one individual. The congeneric model supposes that there is a single underlying property ("factor") of the individual
2236:{\displaystyle {\hat {\rho }}_{C}={\frac {\left(\sum _{i=1}^{k}{\hat {\lambda }}_{i}\right)^{2}}{{\hat {\sigma }}_{X}^{2}}}={\frac {106.22}{124.23}}=.8550}
2819:
426:
2731:
Cho, E. (2016). Making reliability reliable: A systematic approach to reliability coefficients. Organizational
Research Methods, 19(4), 651–682.
1491:
2912:
Revelle, W., & Zinbarg, R. E. (2009). Coefficients alpha, beta, omega, and the glb: Comments on
Sijtsma. Psychometrika, 74(1), 145–154.
162:
A quantity similar (but not mathematically equivalent) to congeneric reliability first appears in the appendix to McDonald's 1970 paper on
2617:). In reality, this is rarely the case and, thus, it systematically underestimates the reliability. In contrast, congeneric reliability (
2973:
2755:
invented congeneric reliability, there is a subtle difference between the formula given there and the modern one. As discussed in
2698:
values close to 1 might indicate that items are too similar. Another property of a "good" measurement model besides reliability is
2983:
2555:
2879:
Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological
Bulletin, 52(4), 281–302.
2759:, McDonald's denominator totals observed covariances, but the modern definition divides by the sum of fitted covariances.
187:
329:, some SEM-based reliability coefficients, including congeneric reliability, are referred to as "reliability coefficient
567:
2900:
Padilla, M. (2019). A Primer on
Reliability via Coefficient Alpha and Omega. Archives of Psychology, 3(8), Article 8.
2891:
Hair, J. F., Babin, B. J., Anderson, R. E., & Black, W. C. (2018). Multivariate data analysis (8th ed.). Cengage.
96:
is a structural equation model (SEM)-based reliability coefficients and is obtained from on a unidimensional model.
2706:
2502:
2491:
563:
124:
2960:, Wikibook that contains management related measurement models, their indicators and often congeneric reliability.
1646:
186:. In McDonald's work, the new quantity is primarily a mathematical convenience: a well-behaved intermediate that
507:
17:
2644:) explicitly acknowledges the existence of different factor loadings. According to Bagozzi & Yi (1988),
285:
1609:
2978:
289:
2803:
Jöreskog, K. G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36(2), 109–133.
2951:
557:
326:
325:
has also been called "construct reliability". Following McDonald's more recent expository work on
2699:
2050:
299:
258:
229:
2674:
2647:
2620:
2508:
357:
199:
130:
99:
72:
33:
550:
2535:
1985:
1470:
671:{\displaystyle \rho _{i}={\frac {\lambda _{i}^{2}}{\lambda _{i}^{2}+\mathbb {V} }}{\text{.}}}
332:
169:
2827:
2078:
2027:
2006:
1913:
1841:
1769:
1697:
1447:
1356:
1333:
1263:
1240:
1191:
1168:
1140:
1110:
1082:
1054:
1026:
1941:
1890:
1869:
1818:
1797:
1746:
1725:
1426:
1405:
1384:
1312:
1291:
1219:
542:
293:
192:
163:
1962:
795:{\displaystyle \rho ={\frac {(w\lambda )^{2}}{(w\lambda )^{2}+\mathbb {E} }}{\text{,}}}
523:
2967:
412:
370:
24:
2937:
2925:
154:; also known as Cronbach's alpha), and is often recommended as its alternative.
2831:
2868:
2913:
2856:
2843:
2732:
2957:
679:
2901:
1584:{\displaystyle 124.23=\Sigma _{diagonal}+2\times \Sigma _{subdiagonal}}
366:
2804:
2954:, tools to calculate congeneric reliability and other coefficients.
2880:
2820:
Intraclass reliability estimates: Testing structural assumptions
226:
Applied statisticians have subsequently coined many names for
490:{\displaystyle X_{i}=\lambda _{i}F+\mu _{i}+E_{i}{\text{,}}}
1596:
These are the estimates of the factor loadings and errors:
820:
is this proportion of explained variance in the case where
2610:{\displaystyle \lambda _{1}=\lambda _{2}=...=\lambda _{k}}
123:
is the second most commonly used reliability factor after
2818:
Werts, C. E., Linn, R. L., & Jöreskog, K. G. (1974).
2677:
2650:
2623:
2558:
2538:
2511:
2252:
2106:
2081:
2053:
2030:
2009:
1988:
1965:
1944:
1916:
1893:
1872:
1844:
1821:
1800:
1772:
1749:
1728:
1700:
1649:
1612:
1494:
1473:
1450:
1429:
1408:
1387:
1359:
1336:
1315:
1294:
1266:
1243:
1222:
1194:
1171:
1143:
1113:
1085:
1057:
1029:
837:
701:
589:
429:
335:
302:
261:
232:
202:
172:
133:
102:
75:
36:
2552:", assumes that all factor loadings are equal (i.e.
2532:), which has traditionally been called "Cronbach's
2690:
2663:
2636:
2609:
2544:
2524:
2479:
2235:
2087:
2066:
2036:
2015:
1994:
1971:
1950:
1929:
1899:
1878:
1857:
1827:
1806:
1785:
1755:
1734:
1713:
1683:
1634:
1583:
1479:
1456:
1435:
1414:
1393:
1372:
1342:
1321:
1300:
1279:
1249:
1228:
1207:
1177:
1156:
1126:
1098:
1070:
1042:
1001:
794:
670:
489:
341:
317:
276:
247:
215:
178:
146:
115:
88:
49:
2938:https://dx.doi.org/10.1016/S0272-6963(15)00056-X
2747:. Hillsdale, NJ: Lawrence Erlbaum and (1999).
2490:Compare this value with the value of applying
2926:https://dx.doi.org/10.1177/009207038801600107
8:
1684:{\displaystyle {\hat {\sigma }}_{e_{i}}^{2}}
403:. Moreover, that the relationship between
288:of composite scores. As psychology calls "
255:. "Composite reliability" emphasizes that
2869:https://doi.org/10.1177/001316447803800412
2799:
2797:
2795:
2793:
2791:
2751:. Mahwah, NJ: Lawrence Erlbaum claim that
296:only measurable through composite scores,
2914:https://doi.org/10.1007/s11336-008-9102-z
2824:Educational and Psychological Measurement
2779:
2777:
2682:
2676:
2655:
2649:
2628:
2622:
2601:
2576:
2563:
2557:
2537:
2516:
2510:
2453:
2441:
2434:
2429:
2418:
2417:
2410:
2399:
2386:
2375:
2364:
2363:
2356:
2345:
2328:
2317:
2306:
2305:
2298:
2287:
2275:
2266:
2255:
2254:
2251:
2217:
2206:
2201:
2190:
2189:
2182:
2171:
2160:
2159:
2152:
2141:
2129:
2120:
2109:
2108:
2105:
2080:
2058:
2052:
2029:
2008:
1987:
1964:
1943:
1921:
1915:
1892:
1871:
1849:
1843:
1820:
1799:
1777:
1771:
1748:
1727:
1705:
1699:
1675:
1668:
1663:
1652:
1651:
1648:
1626:
1615:
1614:
1611:
1545:
1505:
1493:
1472:
1449:
1428:
1407:
1386:
1364:
1358:
1335:
1314:
1293:
1271:
1265:
1242:
1221:
1199:
1193:
1170:
1148:
1142:
1118:
1112:
1090:
1084:
1062:
1056:
1034:
1028:
990:
983:
978:
968:
957:
944:
933:
923:
912:
895:
884:
874:
863:
851:
842:
836:
787:
775:
755:
754:
745:
724:
708:
700:
663:
651:
640:
639:
630:
625:
614:
609:
603:
594:
588:
482:
476:
463:
447:
434:
428:
334:
309:
304:
301:
268:
263:
260:
239:
234:
231:
207:
201:
171:
138:
132:
107:
101:
80:
74:
41:
35:
2857:https://doi.org/10.1177/0146621604272739
2844:https://doi.org/10.1177/0013164406288165
2752:
2733:https://doi.org/10.1177/1094428116656239
1598:
1015:
541:are free parameters, the model exhibits
356:
16:For broader coverage of this topic, see
2770:doi:10.1111/j.2044-8317.1970.tb00432.x.
2756:
2717:
2743:Although McDonald, R. P. (1985).
2902:https://doi.org/10.31296/aop.v3i8.125
2814:
2812:
2727:
2725:
2723:
2721:
1635:{\displaystyle {\hat {\lambda }}_{i}}
7:
2745:Factor analysis and related methods
415:: there exist (non-random) vectors
2805:https://doi.org/10.1007/BF02291393
2055:
1989:
1542:
1502:
1474:
365:Congeneric reliability applies to
14:
1017:Fitted/implied covariance matrix
390:, such that each numerical score
23:In statistical models applied to
2881:https://doi.org/10.1037/h0040957
685:, the proportion of variance in
349:", often without a definition.
2423:
2369:
2311:
2260:
2195:
2165:
2114:
1657:
1620:
781:
772:
762:
759:
742:
732:
721:
711:
657:
644:
568:fraction of variance explained
1:
2958:Handbook of Management Scales
2936:Guide & Ketokivi (2015),
522:is often referred to as the
361:Congeneric measurement model
2067:{\displaystyle \Sigma ^{2}}
1600:Factor loadings and errors
678:More generally, given any
318:{\displaystyle {\rho }_{C}}
277:{\displaystyle {\rho }_{C}}
248:{\displaystyle {\rho }_{C}}
3000:
2832:10.1177/001316447403400104
2707:average variance extracted
2503:Tau-equivalent reliability
2492:tau-equivalent reliability
564:without loss of generality
399:is a noisy measurement of
223:: a "congeneric model".
125:tau-equivalent reliability
15:
2974:Comparison of assessments
2924:Bagozzi & Yi (1988),
2705:A related coefficient is
2691:{\displaystyle \rho _{C}}
2664:{\displaystyle \rho _{C}}
2637:{\displaystyle \rho _{C}}
2525:{\displaystyle \rho _{T}}
1488:
508:statistically independent
377:in the dataset is a list
216:{\displaystyle \rho _{C}}
147:{\displaystyle \rho _{T}}
116:{\displaystyle \rho _{C}}
89:{\displaystyle \rho _{C}}
50:{\displaystyle \rho _{C}}
802:which is maximized when
18:Reliability (statistics)
2984:Statistical reliability
2545:{\displaystyle \alpha }
1995:{\displaystyle \Sigma }
1480:{\displaystyle \Sigma }
353:Formula and calculation
342:{\displaystyle \omega }
286:statistical reliability
179:{\displaystyle \theta }
2692:
2665:
2638:
2611:
2546:
2526:
2481:
2415:
2361:
2303:
2237:
2157:
2089:
2088:{\displaystyle 106.22}
2068:
2038:
2017:
1996:
1973:
1952:
1931:
1901:
1880:
1859:
1829:
1808:
1787:
1757:
1736:
1715:
1685:
1636:
1585:
1481:
1458:
1437:
1416:
1395:
1374:
1344:
1323:
1302:
1281:
1251:
1230:
1209:
1179:
1158:
1128:
1100:
1072:
1044:
1003:
973:
928:
879:
807: ∝ 𝔼λ
796:
672:
491:
362:
343:
319:
294:latent characteristics
278:
249:
217:
180:
148:
117:
90:
51:
29:congeneric reliability
2693:
2666:
2639:
2612:
2547:
2527:
2482:
2395:
2341:
2283:
2238:
2137:
2090:
2069:
2039:
2037:{\displaystyle 18.01}
2018:
2016:{\displaystyle 10.30}
1997:
1974:
1953:
1932:
1930:{\displaystyle X_{4}}
1902:
1881:
1860:
1858:{\displaystyle X_{3}}
1830:
1809:
1788:
1786:{\displaystyle X_{2}}
1758:
1737:
1716:
1714:{\displaystyle X_{1}}
1686:
1637:
1586:
1482:
1459:
1457:{\displaystyle 13.00}
1438:
1417:
1396:
1375:
1373:{\displaystyle X_{4}}
1345:
1343:{\displaystyle 12.00}
1324:
1303:
1282:
1280:{\displaystyle X_{3}}
1252:
1250:{\displaystyle 11.00}
1231:
1210:
1208:{\displaystyle X_{2}}
1180:
1178:{\displaystyle 10.00}
1159:
1157:{\displaystyle X_{1}}
1129:
1127:{\displaystyle X_{4}}
1101:
1099:{\displaystyle X_{3}}
1073:
1071:{\displaystyle X_{2}}
1045:
1043:{\displaystyle X_{1}}
1004:
953:
908:
859:
797:
673:
549:may be normalized to
492:
360:
344:
320:
279:
250:
218:
181:
149:
118:
91:
63:construct reliability
59:composite reliability
52:
2675:
2648:
2621:
2556:
2536:
2509:
2498:Related coefficients
2250:
2104:
2079:
2051:
2028:
2007:
1986:
1963:
1951:{\displaystyle 3.55}
1942:
1914:
1900:{\displaystyle 5.56}
1891:
1879:{\displaystyle 2.53}
1870:
1842:
1828:{\displaystyle 5.92}
1819:
1807:{\displaystyle 2.25}
1798:
1770:
1756:{\displaystyle 6.13}
1747:
1735:{\displaystyle 1.96}
1726:
1698:
1647:
1610:
1492:
1471:
1448:
1436:{\displaystyle 9.01}
1427:
1415:{\displaystyle 7.99}
1406:
1394:{\displaystyle 6.98}
1385:
1357:
1334:
1322:{\displaystyle 5.71}
1313:
1301:{\displaystyle 4.98}
1292:
1264:
1241:
1229:{\displaystyle 4.42}
1220:
1192:
1169:
1141:
1111:
1083:
1055:
1027:
835:
831:equally important):
699:
587:
427:
413:approximately linear
333:
300:
259:
230:
200:
170:
131:
100:
73:
34:
2757:Cho & Chun 2018
2446:
2211:
1972:{\displaystyle .37}
1680:
1601:
1018:
995:
827:(all components of
635:
619:
2700:construct validity
2688:
2661:
2634:
2607:
2542:
2522:
2494:to the same data.
2477:
2416:
2233:
2188:
2085:
2064:
2034:
2013:
1992:
1969:
1948:
1927:
1897:
1876:
1855:
1825:
1804:
1783:
1753:
1732:
1711:
1681:
1650:
1632:
1599:
1581:
1477:
1454:
1433:
1412:
1391:
1370:
1340:
1319:
1298:
1277:
1247:
1226:
1205:
1175:
1154:
1124:
1096:
1068:
1040:
1016:
999:
974:
792:
668:
621:
605:
487:
363:
339:
315:
274:
245:
213:
176:
144:
113:
86:
47:
2469:
2448:
2426:
2372:
2314:
2263:
2225:
2212:
2198:
2168:
2117:
2098:
2097:
1660:
1623:
1594:
1593:
997:
790:
785:
666:
661:
543:affine invariance
513:In this context,
485:
158:History and names
67:coefficient omega
2991:
2940:
2934:
2928:
2922:
2916:
2910:
2904:
2898:
2892:
2889:
2883:
2877:
2871:
2865:
2859:
2852:
2846:
2840:
2834:
2816:
2807:
2801:
2786:
2785:
2781:
2772:
2771:
2766:
2760:
2741:
2735:
2729:
2697:
2695:
2694:
2689:
2687:
2686:
2670:
2668:
2667:
2662:
2660:
2659:
2643:
2641:
2640:
2635:
2633:
2632:
2616:
2614:
2613:
2608:
2606:
2605:
2581:
2580:
2568:
2567:
2551:
2549:
2548:
2543:
2531:
2529:
2528:
2523:
2521:
2520:
2486:
2484:
2483:
2478:
2470:
2468:
2454:
2449:
2447:
2445:
2440:
2439:
2438:
2428:
2427:
2419:
2414:
2409:
2391:
2390:
2385:
2381:
2380:
2379:
2374:
2373:
2365:
2360:
2355:
2333:
2332:
2327:
2323:
2322:
2321:
2316:
2315:
2307:
2302:
2297:
2276:
2271:
2270:
2265:
2264:
2256:
2242:
2240:
2239:
2234:
2226:
2218:
2213:
2210:
2205:
2200:
2199:
2191:
2187:
2186:
2181:
2177:
2176:
2175:
2170:
2169:
2161:
2156:
2151:
2130:
2125:
2124:
2119:
2118:
2110:
2094:
2092:
2091:
2086:
2073:
2071:
2070:
2065:
2063:
2062:
2043:
2041:
2040:
2035:
2022:
2020:
2019:
2014:
2001:
1999:
1998:
1993:
1978:
1976:
1975:
1970:
1957:
1955:
1954:
1949:
1936:
1934:
1933:
1928:
1926:
1925:
1906:
1904:
1903:
1898:
1885:
1883:
1882:
1877:
1864:
1862:
1861:
1856:
1854:
1853:
1834:
1832:
1831:
1826:
1813:
1811:
1810:
1805:
1792:
1790:
1789:
1784:
1782:
1781:
1762:
1760:
1759:
1754:
1741:
1739:
1738:
1733:
1720:
1718:
1717:
1712:
1710:
1709:
1690:
1688:
1687:
1682:
1679:
1674:
1673:
1672:
1662:
1661:
1653:
1641:
1639:
1638:
1633:
1631:
1630:
1625:
1624:
1616:
1602:
1590:
1588:
1587:
1582:
1580:
1579:
1531:
1530:
1486:
1484:
1483:
1478:
1463:
1461:
1460:
1455:
1442:
1440:
1439:
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324:
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56:
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2999:
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2817:
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2077:
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2054:
2049:
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2026:
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2005:
2004:
1984:
1983:
1961:
1960:
1940:
1939:
1917:
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1911:
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1490:
1489:
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1167:
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1114:
1109:
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1086:
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1058:
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1024:
1014:
979:
929:
907:
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858:
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832:
828:
821:
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803:
771:
741:
731:
720:
710:
697:
696:
692:
686:
682:
647:
620:
590:
585:
584:
583:is then simply
580:
576:
571:
560:
553:
546:
538:
534:
527:
520:
514:
510:noise term.
503:
498:
472:
459:
443:
430:
425:
424:
420:
416:
408:
404:
400:
396:
391:
387:
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331:
330:
303:
298:
297:
262:
257:
256:
233:
228:
227:
203:
198:
197:
193:coordinate-free
168:
167:
164:factor analysis
160:
134:
129:
128:
103:
98:
97:
76:
71:
70:
37:
32:
31:
21:
12:
11:
5:
2997:
2995:
2987:
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2955:
2947:
2946:External links
2944:
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845:
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825: ∝
814:
783:
778:
774:
770:
767:
764:
761:
757:
753:
748:
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740:
737:
734:
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628:
624:
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612:
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602:
597:
593:
574:
524:factor loading
516:
501:
479:
475:
471:
466:
462:
458:
455:
450:
446:
442:
437:
433:
394:
381:
354:
351:
338:
327:testing theory
312:
307:
271:
266:
242:
237:
210:
206:
175:
159:
156:
141:
137:
110:
106:
83:
79:
44:
40:
13:
10:
9:
6:
4:
3:
2:
2996:
2985:
2982:
2980:
2979:Psychometrics
2977:
2975:
2972:
2971:
2969:
2959:
2956:
2953:
2950:
2949:
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2939:
2933:
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2897:
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2864:
2861:
2858:
2851:
2848:
2845:
2839:
2836:
2833:
2829:
2826:, 34, 25–33.
2825:
2821:
2815:
2813:
2809:
2806:
2800:
2798:
2796:
2794:
2792:
2788:
2780:
2778:
2774:
2765:
2762:
2758:
2754:
2753:McDonald 1970
2750:
2746:
2740:
2737:
2734:
2728:
2726:
2724:
2722:
2718:
2712:
2710:
2708:
2703:
2701:
2683:
2679:
2656:
2652:
2629:
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2591:
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2183:
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2133:
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2121:
2111:
2100:
2099:
2082:
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2059:
2047:
2046:
2031:
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2010:
2003:
1982:
1981:
1966:
1959:
1945:
1938:
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1918:
1910:
1909:
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1196:
1188:
1187:
1172:
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1145:
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1136:
1119:
1115:
1107:
1091:
1087:
1079:
1063:
1059:
1051:
1035:
1031:
1023:
1021:
1020:
1011:
1009:
991:
984:
980:
975:
969:
964:
961:
958:
954:
950:
945:
940:
934:
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924:
919:
916:
913:
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904:
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891:
885:
881:
875:
870:
867:
864:
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855:
848:
843:
839:
824:
817:
810:
806:
776:
768:
765:
751:
746:
738:
735:
725:
717:
714:
705:
702:
691:explained by
689:
681:
652:
648:
636:
631:
626:
622:
615:
610:
606:
600:
595:
591:
577:
569:
565:
559:
552:
544:
531:
525:
519:
511:
509:
504:
477:
473:
469:
464:
460:
456:
453:
448:
444:
440:
435:
431:
414:
397:
384:
372:
368:
359:
352:
350:
336:
328:
310:
305:
295:
291:
287:
284:measures the
269:
264:
240:
235:
224:
208:
204:
194:
189:
173:
165:
157:
155:
139:
135:
126:
108:
104:
81:
77:
68:
64:
60:
42:
38:
30:
26:
25:psychometrics
19:
2932:
2920:
2908:
2896:
2887:
2875:
2863:
2850:
2838:
2823:
2764:
2748:
2744:
2739:
2704:
2501:
2489:
1595:
822:
815:
811:
804:
687:
572:
532:
517:
512:
499:
392:
379:
364:
225:
161:
66:
62:
58:
28:
22:
2749:Test theory
373:: each row
2968:Categories
2713:References
423:such that
290:constructs
166:, labeled
2680:ρ
2653:ρ
2626:ρ
2599:λ
2574:λ
2561:λ
2540:α
2514:ρ
2424:^
2421:σ
2397:∑
2370:^
2367:λ
2343:∑
2312:^
2309:λ
2285:∑
2261:^
2258:ρ
2196:^
2193:σ
2166:^
2163:λ
2139:∑
2115:^
2112:ρ
2056:Σ
1990:Σ
1658:^
1655:σ
1621:^
1618:λ
1543:Σ
1539:×
1503:Σ
1475:Σ
976:σ
955:∑
931:λ
910:∑
882:λ
861:∑
840:ρ
739:λ
718:λ
703:ρ
623:λ
607:λ
592:ρ
461:μ
445:λ
337:ω
306:ρ
265:ρ
236:ρ
205:ρ
188:separates
174:θ
136:ρ
105:ρ
78:ρ
39:ρ
680:covector
570:in item
558:variance
533:Because
526:on item
367:datasets
2952:RelCalc
1012:Example
566:. The
371:vectors
2460:106.22
2456:106.22
2223:124.23
2220:106.22
2083:106.22
1496:124.23
813:ρ
545:, and
539:μ
535:λ
515:λ
497:where
421:μ
417:λ
292:" any
65:, and
2475:.8550
2466:18.01
2231:.8550
2032:18.01
2011:10.30
1452:13.00
1338:12.00
1245:11.00
1173:10.00
809:.
506:is a
1946:3.55
1895:5.56
1874:2.53
1823:5.92
1802:2.25
1751:6.13
1730:1.96
1431:9.01
1410:7.99
1389:6.98
1317:5.71
1296:4.98
1224:4.42
556:and
551:mean
537:and
530:.
419:and
407:and
2828:doi
1967:.37
695:is
579:by
411:is
369:of
69:.
2970::
2822:.
2811:^
2790:^
2776:^
2720:^
2709:.
2702:.
688:wX
61:,
27:,
2830::
2684:C
2657:C
2630:C
2603:k
2595:=
2592:.
2589:.
2586:.
2583:=
2578:2
2570:=
2565:1
2518:T
2505:(
2472:=
2463:+
2451:=
2443:2
2436:i
2432:e
2412:k
2407:1
2404:=
2401:i
2393:+
2388:2
2383:)
2377:i
2358:k
2353:1
2350:=
2347:i
2338:(
2330:2
2325:)
2319:i
2300:k
2295:1
2292:=
2289:i
2280:(
2273:=
2268:C
2228:=
2215:=
2208:2
2203:X
2184:2
2179:)
2173:i
2154:k
2149:1
2146:=
2143:i
2134:(
2127:=
2122:C
2060:2
1923:4
1919:X
1851:3
1847:X
1779:2
1775:X
1707:1
1703:X
1677:2
1670:i
1666:e
1628:i
1577:l
1574:a
1571:n
1568:o
1565:g
1562:a
1559:i
1556:d
1553:b
1550:u
1547:s
1536:2
1533:+
1528:l
1525:a
1522:n
1519:o
1516:g
1513:a
1510:i
1507:d
1499:=
1366:4
1362:X
1273:3
1269:X
1201:2
1197:X
1150:1
1146:X
1120:4
1116:X
1092:3
1088:X
1064:2
1060:X
1036:1
1032:X
992:2
985:i
981:E
970:k
965:1
962:=
959:i
951:+
946:2
941:)
935:i
925:k
920:1
917:=
914:i
905:(
897:2
892:)
886:i
876:k
871:1
868:=
865:i
856:(
849:=
844:C
829:X
823:w
816:C
805:w
789:,
782:]
777:2
773:)
769:E
766:w
763:(
760:[
756:E
752:+
747:2
743:)
736:w
733:(
726:2
722:)
715:w
712:(
706:=
693:F
683:w
665:.
658:]
653:i
649:E
645:[
641:V
637:+
632:2
627:i
616:2
611:i
601:=
596:i
581:F
575:i
573:X
561:1
554:0
547:F
528:i
518:i
502:i
500:E
484:,
478:i
474:E
470:+
465:i
457:+
454:F
449:i
441:=
436:i
432:X
409:F
405:X
401:F
395:i
393:X
388:F
382:i
380:X
375:X
311:C
270:C
241:C
209:C
140:T
127:(
109:C
82:C
43:C
20:.
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