. 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 5(a).

Type I errors of exact chi-square and three approximations to the distributions of quadratic forms when CV(λ) changes, d = 10, λ_k = 1₁₀ + k(0, 0.1, 0.2, …, 0.9)′, 2000 replications.

		nominal level α = .01				nominal level α = .025
k	CV(λ)	$χ_{d}^{2}$	$L χ_{d}^{2}$	$c χ_{d}^{2}$	$a χ_{b}^{2}$	$χ_{d}^{2}$	$L χ_{d}^{2}$	$c χ_{d}^{2}$	$a χ_{b}^{2}$
1	0.198	0.014	0.108	0.016	0.014	0.033	0.174	0.036	0.034
2	0.302	0.011	0.279	0.013	0.010	0.024	0.376	0.027	0.023
3	0.367	0.009	0.431	0.015	0.009	0.026	0.520	0.032	0.028
4	0.410	0.006	0.553	0.012	0.009	0.022	0.655	0.027	0.019
5	0.442	0.011	0.711	0.019	0.013	0.027	0.782	0.035	0.026
6	0.466	0.011	0.766	0.019	0.012	0.028	0.824	0.040	0.030
7	0.484	0.010	0.817	0.021	0.011	0.022	0.862	0.037	0.028
8	0.500	0.011	0.849	0.019	0.012	0.028	0.895	0.043	0.030
9	0.512	0.008	0.894	0.017	0.011	0.020	0.924	0.040	0.026
10	0.522	0.008	0.928	0.019	0.009	0.024	0.948	0.037	0.023

AAD		0.002	0.623	0.007	0.002	0.003	0.671	0.010	0.004

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

1	0.198	0.057	0.249	0.060	0.057	0.110	0.361	0.108	0.107
2	0.302	0.050	0.465	0.054	0.051	0.097	0.590	0.105	0.099
3	0.367	0.048	0.627	0.054	0.047	0.094	0.717	0.097	0.089
4	0.410	0.038	0.729	0.052	0.042	0.090	0.797	0.106	0.092
5	0.442	0.056	0.840	0.067	0.053	0.109	0.893	0.120	0.104
6	0.466	0.054	0.871	0.065	0.051	0.108	0.912	0.121	0.097
7	0.484	0.053	0.903	0.063	0.052	0.102	0.938	0.112	0.095
8	0.500	0.055	0.924	0.072	0.055	0.110	0.950	0.126	0.112
9	0.512	0.045	0.945	0.071	0.057	0.097	0.971	0.124	0.105
10	0.522	0.048	0.962	0.063	0.049	0.108	0.978	0.122	0.100

AAD		0.005	0.701	0.012	0.004	0.007	0.710	0.014	0.006