Table 1.

Mean Estimates for First, Third, and Fifth Random Eigenvalues From Parallel Analyses Using Principal Component Analysis with No Rotation

Data Set		Distribution method
N	P	A	B	C	D	E	F	G	H	I	J
First eigenvalue
l	l	1.620 (1.438,1.853)	1.621 (1.44,1.863)	1.619 (1.44,1.846)	1.623 (1.445,1.844)	1.619 (1.437,1.844)	1.618 (1.436,1.846)	1.626 (1.443,1.861)	1.622 (1.438,1.86)	1.621 (1.443,1.85)	1.621 (1.443,1.851)
m	l	1.295 (1.214,1.396)	1.296 (1.215,1.399)	1.296 (1.214,1.395)	1.296 (1.215,1.398)	1.297 (1.214,1.4)	1.295 (1.211,1.393)	1.296 (1.212,1.399)	1.296 (1.213,1.401)	1.295 (1.213,1.397)	1.296 (1.214,1.399)
h	l	1.144 (1.105,1.191)	1.144 (1.105,1.193)	1.143 (1.104,1.189)	1.144 (1.105,1.191)	1.144 (1.106,1.192)	1.143 (1.104,1.189)	1.144 (1.105,1.192)	1.144 (1.104,1.19)	1.144 (1.104,1.191)	1.144 (1.106,1.191)
l	m	2.244 (2.034,2.508)	2.248 (2.035,2.515)	2.248 (2.037,2.524)	2.245 (2.037,2.514)	2.246 (2.033,2.505)	2.249 (2.034,2.511)	2.246 (2.037,2.499)	2.246 (2.028,2.521)	2.244 (2.031,2.505)	2.249 (2.031,2.518)
m	m	1.568 (1.479,1.676)	1.566 (1.476,1.676)	1.566 (1.479,1.67)	1.568 (1.481,1.674)	1.567 (1.478,1.674)	1.567 (1.478,1.674)	1.568 (1.477,1.677)	1.568 (1.477,1.674)	1.566 (1.477,1.675)	1.568 (1.48,1.676)
h	m	1.269 (1.23,1.316)	1.269 (1.23,1.315)	1.269 (1.23,1.316)	1.269 (1.229,1.317)	1.271 (1.229,1.318)	1.270 (1.231,1.319)	1.269 (1.23,1.318)	1.269 (1.23,1.317)	1.270 (1.23,1.319)	1.269 (1.23,1.317)
l	h	3.052 (2.807,3.349)	3.053 (2.81,3.351)	3.050 (2.811,3.354)	3.057 (2.808,3.358)	3.054 (2.807,3.351)	3.055 (2.813,3.354)	3.053 (2.805,3.347)	3.057 (2.803,3.357)	3.056 (2.806,3.36)	3.054 (2.818,3.353)
m	h	1.894 (1.796,2.008)	1.895 (1.798,2.009)	1.895 (1.8,2.004)	1.893 (1.799,2.005)	1.893 (1.801,2.006)	1.893 (1.8,2.004)	1.895 (1.801,2.008)	1.895 (1.798,2.008)	1.894 (1.8,2.008)	1.893 (1.801,2.004)
h	h	1.414 (1.374,1.462)	1.413 (1.374,1.461)	1.414 (1.373,1.46)	1.414 (1.375,1.463)	1.414 (1.374,1.462)	1.413 (1.374,1.46)	1.413 (1.374,1.46)	1.413 (1.374,1.459)	1.414 (1.374,1.461)	1.413 (1.373,1.461)
Third eigenvalue
l	l	1.264 (1.155,1.385)	1.262 (1.154,1.382)	1.264 (1.156,1.388)	1.263 (1.151,1.387)	1.264 (1.153,1.384)	1.264 (1.155,1.383)	1.264 (1.151,1.386)	1.262 (1.151,1.382)	1.263 (1.151,1.381)	1.263 (1.151,1.384)
m	l	1.135 (1.081,1.195)	1.134 (1.081,1.194)	1.134 (1.082,1.193)	1.134 (1.079,1.193)	1.135 (1.082,1.192)	1.134 (1.083,1.19)	1.135 (1.081,1.194)	1.134 (1.081,1.196)	1.134 (1.081,1.193)	1.134 (1.081,1.192)
h	l	1.068 (1.043,1.096)	1.068 (1.043,1.097)	1.068 (1.042,1.098)	1.068 (1.042,1.096)	1.068 (1.041,1.096)	1.068 (1.043,1.096)	1.067 (1.041,1.095)	1.068 (1.042,1.097)	1.068 (1.042,1.097)	1.068 (1.042,1.097)
l	m	1.857 (1.723,2.009)	1.859 (1.724,2.008)	1.857 (1.725,2.003)	1.859 (1.723,2.007)	1.860 (1.72,2.008)	1.860 (1.723,2.011)	1.858 (1.725,2.007)	1.856 (1.715,2.009)	1.858 (1.723,2.009)	1.859 (1.714,2.01)
m	m	1.408 (1.348,1.474)	1.408 (1.348,1.472)	1.409 (1.35,1.474)	1.409 (1.351,1.473)	1.408 (1.349,1.473)	1.408 (1.35,1.474)	1.409 (1.348,1.474)	1.409 (1.35,1.476)	1.409 (1.349,1.475)	1.409 (1.351,1.476)
h	m	1.199 (1.172,1.23)	1.199 (1.172,1.23)	1.199 (1.172,1.229)	1.199 (1.172,1.229)	1.200 (1.172,1.23)	1.199 (1.172,1.23)	1.199 (1.173,1.227)	1.199 (1.171,1.23)	1.199 (1.171,1.229)	1.199 (1.171,1.23)
l	h	2.622 (2.467,2.791)	2.624 (2.468,2.799)	2.622 (2.464,2.802)	2.622 (2.464,2.793)	2.623 (2.467,2.801)	2.623 (2.46,2.8)	2.620 (2.461,2.793)	2.619 (2.457,2.801)	2.623 (2.466,2.796)	2.622 (2.462,2.795)
m	h	1.733 (1.668,1.806)	1.733 (1.667,1.803)	1.733 (1.67,1.802)	1.732 (1.668,1.8)	1.733 (1.669,1.805)	1.733 (1.667,1.802)	1.733 (1.67,1.804)	1.733 (1.667,1.804)	1.733 (1.667,1.805)	1.732 (1.669,1.801)
h	h	1.346 (1.318,1.377)	1.346 (1.318,1.376)	1.346 (1.318,1.377)	1.347 (1.317,1.376)	1.347 (1.318,1.378)	1.346 (1.318,1.379)	1.347 (1.318,1.376)	1.346 (1.318,1.376)	1.346 (1.318,1.376)	1.346 (1.318,1.376)
Fifth eigenvalue
l	l	1.021 (0.926,1.118)	1.022 (0.926,1.118)	1.021 (0.928,1.117)	1.020 (0.927,1.115)	1.021 (0.925,1.118)	1.022 (0.927,1.115)	1.020 (0.925,1.112)	1.021 (0.93,1.115)	1.021 (0.925,1.114)	1.022 (0.93,1.116)
m	l	1.018 (0.972,1.066)	1.019 (0.972,1.066)	1.018 (0.972,1.063)	1.017 (0.971,1.064)	1.018 (0.973,1.066)	1.019 (0.973,1.065)	1.019 (0.973,1.066)	1.019 (0.974,1.065)	1.019 (0.972,1.065)	1.019 (0.974,1.064)
h	l	1.012 (0.99,1.036)	1.011 (0.988,1.035)	1.011 (0.988,1.035)	1.011 (0.989,1.034)	1.011 (0.989,1.034)	1.011 (0.988,1.034)	1.011 (0.988,1.034)	1.011 (0.988,1.035)	1.011 (0.988,1.034)	1.011 (0.988,1.035)
l	m	1.598 (1.487,1.715)	1.598 (1.485,1.714)	1.598 (1.487,1.71)	1.599 (1.489,1.714)	1.600 (1.492,1.714)	1.599 (1.49,1.712)	1.598 (1.492,1.713)	1.597 (1.486,1.716)	1.600 (1.493,1.715)	1.598 (1.489,1.712)
m	m	1.298 (1.25,1.352)	1.299 (1.249,1.351)	1.299 (1.249,1.352)	1.299 (1.25,1.352)	1.299 (1.25,1.35)	1.298 (1.251,1.349)	1.299 (1.249,1.351)	1.299 (1.25,1.351)	1.299 (1.25,1.351)	1.299 (1.249,1.352)
h	m	1.149 (1.125,1.174)	1.149 (1.126,1.173)	1.149 (1.127,1.174)	1.149 (1.126,1.174)	1.149 (1.126,1.174)	1.149 (1.125,1.174)	1.149 (1.125,1.173)	1.149 (1.126,1.175)	1.149 (1.126,1.173)	1.149 (1.125,1.173)
l	h	2.331 (2.204,2.469)	2.333 (2.201,2.472)	2.332 (2.203,2.474)	2.332 (2.204,2.467)	2.330 (2.201,2.47)	2.330 (2.199,2.47)	2.331 (2.202,2.47)	2.329 (2.199,2.468)	2.333 (2.206,2.475)	2.330 (2.201,2.463)
m	h	1.621 (1.568,1.679)	1.622 (1.568,1.679)	1.622 (1.568,1.679)	1.622 (1.569,1.681)	1.621 (1.568,1.678)	1.622 (1.57,1.679)	1.622 (1.569,1.679)	1.621 (1.569,1.677)	1.621 (1.568,1.679)	1.622 (1.568,1.68)
h	h	1.299 (1.275,1.324)	1.299 (1.275,1.323)	1.299 (1.275,1.324)	1.299 (1.276,1.325)	1.299 (1.275,1.324)	1.299 (1.274,1.324)	1.299 (1.275,1.325)	1.299 (1.275,1.324)	1.299 (1.275,1.324)	1.299 (1.275,1.324)

Analyses using 5,000 iterations each with 95% quantile intervals of nine data sets using ten different distributions. Simulated data sets vary in terms of low (l), medium (m), or high (h) numbers of observations (N) and numbers of variables (P). The upper quantile is an implementation of Glorfeld’s (1995) estimate.