Journal of Statistical Distributions and Applications

Table 1 Comparison of p-values of the observed test statistics evaluated at both the limiting and the bootstrap distribution

From: Testing the Rasch model with the conditional likelihood ratio test: sample size requirements and bootstrap algorithms

		Normal marginals				Free marginals				Fixed marginals
k=5/df=4		\({\chi ^{2}_{l}}\)	\({\chi ^{2}_{b}}\)	Diff.		\({\chi ^{2}_{l}}\)	\({\chi ^{2}_{b}}\)	Diff.		\({\chi ^{2}_{l}}\)	\({\chi ^{2}_{b}}\)	Diff.
100		0.01	0.01	0.000		0.01	0.01	0.001		0.01	0.01	0.000
250		0.97	0.97	0.001		0.97	0.96	0.008		0.97	0.96	0.008
500		0.03	0.03	0.000		0.03	0.03	0.001		0.03	0.03	0.000
750		0.39	0.39	0.000		0.39	0.39	0.004		0.39	0.38	0.007
1000		0.69	0.69	0.001		0.69	0.68	0.004		0.69	0.68	0.004
2500		0.44	0.44	−0.001		0.44	0.44	0.000		0.44	0.44	0.001
5000		0.96	0.96	0.001		0.96	0.96	0.000		0.96	0.96	−0.001
k=10/df=9
100		0.48	0.46	0.017		0.48	0.43	0.046		0.48	0.43	0.049
250		0.32	0.32	0.006		0.32	0.31	0.010		0.32	0.31	0.010
500		0.96	0.95	0.002		0.96	0.96	0.000		0.96	0.95	0.002
750		0.63	0.63	0.002		0.63	0.63	0.004		0.63	0.63	0.000
1000		0.79	0.79	−0.002		0.79	0.79	0.000		0.79	0.79	0.001
2500		0.26	0.26	0.000		0.26	0.25	0.000		0.26	0.25	0.001
5000		0.31	0.31	0.000		0.31	0.31	0.002		0.31	0.31	0.002
k=15/df=14
100		0.08	0.07	0.006		0.08	0.07	0.011		0.08	0.07	0.010
250		0.60	0.59	0.007		0.60	0.58	0.012		0.60	0.59	0.009
500		0.07	0.07	0.001		0.07	0.07	0.002		0.07	0.07	0.003
750		0.58	0.58	0.001		0.58	0.57	0.002		0.58	0.58	0.000
1000		0.96	0.96	0.002		0.96	0.96	−0.001		0.96	0.96	0.001
2500		0.34	0.34	0.003		0.34	0.34	0.000		0.34	0.34	0.001
5000		0.63	0.63	0.001		0.63	0.63	0.000		0.63	0.63	0.000

Notes: \({\chi ^{2}_{l}}\) : limiting distribution of the test statistic; \({\chi ^{2}_{b}}\): bootstrap distribution of the test statistic; Diff. = Difference of p-values

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