Phụ lục 2.3 Bảng Pillai

Bảng Pillai được dùng để xác định giá trị tới hạn `V_s"*"` trong phân tích phương sai một yếu tố nhiều biến phụ thuộc. Trong phụ lục này, ta có 5 bảng tương ứng với 5 giá trị của `s` từ 2 đến 6 với `alpha=0,05`. Khi `s=1` thì `V_1=1-Lambda` và ta chuyển sang sử dụng bảng Wilks `Lambda`.

Bảng Pillai với `s=2`

Bảng 1 Bảng Pillai với `s=2`
`m`	`N`
`m`	0	1	2	3	4	5	6	7	8	9	10	15	20	25
0	1,536	1,232	1,031	0,890	0,782	0,698	0,629	0,573	0,526	0,485	0,451	0,333	0,263	0,218
1	1,706	1,452	1,258	1,109	0,991	0,896	0,817	0,751	0,694	0,646	0,604	0,455	0,364	0,304
2	1,784	1,573	1,397	1,254	1,137	1,039	0,956	0,886	0,825	0,772	0,725	0,556	0,451	0,379
3	1,829	1,649	1,492	1,358	1,245	1,149	1,065	0,993	0,930	0,875	0,825	0,643	0,526	0,445
4	1,859	1,703	1,560	1,436	1,329	1,235	1,153	1,081	1,018	0,961	0,910	0,719	0,594	0,506
5	1,880	1,742	1,613	1,497	1,395	1,305	1,226	1,155	1,091	1,034	0,983	0,786	0,655	0,561
6	1,895	1,772	1,654	1,546	1,450	1,364	1,286	1,217	1,154	1,098	1,046	0,846	0,710	0,612
7	1,907	1,796	1,687	1,586	1,495	1,413	1,338	1,270	1,209	1,153	1,102	0,901	0,761	0,658
8	1,917	1,815	1,714	1,620	1,534	1,455	1,383	1,317	1,257	1,202	1,151	0,950	0,808	0,702
9	1,924	1,831	1,737	1,649	1,567	1,491	1,422	1,358	1,299	1,245	1,195	0,995	0,851	0,743
10	1,931	1,844	1,757	1,673	1,595	1,523	1,456	1,394	1,337	1,284	1,235	1,036	0,891	0,781
15	1,951	1,888	1,822	1,758	1,695	1,636	1,580	1,527	1,477	1,430	1,386
20	1,963	1,913	1,860	1,807	1,756	1,706	1,658	1,612	1,568	1,527	1,487
25	1,969	1,929	1,885	1,840	1,796	1,753	1,711	1,671	1,632	1,595	1,559

Bảng Pillai với `s=3`

Bảng 2 Bảng Pillai với `s=3`
`m`	`N`
`m`	0	1	2	3	4	5	6	7	8	9	10	15	20	25
0	2,037	1,710	1,473	1,294	1,153	1,040	0,947	0,869	0,803	0,746	0,697	0,524	0,420	0,350
1	2,297	1,988	1,751	1,564	1,412	1,287	1,183	1,094	1,017	0,950	0,892	0,682	0,552	0,453
2	2,447	2,168	1,943	1,759	1,606	1,477	1,367	1,273	1,190	1,117	1,053	0,818	0,668	0,565
3	2,544	2,294	2,084	1,907	1,757	1,628	1,517	1,420	1,334	1,258	1,190	0,937	0,772	0,656
4	2,612	2,386	2,191	2,023	1,878	1,752	1,641	1,543	1,456	1,378	1,308	1,042	0,866	0,740
5	2,662	2,457	2,276	2,117	1,978	1,854	1,745	1,648	1,561	1,482	1,411	1,137	0,952	0,818
6	2,701	2,514	2,345	2,194	2,061	1,941	1,835	1,739	1,652	1,573	1,502	1,222	1,030	0,890
7	2,732	2,559	2,402	2,259	2,131	2,016	1,912	1,818	1,732	1,654	1,582	1,300	1,103	0,957
8	2,757	2,597	2,449	2,314	2,192	2,081	1,979	1,887	1,803	1,726	1,655	1,371	1,170	1,020
9	2,777	2,629	2,490	2,362	2,244	2,137	2,039	1,949	1,866	1,790	1,720	1,436	1,23
10	2,795	2,656	2,525	2,403	2,291	2,187	2,092	2,004	1,923	1,848	1,779	1,496	1,3
15	2,853	2,748	2,646	2,549	2,457	2,370	2,288	2,211	2,139	2,071	2,007
20	2,885	2,802	2,718	2,637	2,560	2,485	2,414	2,347	2,283	2,222	2,163
25	2,906	2,836	2,766	2,697	2,630	2,565	2,503	2,443	2,385

Bảng Pillai với `s=4`

Bảng 3 Bảng Pillai với `s=4`
`m`	`N`
`m`	0	1	2	3	4	5	6	7	8	9	10	15	20
0	2,549	2,194	1,926	1,717	1,548	1,410	1,294	1,196	1,112	1,038	0,974	0,744	0,602
1	2,852	2,510	2,241	2,023	1,844	1,693	1,566	1,456	1,360	1,277	1,203	0,932	0,761
2	3,052	2,733	2,472	2,256	2,074	1,919	1,786	1,670	1,567	1,477	1,396	1,097	0,903
3	3,193	2,898	2,650	2,440	2,260	2,104	1,969	1,849	1,743	1,649	1,564	1,243	1,032
4	3,298	3,025	2,791	2,589	2,413	2,259	2,123	2,002	1,895	1,798	1,710	1,375	1,149
5	3,378	3,126	2,905	2,711	2,541	2,390	2,255	2,135	2,027	1,929	1,840	1,494
6	3,442	3,208	2,999	2,814	2,649	2,502	2,370	2,251	2,143	2,044	1,955	1,602
7	3,494	3,276	3,079	2,902	2,743	2,600	2,470	2,353	2,246	2,148	2,058	1,70
8	3,537	3,333	3,146	2,977	2,824	2,685	2,559	2,444	2,338	2,241	2,151	1,8
9	3,574	3,382	3,205	3,043	2,896	2,761	2,638	2,525	2,421	2,325	2,236
10	3,605	3,424	3,256	3,101	2,959	2,829	2,708	2,598	2,496	2,401	2,313
15	3,710	3,570	3,436	3,310	3,191	3,079	2,974	2,876	2,783	2,696	2,615
20	3,771	3,657	3,546	3,440	3,338	3,241	3,149

Bảng Pillai với `s=5`

Bảng 4 Bảng Pillai với `s=5`
`m`	`N`
`m`	0	1	2	3	4	5	6	7	8	9	10
0	3,055	2,681	2,389	2,155	1,962	1,801	1,664	1,547	1,445	1,356	1,277
1	3,390	3,025	2,731	2,488	2,285	2,122	1,964	1,835	1,722	1,622	1,533
2	3,628	3,281	2,993	2,751	2,545	2,367	2,213	2,077	1,957	1,850	1,754
3	3,805	3,478	3,201	2,964	2,759	2,580	2,423	2,284	2,160	2,048	1,948
4	3,941	3,635	3,370	3,140	2,938	2,761	2,604	2,463	2,337	2,222	2,119
5	4,050	3,762	3,510	3,288	3,091	2,916	2,760	2,619	2,492	2,377	2,271
6	4,138	3,868	3,627	3,414	3,223	3,052	2,897	2,758	2,630	2,514	2,408
7	4,212	3,957	3,728	3,522	3,337	3,170	3,018	2,880
8	4,274	4,033	3,815	3,617	3,438	3,275	3,126
9	4,327	4,099	3,890	3,700	3,527	3,369
10	4,372	4,156	3,957	3,774	3,607	3,45

Bảng Pillai với `s=6`

Bảng 5 Bảng Pillai với `s=6`
`m`	`N`
`m`	0	1	2	3	4	5	6	7	8	9	10
0	3,559	3,171	2,859	2,604	2,390	2,209	2,053	1,918	1,799	1,694	1,601
1	3,917	3,535	3,221	2,958	2,734	2,542	2,375	2,229	2,099	1,984	1,881
2	4,185	3,817	3,508	3,245	3,018	2,821	2,647	2,494	2,358	2,235	2,125
3	4,391	4,041	3,741	3,482	3,256	3,057	2,881	2,724	2,583	2,456	2,341
4	4,556	4,223	3,934	3,681	3,458	3,260	3,084	2,925	2,782	2,652	2,534
5	4,690	4,375	4,097	3,851	3,633	3,438	3,262	3,103	2,959	2,827	2,706
6	4,802	4,502	4,236	3,998	3,785
7	4,896	4,611	4,356	4,126	3,919
8	4,976	4,706	4,461	4,239
9	5,045	4,788	4,553
10	5,106	4,860	4,635

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