. Author manuscript; available in PMC: 2011 May 1.

Published in final edited form as: Br J Math Stat Psychol. 2009 Sep 29;63(Pt 2):273–291. doi: 10.1348/000711009X449771

Table 4(c).

Type I errors of exact chi-square and three approximations to the distributions of quadratic forms when CV(λ) changes, d = 10, $λ_{k} = {(1_{5}^{'}, k 1_{5}^{'})}^{'}$ , 2000 replications.

		nominal level α = .01				nominal level α = .025
k	CV(λ)	$χ_{d}^{2}$	$L χ_{d}^{2}$	$c χ_{d}^{2}$	$a χ_{b}^{2}$	$χ_{d}^{2}$	$L χ_{d}^{2}$	$c χ_{d}^{2}$	$a χ_{b}^{2}$
2	0.333	0.014	0.126	0.020	0.017	0.033	0.194	0.039	0.033
3	0.500	0.011	0.323	0.018	0.012	0.024	0.424	0.037	0.023
4	0.600	0.009	0.468	0.024	0.010	0.026	0.557	0.039	0.028
5	0.667	0.006	0.583	0.018	0.009	0.022	0.660	0.042	0.020
6	0.714	0.011	0.710	0.028	0.009	0.027	0.784	0.051	0.027
7	0.750	0.011	0.765	0.030	0.014	0.028	0.821	0.052	0.028
8	0.778	0.010	0.804	0.028	0.013	0.022	0.851	0.053	0.024
9	0.800	0.011	0.837	0.035	0.014	0.028	0.874	0.066	0.031
10	0.818	0.008	0.876	0.031	0.012	0.020	0.901	0.062	0.026

AAD		0.002	0.600	0.016	0.003	0.003	0.649	0.024	0.003

		nominal level α = .05				nominal level α = .10
k	CV(λ)	$χ_{d}^{2}$	$L χ_{d}^{2}$	$c χ_{d}^{2}$	$a χ_{b}^{2}$	$χ_{d}^{2}$	$L χ_{d}^{2}$	$c χ_{d}^{2}$	$a χ_{b}^{2}$

2	0.333	0.057	0.272	0.064	0.056	0.110	0.388	0.114	0.105
3	0.500	0.050	0.506	0.068	0.052	0.097	0.609	0.118	0.100
4	0.600	0.048	0.639	0.062	0.045	0.094	0.715	0.119	0.087
5	0.667	0.038	0.728	0.074	0.046	0.090	0.797	0.131	0.096
6	0.714	0.056	0.834	0.084	0.052	0.109	0.874	0.140	0.109
7	0.750	0.054	0.865	0.083	0.052	0.108	0.900	0.141	0.099
8	0.778	0.053	0.885	0.085	0.048	0.102	0.916	0.141	0.096
9	0.800	0.055	0.908	0.095	0.059	0.110	0.940	0.150	0.106
10	0.818	0.045	0.930	0.097	0.055	0.097	0.956	0.149	0.108

AAD		0.005	0.679	0.029	0.004	0.007	0.688	0.033	0.006